Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/BilanFlux.txt
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/BilanFlux.txt	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/BilanFlux.txt	(revision 392)
@@ -0,0 +1,130 @@
+
+ 2.2 GeV
+ -------
+ FLUXES from JECDesign/40cm/2.2/10m/plus/
+ numu  : 5.8253e+13 /100m^2/year 
+ anumu : 2.94562e+12 /100m^2/year 
+ nue   : 1.72429e+11 /100m^2/year 
+ anue  : 1.04689e+10 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/2.2/20m/1.5m/plus/
+ numu  : 9.01155e+13 /100m^2/year 
+ anumu : 4.36335e+12 /100m^2/year 
+ nue   : 4.37348e+11 /100m^2/year 
+ anue  : 1.88918e+10 /100m^2/year 
+ FLUXES from JECDesign/40cm/2.2/20m/1m/minus/
+ numu  : 4.47636e+12 /100m^2/year 
+ anumu : 5.77297e+13 /100m^2/year 
+ nue   : 2.38622e+10 /100m^2/year 
+ anue  : 1.56932e+11 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/2.2/20m/1m/plus/
+ numu  : 7.62496e+13 /100m^2/year 
+ anumu : 3.13076e+12 /100m^2/year 
+ nue   : 3.23407e+11 /100m^2/year 
+ anue  : 1.15068e+10 /100m^2/year 
+l FLUXES from JECDesign/40cm/2.2/40m/plus/
+ numu  : 8.89234e+13 /100m^2/year 
+ anumu : 3.47339e+12 /100m^2/year 
+ nue   : 5.0804e+11 /100m^2/year 
+ anue  : 1.23206e+10 /100m^2/year 
+
+ 3.5GeV
+ ------
+ FLUXES from JECDesign/40cm/3.5/10m/plus/
+ numu  : 7.70066e+13 /100m^2/year 
+ anumu : 6.21415e+12 /100m^2/year 
+ nue   : 2.54552e+11 /100m^2/year 
+ anue  : 2.67003e+10 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/3.5/20m/minus/
+ numu  : 8.6623e+12 /100m^2/year 
+ anumu : 8.53839e+13 /100m^2/year 
+ nue   : 6.09787e+10 /100m^2/year 
+ anue  : 2.19709e+11 /100m^2/year 
+ FLUXES from JECDesign/40cm/3.5/20m/plus/
+ numu  : 9.97273e+13 /100m^2/year 
+ anumu : 7.01892e+12 /100m^2/year 
+ nue   : 4.39335e+11 /100m^2/year 
+ anue  : 2.85589e+10 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/3.5/40m/plus/
+ numu  : 1.13378e+14 /100m^2/year 
+ anumu : 7.48561e+12 /100m^2/year 
+ nue   : 6.48856e+11 /100m^2/year 
+ anue  : 2.95911e+10 /100m^2/year 
+
+ 4.5GeV
+ ------
+ FLUXES from JECDesign/40cm/4.5/10m/plus/
+ numu  : 7.08546e+13 /100m^2/year 
+ anumu : 5.05612e+12 /100m^2/year 
+ nue   : 2.75083e+11 /100m^2/year 
+ anue  : 3.36888e+10 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/4.5/20m/minus/
+ numu  : 1.14341e+13 /100m^2/year 
+ anumu : 6.66837e+13 /100m^2/year 
+ nue   : 9.63459e+10 /100m^2/year 
+ anue  : 1.82477e+11 /100m^2/year 
+ FLUXES from JECDesign/40cm/4.5/20m/plus/
+ numu  : 1.08768e+14 /100m^2/year 
+ anumu : 6.85071e+12 /100m^2/year 
+ nue   : 5.04684e+11 /100m^2/year 
+ anue  : 3.89201e+10 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/4.5/40m/plus/
+ numu  : 1.22689e+14 /100m^2/year 
+ anumu : 7.65198e+12 /100m^2/year 
+ nue   : 7.21357e+11 /100m^2/year 
+ anue  : 4.10623e+10 /100m^2/year 
+
+ 6.5GeV
+ ------
+ FLUXES from JECDesign/40cm/6.5/10m/plus
+ numu  : 8.30579e+13 /100m^2/year 
+ anumu : 7.98168e+12 /100m^2/year 
+ nue   : 4.74211e+11 /100m^2/year 
+ anue  : 8.55203e+10 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/6.5/20m/minus/
+ numu  : 1.43997e+13 /100m^2/year 
+ anumu : 7.04681e+13 /100m^2/year 
+ nue   : 1.99589e+11 /100m^2/year 
+ anue  : 2.48141e+11 /100m^2/year 
+ FLUXES from JECDesign/40cm/6.5/20m/plus/
+ numu  : 1.04026e+14 /100m^2/year 
+ anumu : 9.63384e+12 /100m^2/year 
+ nue   : 6.42379e+11 /100m^2/year 
+ anue  : 9.17983e+10 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/6.5/40m/plus/
+ numu  : 1.17097e+14 /100m^2/year 
+ anumu : 1.08172e+13 /100m^2/year 
+ nue   : 8.32018e+11 /100m^2/year 
+ anue  : 9.29281e+10 /100m^2/year 
+
+ 8.GeV
+ -----
+ FLUXES from JECDesign/40cm/8.0/10m/plus/
+ numu  : 7.66568e+13 /100m^2/year 
+ anumu : 9.18611e+12 /100m^2/year 
+ nue   : 5.0453e+11 /100m^2/year 
+ anue  : 1.09869e+11 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/8.0/20m/minus/
+ numu  : 1.47676e+13 /100m^2/year 
+ anumu : 7.14875e+13 /100m^2/year 
+ nue   : 2.27329e+11 /100m^2/year 
+ anue  : 2.83681e+11 /100m^2/year 
+ FLUXES from JECDesign/40cm/8.0/20m/plus/
+ numu  : 9.7058e+13 /100m^2/year 
+ anumu : 1.15676e+13 /100m^2/year 
+ nue   : 6.64642e+11 /100m^2/year 
+ anue  : 1.11584e+11 /100m^2/year 
+
+ FLUXES from JECDesign/40cm/8.0/40m/plus/
+ numu  : 1.09425e+14 /100m^2/year 
+ anumu : 1.29416e+13 /100m^2/year 
+ nue   : 8.46651e+11 /100m^2/year 
+ anue  : 1.1674e+11 /100m^2/year 
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/Original-LALReport-Xarchiv/svepj.clo
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/Original-LALReport-Xarchiv/svepj.clo	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/Original-LALReport-Xarchiv/svepj.clo	(revision 392)
@@ -0,0 +1,307 @@
+% SVJour DOCUMENT CLASS OPTION EPJ -- The European Physical Journal
+%
+% This is an enhancement for the
+% LaTeX document class for Springer journals (two column version)
+%
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+%%
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
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+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
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+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+\ProvidesFile{svepj.clo}
+              [2002/03/11 v1.2
+      style option for The European Physical Journal]
+\typeout{SVJour Class option: svepj.clo for The European Physical Journal}
+\DeclareOption{leqno}{\input{leqno.clo}}
+\let\if@nopacs\iffalse
+\DeclareOption{nopacs}{\let\if@nopacs\iftrue}
+\ExecuteOptions{final,twocolumn,10pt}
+\newif\if@normhead \@normheadtrue
+\def\hugehead{\@normheadfalse
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+\long\def\@makefntext##1{\parindent\bibindent
+     \columnwidth\textwidth
+     \advance\columnwidth -\columnsep
+     \divide\columnwidth\tw@
+     \hsize\columnwidth
+     \linewidth\columnwidth
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+}
+\let\if@mathematic\iffalse
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+   \@setfontsize\normalsize\@xpt{10.5dd}%
+   \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
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+   \belowdisplayskip \abovedisplayskip
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+   \@setfontsize\small\@ixpt{10dd}%
+   \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@
+   \abovedisplayshortskip \z@ \@plus2\p@
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+   \def\@listi{\leftmargin\leftmargini
+               \parsep 0\p@ \@plus1\p@ \@minus\p@
+               \topsep 8\p@ \@plus2\p@ \@minus4\p@
+               \itemsep0\p@}%
+   \belowdisplayskip \abovedisplayskip
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+\newcommand\large{\@setfontsize\large\@xiipt{13dd}}
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+\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}
+%
+\setlength{\textwidth}{180mm}
+\setlength{\textheight}{56pc}
+%
+\def\epj@maketitle{\par
+\ch@ckobl{journalname}{Noname}
+\ch@ckobl{date}{the date of receipt and acceptance should be inserted
+later}
+\ch@ckobl{title}{A title should be given}
+\ch@ckobl{author}{Name(s) and initial(s) of author(s) should be given}
+\ch@ckobl{institute}{Address(es) of author(s) should be given}
+\ch@ckobl{abstract}{Abstract is missing.}
+\begingroup
+%
+    \renewcommand\thefootnote{\@fnsymbol\c@footnote}%
+    \def\@makefnmark{$^{\@thefnmark}$}%
+    \def\switch@fnmark{\def\thefootnote{\mathrm{\alph{footnote}}}}
+%
+ \def\lastand{\ifnum\value{inst}=2\relax
+                 \unskip{} \andname\
+              \else
+                 \unskip, \andname\
+              \fi}%
+ \def\and{\stepcounter{auth}\relax
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+          \fi}%
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+ \if@normhead
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+    \twocolumn[\vspace{\@tempdima}]
+    \addtocounter{page}{-1}
+    \if!\the\authorrunning!
+       \authorrunning{ }%
+    \fi
+ \fi
+ \if!\@mail!\else
+    \footnotetext[0]{\kern-\bibindent\mailname\
+    \ignorespaces\@mail}%
+ \fi
+%
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+    \ProcessRunnHead
+ \fi
+%
+ \endgroup
+ \setcounter{footnote}{0}
+ \global\let\thanks\relax
+ \global\let\maketitle\relax
+ \global\let\@maketitle\relax
+ \global\let\@thanks\@empty
+ \global\let\@author\@empty
+ \global\let\@date\@empty
+ \global\let\@title\@empty
+ \global\let\@subtitle\@empty
+ \global\let\title\relax
+ \global\let\author\relax
+ \global\let\date\relax
+ \global\let\and\relax}
+%
+\def\epj@@maketitle{\newpage
+ \normalfont
+ \vbox to0pt{\vskip-40pt
+ \nointerlineskip
+ \makeheadbox\vss}\nointerlineskip
+ \if@normhead
+    \setbox\authrun=\vbox\bgroup
+ \fi
+ {\LARGE \sffamily\bfseries
+  \hrule\@height\logodepth\@width\z@
+  \pretolerance=10000
+  \rightskip=0pt plus 4cm
+ \if!\@headnote!\else
+   \noindent
+   {\LARGE\normalfont\itshape\ignorespaces\@headnote\par}\vskip 3.5mm
+ \fi
+  \noindent\ignorespaces
+  \@title \par}\vskip 11.24pt\relax
+ \authorfont
+ \if!\@subtitle!\else
+   {\large\sffamily\bfseries
+   \pretolerance=10000
+   \rightskip=0pt plus 3cm
+   \noindent\ignorespaces\@subtitle \par}\vskip 11.24pt
+ \fi
+ \lineskip .5em
+ \switch@fnmark
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+ \protected@xdef\@thanks{\@thanks\protect\switch@fnmark}%
+ \setbox0=\vbox{\setcounter{auth}{1}\def\and{\stepcounter{auth} }%
+                \hfuzz=2\textwidth\def\thanks##1{}\@author}%
+ \setcounter{footnote}{0}%
+ \value{inst}=\value{auth}%
+ \setcounter{auth}{1}%
+ \rightskip=0pt plus 2cm
+ \noindent\ignorespaces\@author\vskip7.23pt
+ \rightskip=0pt\relax
+ \small\rm
+ \institutename
+ \vskip 12.85pt
+ \leftskip=1.5cm\rightskip=\leftskip
+ \noindent\@date
+ \if!\@dedic!\else
+    \par
+    \normalsize\it
+    \addvspace\baselineskip
+    \noindent\@dedic
+ \fi
+ \vskip 12.85pt
+ {\topsep=0pt\partopsep=0pt\parsep=0pt\itemsep=0pt\relax
+  \def\pacsstart##1##2{##1\hskip5pt plus2ptminus2pt##2}%
+  \def\and##1##2{\unskip\ -- ##1\hskip5pt plus2ptminus2pt##2}%
+  \trivlist\item[\hskip\labelsep
+  {\sffamily\bfseries\abstractname}]%
+  \leftskip=1.5cm\rightskip=\leftskip
+  \@abstract
+  \if@nopacs\else
+     \ch@ckobl{PACS}{{XX.XX.XX}{No PACS code given}}%
+     \@@PACS
+  \fi
+  \endtrivlist}%
+ \if@normhead
+    \egroup % end of header box
+    \@tempdima=\headerboxheight
+    \advance\@tempdima by-\ht\authrun
+    \ifdim\@tempdima>0pt
+       \vrule width0pt height\@tempdima
+    \fi
+    \unvbox\authrun
+    \global\@minipagetrue
+    \global\everypar{\global\@minipagefalse\global\everypar{}}
+ \else
+    \typeout{\the\c@auth\space author names and}
+    \typeout{\the\c@inst\space institutes processed}
+    \global\@tempdima=\pagetotal
+    \global\advance\@tempdima by22.47pt
+ \fi
+ \vskip22.47pt
+}
+%
+\def\PACS#1{\gdef\@PACS{#1}}
+\def\@@PACS{\par\addvspace\baselineskip\noindent{\sffamily\bfseries
+PACS.\enspace}\ignorespaces\expandafter\pacsstart\@PACS\par}
+%
+\def\epjabstract#1{\gdef\@abstract{#1}}
+%
+\def\epjrunnhead{%
+    \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}%
+    \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}%
+    \instindent=\textwidth
+    \advance\instindent by-\headlineindent
+    \if!\the\titlerunning!\else
+      \edef\@title{\the\titlerunning}%
+    \fi
+    \global\setbox\titrun=\hbox{\small\rm\ignorespaces\@title}%
+    \ifdim\wd\titrun>\instindent
+       \typeout{^^JSVJour Warning: Title too long for running head.}%
+       \typeout{Please supply a shorter form with \string\titlerunning
+                \space prior to \string\maketitle}%
+       \global\setbox\titrun=\hbox{\small\rm
+       Title Suppressed Due to Excessive Length}%
+    \fi
+    \xdef\@title{\copy\titrun}%
+%
+    \if!\the\authorrunning!
+    \else
+      \setcounter{auth}{1}%
+      \edef\@author{\the\authorrunning}%
+    \fi
+    \ifnum\value{auth}>2
+       \def\stripauthor##1\and##2\endauthor{%
+       \protected@xdef\@author{##1\unskip\unskip\if!##2!\else\ et al.\fi}}%
+       \expandafter\stripauthor\@author\and\endauthor
+    \else
+       \gdef\and{\unskip, \ignorespaces}%
+       {\def\and{\noexpand\protect\noexpand\and}%
+       \protected@xdef\@author{\@author}}
+    \fi
+    \global\setbox\authrun=\hbox{\small\ignorespaces
+                                 \@author\unskip: \unhbox\titrun}%
+    \ifdim\wd\authrun>\instindent
+    \typeout{^^JSVJour Warning: The running head built automatically from
+             \string\author\space and \string\title
+             ^^Jexceeds the pagewidth, please supply a shorter form
+             ^^Jwith \string\authorrunning\space and
+             \string\titlerunning\space prior to \string\maketitle}%
+    \global\setbox\authrun=\hbox{\small\rm Please give a shorter version
+          with: {\tt\string\authorrunning\space and
+             \string\titlerunning\space prior to \string\maketitle}}%
+    \fi
+    \xdef\@author{\copy\authrun}%
+    \markboth{\@author}{\@author}%
+}
+%
+\AtEndOfClass{\let\ackname\@empty
+\let\if@runhead\iftrue
+\let\if@smartand\iftrue
+\let\@maketitle=\epj@@maketitle
+\let\maketitle=\epj@maketitle
+\let\ProcessRunnHead=\epjrunnhead
+\let\abstract=\epjabstract
+\def\@evenhead{\small\rlap{\thepage}\hfil\leftmark\hfil}%
+\def\@oddhead{\small\hfil\rightmark\hfil\llap{\thepage}}%
+\def\sectcounterend{}
+\setlength\columnsep{4mm}
+\def\section{\@startsection{section}{1}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\large\sffamily\bfseries}}
+\def\subsection{\@startsection{subsection}{2}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\normalsize\sffamily\bfseries}}
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\normalsize\sffamily}}
+\def\paragraph{\@startsection{subsubsection}{4}{\z@}%
+    {-21dd plus-4pt minus-4pt}{-1pt}{\normalsize\sffamily\bfseries}}
+\def\authorfont{\rmfamily}
+\def\leftlegendglue{\hfil}
+\journalname{EPJ}}
+%%
+%% End of copy of file `svepj.clo'.
+\endinput
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/Original-LALReport-Xarchiv/svjour.cls
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/Original-LALReport-Xarchiv/svjour.cls	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/Original-LALReport-Xarchiv/svjour.cls	(revision 392)
@@ -0,0 +1,1246 @@
+% SVJour DOCUMENT CLASS -- version 1.11 for LaTeX2e
+%
+% LaTeX document class for Springer journals
+%
+%%
+%%
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\ProvidesClass{svjour}[2003/04/15
+^^JLaTeX document class for Springer journals - version 1.11]
+\newcommand\@ptsize{}
+\newif\if@restonecol
+\newif\if@titlepage
+\@titlepagefalse
+\DeclareOption{a4paper}
+   {\setlength\paperheight {297mm}%
+    \setlength\paperwidth  {210mm}}
+\DeclareOption{10pt}{\renewcommand\@ptsize{0}}
+\DeclareOption{twoside}{\@twosidetrue  \@mparswitchtrue}
+\DeclareOption{draft}{\setlength\overfullrule{5pt}}
+\DeclareOption{final}{\setlength\overfullrule{0pt}}
+\DeclareOption{twocolumn}{\@twocolumntrue}
+\DeclareOption{fleqn}{\input{fleqn.clo}\AtEndOfClass{\mathindent\z@}}
+\let\if@mathematic\iftrue
+\let\if@numbook\iffalse
+\DeclareOption{numbook}{\let\if@envcntsect\iftrue
+  \AtEndOfPackage{%
+   \renewcommand\thefigure{\thesection.\@arabic\c@figure}%
+   \renewcommand\thetable{\thesection.\@arabic\c@table}%
+   \renewcommand\theequation{\thesection.\@arabic\c@equation}%
+   \@addtoreset{figure}{section}%
+   \@addtoreset{table}{section}%
+   \@addtoreset{equation}{section}%
+  }%
+}
+\DeclareOption{openbib}{%
+  \AtEndOfPackage{%
+   \renewcommand\@openbib@code{%
+      \advance\leftmargin\bibindent
+      \itemindent -\bibindent
+      \listparindent \itemindent
+      \parsep \z@
+      }%
+   \renewcommand\newblock{\par}}%
+}
+%
+\let\if@runhead\iffalse
+\DeclareOption{runningheads}{\let\if@runhead\iftrue}
+\let\if@smartrunh\iffalse
+\DeclareOption{smartrunhead}{\let\if@smartrunh\iftrue}
+\DeclareOption{nosmartrunhead}{\let\if@smartrunh\iffalse}
+\let\if@envcntreset\iffalse
+\DeclareOption{envcountreset}{\let\if@envcntreset\iftrue}
+\let\if@envcntsame\iffalse
+\DeclareOption{envcountsame}{\let\if@envcntsame\iftrue}
+\let\if@envcntsect\iffalse
+\DeclareOption{envcountsect}{\let\if@envcntsect\iftrue}
+\let\if@referee\iffalse
+\DeclareOption{referee}{\let\if@referee\iftrue}
+\def\makereferee{\def\baselinestretch{2}}
+\let\if@instindent\iffalse
+\DeclareOption{instindent}{\let\if@instindent\iftrue}
+\let\if@smartand\iffalse
+\DeclareOption{smartand}{\let\if@smartand\iftrue}
+\let\if@spthms\iftrue
+\DeclareOption{nospthms}{\let\if@spthms\iffalse}
+\let\switch@texts\relax
+\DeclareOption{deutsch}{\def\switch@texts{\ds@deutsch}}
+\DeclareOption{francais}{\def\switch@texts{\ds@francais}}
+%
+\let\journalopt\@empty
+\DeclareOption*{\InputIfFileExists{sv\CurrentOption.clo}{%
+\let\journalopt\CurrentOption}{%
+\ClassWarning{Springer-SVJour}{Specified option or subpackage
+"\CurrentOption" not found -}\OptionNotUsed}}
+\ExecuteOptions{a4paper,twoside,10pt,instindent}
+\ProcessOptions
+\ifx\journalopt\@empty
+\ClassError{Springer-SVJour}{No valid journal specified in option list}{}
+\expandafter\stop
+\fi
+%
+\if@smartrunh\AtEndDocument{\islastpageeven\getlastpagenumber}\fi
+%
+\DeclareMathSymbol{\Gamma}{\mathalpha}{letters}{"00}
+\DeclareMathSymbol{\Delta}{\mathalpha}{letters}{"01}
+\DeclareMathSymbol{\Theta}{\mathalpha}{letters}{"02}
+\DeclareMathSymbol{\Lambda}{\mathalpha}{letters}{"03}
+\DeclareMathSymbol{\Xi}{\mathalpha}{letters}{"04}
+\DeclareMathSymbol{\Pi}{\mathalpha}{letters}{"05}
+\DeclareMathSymbol{\Sigma}{\mathalpha}{letters}{"06}
+\DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07}
+\DeclareMathSymbol{\Phi}{\mathalpha}{letters}{"08}
+\DeclareMathSymbol{\Psi}{\mathalpha}{letters}{"09}
+\DeclareMathSymbol{\Omega}{\mathalpha}{letters}{"0A}
+%
+\setlength\parindent{15\p@}
+\setlength\smallskipamount{3\p@ \@plus 1\p@ \@minus 1\p@}
+\setlength\medskipamount{6\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\bigskipamount{12\p@ \@plus 4\p@ \@minus 4\p@}
+\setlength\headheight{12\p@}
+\setlength\headsep   {16.74dd}
+\setlength\topskip   {10\p@}
+\setlength\footskip{30\p@}
+\setlength\maxdepth{.5\topskip}
+%
+\@settopoint\textwidth
+\setlength\marginparsep {10\p@}
+\setlength\marginparpush{5\p@}
+\setlength\topmargin{-10pt}
+\if@twocolumn
+   \setlength\oddsidemargin {-30\p@}
+   \setlength\evensidemargin{-30\p@}
+\else
+   \setlength\oddsidemargin {\z@}
+   \setlength\evensidemargin{\z@}
+\fi
+\setlength\marginparwidth  {48\p@}
+\setlength\footnotesep{8\p@}
+\setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@}
+\setlength\floatsep    {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\textfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\intextsep   {20\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\dblfloatsep    {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\@fptop{0\p@}
+\setlength\@fpsep{12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\@fpbot{0\p@ \@plus 1fil}
+\setlength\@dblfptop{0\p@}
+\setlength\@dblfpsep{12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\@dblfpbot{0\p@ \@plus 1fil}
+\setlength\partopsep{2\p@ \@plus 1\p@ \@minus 1\p@}
+\def\@listi{\leftmargin\leftmargini
+            \parsep \z@
+            \topsep 6\p@ \@plus2\p@ \@minus4\p@
+            \itemsep\parsep}
+\let\@listI\@listi
+\@listi
+\def\@listii {\leftmargin\leftmarginii
+              \labelwidth\leftmarginii
+              \advance\labelwidth-\labelsep
+              \topsep    \z@
+              \parsep    \topsep
+              \itemsep   \parsep}
+\def\@listiii{\leftmargin\leftmarginiii
+              \labelwidth\leftmarginiii
+              \advance\labelwidth-\labelsep
+              \topsep    \z@
+              \parsep    \topsep
+              \itemsep   \parsep}
+\def\@listiv {\leftmargin\leftmarginiv
+              \labelwidth\leftmarginiv
+              \advance\labelwidth-\labelsep}
+\def\@listv  {\leftmargin\leftmarginv
+              \labelwidth\leftmarginv
+              \advance\labelwidth-\labelsep}
+\def\@listvi {\leftmargin\leftmarginvi
+              \labelwidth\leftmarginvi
+              \advance\labelwidth-\labelsep}
+%
+\setlength\lineskip{1\p@}
+\setlength\normallineskip{1\p@}
+\renewcommand\baselinestretch{}
+\setlength\parskip{0\p@ \@plus \p@}
+\@lowpenalty   51
+\@medpenalty  151
+\@highpenalty 301
+\setcounter{topnumber}{4}
+\renewcommand\topfraction{.9}
+\setcounter{bottomnumber}{2}
+\renewcommand\bottomfraction{.7}
+\setcounter{totalnumber}{6}
+\renewcommand\textfraction{.1}
+\renewcommand\floatpagefraction{.85}
+\setcounter{dbltopnumber}{3}
+\renewcommand\dbltopfraction{.85}
+\renewcommand\dblfloatpagefraction{.85}
+\def\ps@headings{%
+    \let\@oddfoot\@empty\let\@evenfoot\@empty
+    \def\@evenhead{\small\rlap{\thepage}\hfil\leftmark\unskip}%
+    \def\@oddhead{\small\rightmark\hfil\llap{\thepage}}%
+    \let\@mkboth\@gobbletwo
+    \let\sectionmark\@gobble
+    \let\subsectionmark\@gobble
+    }
+% make indentations changeable
+\def\setitemindent#1{\settowidth{\labelwidth}{#1}%
+        \leftmargini\labelwidth
+        \advance\leftmargini\labelsep
+   \def\@listi{\leftmargin\leftmargini
+        \labelwidth\leftmargini\advance\labelwidth by -\labelsep
+        \parsep=\parskip
+        \topsep=\medskipamount
+        \itemsep=\parskip \advance\itemsep by -\parsep}}
+\def\setitemitemindent#1{\settowidth{\labelwidth}{#1}%
+        \leftmarginii\labelwidth
+        \advance\leftmarginii\labelsep
+\def\@listii{\leftmargin\leftmarginii
+        \labelwidth\leftmarginii\advance\labelwidth by -\labelsep
+        \parsep=\parskip
+        \topsep=\z@
+        \itemsep=\parskip \advance\itemsep by -\parsep}}
+% labels of description
+\def\descriptionlabel#1{\hspace\labelsep #1\hfil}
+% adjusted environment "description"
+% if an optional parameter (at the first two levels of lists)
+% is present, its width is considered to be the widest mark
+% throughout the current list.
+\def\description{\@ifnextchar[{\@describe}{\list{}{\labelwidth\z@
+          \itemindent-\leftmargin \let\makelabel\descriptionlabel}}}
+\let\enddescription\endlist
+%
+\def\describelabel#1{#1\hfil}
+\def\@describe[#1]{\relax\ifnum\@listdepth=0
+\setitemindent{#1}\else\ifnum\@listdepth=1
+\setitemitemindent{#1}\fi\fi
+\list{--}{\let\makelabel\describelabel}}
+%
+\newdimen\logodepth
+\logodepth=2.2cm
+\newdimen\headerboxheight
+\headerboxheight=180pt % 18 10.5dd-lines - 2\baselineskip
+\newdimen\betweenumberspace          % dimension for space between
+\betweenumberspace=3.33pt            % number and text of titles.
+\newdimen\aftertext                  % dimension for space after
+\aftertext=5pt                       % text of title.
+\newdimen\headlineindent             % dimension for space between
+\headlineindent=1.166cm              % number and text of headings.
+\def\andname{and}
+\if@mathematic
+   \def\runinend{\enspace}
+   \def\floatcounterend{\enspace}
+   \def\sectcounterend{}
+\else
+   \def\runinend{.}
+   \def\floatcounterend{.\ }
+   \def\sectcounterend{.}
+\fi
+\def\keywordname{{\bfseries Key words\runinend}}
+\def\lastandname{, and}
+\def\mailname{{\itshape Correspondence to\/}:}
+\def\email#1{{e-mail: \tt#1}}
+\def\keywords#1{\par\addvspace\baselineskip\noindent\keywordname\enspace
+\ignorespaces#1}
+%
+\newcounter{inst}
+\newcounter{auth}
+\def\authdepth{2}
+\newdimen\instindent
+\newbox\authrun
+\newtoks\authorrunning
+\newbox\titrun
+\newtoks\titlerunning
+\def\authorfont{\bfseries}
+
+\def\combirunning#1{\gdef\@combi{#1}}
+\def\@combi{}
+\newbox\combirun
+%
+\def\ps@last{\def\@evenhead{\small\rlap{\thepage}\hfil
+\lastevenhead}}
+\newcounter{lastpage}
+\def\islastpageeven{\@ifundefined{lastpagenumber}
+{\setcounter{lastpage}{0}}{\setcounter{lastpage}{\lastpagenumber}}
+\ifnum\value{lastpage}>0
+   \ifodd\value{lastpage}%
+   \else
+      \if@smartrunh
+         \thispagestyle{last}%
+      \fi
+   \fi
+\fi}
+\def\getlastpagenumber{\clearpage
+\addtocounter{page}{-1}%
+   \immediate\write\@auxout{\string\gdef\string\lastpagenumber{\thepage}}%
+   \immediate\write\@auxout{\string\newlabel{LastPage}{{}{\thepage}}}%
+   \addtocounter{page}{1}}
+
+\def\journalname#1{\gdef\@journalname{#1}}
+
+\def\dedication#1{\gdef\@dedic{#1}}
+\def\@dedic{}
+
+\let\@date\undefined
+
+\def\institute#1{\gdef\@institute{#1}}
+
+\def\institutename{\par
+ \begingroup
+ \parindent=0pt
+ \parskip=0pt
+ \setcounter{inst}{1}%
+ \def\and{\par\stepcounter{inst}%
+ \if@instindent\hangindent\instindent\fi
+ \noindent
+ \hbox to\instindent{\hss\smash{$^{\theinst}$}\enspace}\ignorespaces}%
+ \setbox0=\vbox{\def\thanks##1{}\@institute}
+ \ifnum\value{inst}>9\relax\setbox0=\hbox{$^{88}$\enspace}%
+                 \else\setbox0=\hbox{$^{8}$\enspace}\fi
+ \instindent=\wd0\relax
+ \ifnum\value{inst}=1\relax
+ \else
+   \setcounter{inst}{1}%
+   \if@instindent\hangindent\instindent\fi
+   \noindent
+   \hbox to\instindent{\hss\smash{$^{\theinst}$}\enspace}\ignorespaces
+ \fi
+ \small
+ \ignorespaces
+ \@institute\par
+ \endgroup}
+
+\def\offprints#1{\begingroup
+\def\protect{\noexpand\protect\noexpand}\xdef\@thanks{\@thanks
+\protect\footnotetext[0]{\unskip\hskip-15pt{\itshape Send offprint requests
+to\/}: \ignorespaces#1}}\endgroup\ignorespaces}
+
+\def\mail#1{\gdef\@mail{#1}}
+\def\@mail{}
+
+\def\@thanks{}
+
+\def\@fnsymbol#1{\ifcase#1\or\star\or{\star\star}\or{\star\star\star}%
+   \or \dagger\or \ddagger\or
+   \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
+   \or \ddagger\ddagger \else\@ctrerr\fi\relax}
+
+\def\inst#1{\unskip$^{#1}$}
+\def\fnmsep{\unskip$^,$}
+
+\def\subtitle#1{\gdef\@subtitle{#1}}
+\def\@subtitle{}
+
+\def\headnote#1{\gdef\@headnote{#1}}
+\def\@headnote{}
+
+\def\ch@ckobl#1#2{\@ifundefined{@#1}
+ {\typeout{SVJour warning: Missing
+\expandafter\string\csname#1\endcsname}%
+  \csname #1\endcsname{#2}}
+ {}}
+%
+\def\ProcessRunnHead{%
+    \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}%
+    \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}%
+    \instindent=\textwidth
+    \advance\instindent by-\headlineindent
+    \if!\the\titlerunning!\else
+      \edef\@title{\the\titlerunning}%
+    \fi
+    \global\setbox\titrun=\hbox{\small\rmfamily\unboldmath\ignorespaces\@title
+                                \unskip}%
+    \ifdim\wd\titrun>\instindent
+       \typeout{^^JSVJour Warning: Title too long for running head.}%
+       \typeout{Please supply a shorter form with \string\titlerunning
+                \space prior to \string\maketitle}%
+       \global\setbox\titrun=\hbox{\small\rmfamily
+       Title Suppressed Due to Excessive Length}%
+    \fi
+    \xdef\@title{\copy\titrun}%
+%
+    \if!\the\authorrunning!
+    \else
+      \setcounter{auth}{1}%
+      \edef\@author{\the\authorrunning}%
+    \fi
+    \ifnum\value{auth}>\authdepth
+       \def\stripauthor##1\and##2\endauthor{%
+       \protected@xdef\@author{##1\unskip\unskip\if!##2!\else\ et al.\fi}}%
+       \expandafter\stripauthor\@author\and\endauthor
+    \else
+       \gdef\and{\unskip, \ignorespaces}%
+       {\def\and{\noexpand\protect\noexpand\and}%
+       \protected@xdef\@author{\@author}}
+    \fi
+    \global\setbox\authrun=\hbox{\small\rmfamily\unboldmath\ignorespaces
+                                 \@author\unskip}%
+    \ifdim\wd\authrun>\instindent
+    \typeout{^^JSVJour Warning: Author name(s) too long for running head.
+             ^^JPlease supply a shorter form with \string\authorrunning
+             \space prior to \string\maketitle}%
+    \global\setbox\authrun=\hbox{\small\rmfamily Please give a shorter version
+          with: {\tt\string\authorrunning\space and
+             \string\titlerunning\space prior to \string\maketitle}}%
+    \fi
+    \xdef\@author{\copy\authrun}%
+    \markboth{\@author}{\@title}%
+}
+%
+\def\maketitle{\par
+\ch@ckobl{journalname}{Noname}
+\ch@ckobl{date}{The date of receipt and acceptance will be inserted by
+the editor}
+\ch@ckobl{title}{A title should be given}
+\ch@ckobl{author}{Name(s) and initial(s) of author(s) should be given}
+\ch@ckobl{institute}{Address(es) of author(s) should be given}
+\begingroup
+%
+    \renewcommand\thefootnote{\@fnsymbol\c@footnote}%
+    \def\@makefnmark{$^{\@thefnmark}$}%
+%
+ \def\lastand{\ifnum\value{inst}=2\relax
+                 \unskip{} \andname\
+              \else
+                 \unskip, \andname\
+              \fi}%
+ \def\and{\stepcounter{auth}\relax
+          \if@smartand
+             \ifnum\value{auth}=\value{inst}%
+                \lastand
+             \else
+                \unskip,
+             \fi
+          \else
+             \unskip,
+          \fi}%
+ \ifnum \col@number=\@ne
+   \@maketitle
+ \else
+   \twocolumn[\@maketitle]%
+ \fi
+%ce \thispagestyle{empty}
+\thispagestyle{plain}
+ \global\@topnum\z@
+ \@thanks
+ \if!\@mail!\else
+    \footnotetext[0]{\kern-\bibindent\mailname\
+    \ignorespaces\@mail}%
+ \fi
+%
+ \if@runhead
+    \ProcessRunnHead
+    \if@smartrunh
+       \instindent=\textwidth
+       \advance\instindent by-\headlineindent
+       \if!\@combi!%
+          \global\setbox\combirun=\hbox{\small\rmfamily\unboldmath\ignorespaces
+                                        \@author\unskip: \@title\unskip}%
+          \def\@tempa{Automatically generated running head}%
+       \else
+          \global\setbox\combirun=\hbox{\small\rmfamily\unboldmath\ignorespaces
+                                        \@combi\unskip}%
+          \def\@tempa{With \string\combirunning\space supplied running head}%
+       \fi
+       \ifdim\wd\combirun>\instindent
+          \typeout{^^JSVJour Warning: \@tempa}%
+          \typeout{for a possible last even numbered page is too long.}%
+          \typeout{Please supply a shorter form with \string\combirunning
+                   \space prior to \string\maketitle.}%
+          \global\setbox\combirun=\hbox{\small\rmfamily
+          Title Suppressed Due to Excessive Length --
+          supply \ttfamily\char92combirunning}%
+       \fi
+       \xdef\lastevenhead{\copy\combirun}%
+    \fi
+ \fi
+%
+ \endgroup
+ \setcounter{footnote}{0}
+ \global\let\thanks\relax
+ \global\let\maketitle\relax
+ \global\let\@maketitle\relax
+ \global\let\@thanks\@empty
+ \global\let\@author\@empty
+ \global\let\@date\@empty
+ \global\let\@title\@empty
+ \global\let\@subtitle\@empty
+ \global\let\title\relax
+ \global\let\author\relax
+ \global\let\date\relax
+ \global\let\and\relax}
+
+\def\makeheadbox{{%
+\begin{flushright}
+{\bf LAL 04-102}\\
+October 2004
+\end{flushright}
+%ce\hbox to0pt{\vbox{\baselineskip=10dd\hrule\hbox
+%ceto\hsize{\vrule\kern3pt\vbox{\kern3pt
+%ce\hbox{\bfseries\@journalname\ manuscript No.}
+%ce\hbox{(will be inserted by the editor)}
+%cekern3pt}\hfil\kern3pt\vrule}\hrule}%
+\hss}}
+
+\def\@maketitle{\newpage
+ \normalfont
+ \vbox to0pt{\vskip-40pt
+ \nointerlineskip
+ \makeheadbox\vss}\nointerlineskip
+ \setbox\authrun=\vbox\bgroup
+ {\Large \bfseries\boldmath
+  \hrule\@height\logodepth\@width\z@
+  \pretolerance=10000
+  \rightskip=0pt plus 4cm
+ \if!\@headnote!\else
+   \noindent
+   {\normalfont\em\ignorespaces\@headnote\par}\vskip 3.5mm
+ \fi
+  \noindent\ignorespaces
+  \@title \par}\vskip 11.24pt\relax
+ \if!\@subtitle!\else
+   {\large\bfseries\boldmath
+   \pretolerance=10000
+   \rightskip=0pt plus 3cm
+   \noindent\ignorespaces\@subtitle \par}\vskip 11.24pt
+ \fi
+ \normalfont\authorfont
+ \lineskip .5em
+ \setbox0=\vbox{\setcounter{auth}{1}\def\and{\stepcounter{auth} }%
+                \hfuzz=2\textwidth\def\thanks##1{}\@author}%
+ \value{inst}=\value{auth}%
+ \setcounter{auth}{1}%
+ \rightskip=0pt plus 2cm
+ \noindent\ignorespaces\@author\vskip7.23pt
+ \rightskip=0pt\relax
+ \normalfont\small\rmfamily
+ \institutename
+ \vskip 12.85pt \noindent\@date
+ \if!\@dedic!\else
+    \par
+    \small\itshape
+    \addvspace\baselineskip
+    \noindent\@dedic
+ \fi
+ \egroup % end of header box
+ \@tempdima=\headerboxheight
+ \advance\@tempdima by-\ht\authrun
+ \ifdim\@tempdima>0pt
+    \vrule width0pt height\@tempdima
+ \fi
+ \unvbox\authrun
+ \global\@minipagetrue
+ \global\everypar{\global\@minipagefalse\global\everypar{}}
+ \vskip22.47pt
+}
+%
+\if@mathematic
+   \def\vec#1{\ensuremath{\mathchoice
+                     {\mbox{\boldmath$\displaystyle\mathbf{#1}$}}
+                     {\mbox{\boldmath$\textstyle\mathbf{#1}$}}
+                     {\mbox{\boldmath$\scriptstyle\mathbf{#1}$}}
+                     {\mbox{\boldmath$\scriptscriptstyle\mathbf{#1}$}}}}
+\else
+   \def\vec#1{\ensuremath{\mathchoice
+                     {\mbox{\boldmath$\displaystyle#1$}}
+                     {\mbox{\boldmath$\textstyle#1$}}
+                     {\mbox{\boldmath$\scriptstyle#1$}}
+                     {\mbox{\boldmath$\scriptscriptstyle#1$}}}}
+\fi
+%
+\def\tens#1{\ensuremath{\mathsf{#1}}}
+%
+\setcounter{secnumdepth}{3}
+\newcounter {section}
+\newcounter {subsection}[section]
+\newcounter {subsubsection}[subsection]
+\newcounter {paragraph}[subsubsection]
+\newcounter {subparagraph}[paragraph]
+\renewcommand\thesection      {\@arabic\c@section}
+\renewcommand\thesubsection   {\thesection.\@arabic\c@subsection}
+\renewcommand\thesubsubsection{\thesubsection.\@arabic\c@subsubsection}
+\renewcommand\theparagraph    {\thesubsubsection.\@arabic\c@paragraph}
+\renewcommand\thesubparagraph {\theparagraph.\@arabic\c@subparagraph}
+%
+\def\@hangfrom#1{\setbox\@tempboxa\hbox{#1}%
+      \hangindent \z@\noindent\box\@tempboxa}
+
+\def\@seccntformat#1{\csname the#1\endcsname\sectcounterend
+\hskip\betweenumberspace}
+
+\def\@sect#1#2#3#4#5#6[#7]#8{%
+  \ifnum #2>\c@secnumdepth
+    \let\@svsec\@empty
+  \else
+    \refstepcounter{#1}%
+    \protected@edef\@svsec{\@seccntformat{#1}\relax}%
+  \fi
+  \@tempskipa #5\relax
+  \ifdim \@tempskipa>\z@
+    \begingroup
+      #6{%
+        \@hangfrom{\hskip #3\relax\@svsec}%
+          \raggedright
+          \hyphenpenalty \@M%
+          \interlinepenalty \@M #8\@@par}%
+    \endgroup
+    \csname #1mark\endcsname{#7}%
+    \addcontentsline{toc}{#1}{%
+      \ifnum #2>\c@secnumdepth \else
+        \protect\numberline{\csname the#1\endcsname\sectcounterend}%
+      \fi
+      #7}%
+  \else
+    \def\@svsechd{%
+      #6{\hskip #3\relax
+      \@svsec #8\hskip\aftertext}%
+      \csname #1mark\endcsname{#7}%
+      \addcontentsline{toc}{#1}{%
+        \ifnum #2>\c@secnumdepth \else
+          \protect\numberline{\csname the#1\endcsname}%
+        \fi
+        #7}}%
+  \fi
+  \@xsect{#5}}
+
+%
+% measures and setting of sections
+%
+\def\section{\@startsection{section}{1}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\normalsize\bfseries\boldmath}}
+\def\subsection{\@startsection{subsection}{2}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\normalsize\itshape}}
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}%
+    {-13dd plus-4pt minus-4pt}{-5.5pt}{\normalsize\itshape}}
+\def\paragraph{\@startsection{paragraph}{4}{\z@}%
+    {-13pt plus-4pt minus-4pt}{-5.5pt}{\normalsize\itshape}}
+
+\setlength\leftmargini  {\parindent}
+\leftmargin  \leftmargini
+\setlength\leftmarginii {\parindent}
+\setlength\leftmarginiii {1.87em}
+\setlength\leftmarginiv  {1.7em}
+\setlength\leftmarginv  {.5em}
+\setlength\leftmarginvi {.5em}
+\setlength  \labelsep  {.5em}
+\setlength  \labelwidth{\leftmargini}
+\addtolength\labelwidth{-\labelsep}
+\@beginparpenalty -\@lowpenalty
+\@endparpenalty   -\@lowpenalty
+\@itempenalty     -\@lowpenalty
+\renewcommand\theenumi{\@arabic\c@enumi}
+\renewcommand\theenumii{\@alph\c@enumii}
+\renewcommand\theenumiii{\@roman\c@enumiii}
+\renewcommand\theenumiv{\@Alph\c@enumiv}
+\newcommand\labelenumi{\theenumi.}
+\newcommand\labelenumii{(\theenumii)}
+\newcommand\labelenumiii{\theenumiii.}
+\newcommand\labelenumiv{\theenumiv.}
+\renewcommand\p@enumii{\theenumi}
+\renewcommand\p@enumiii{\theenumi(\theenumii)}
+\renewcommand\p@enumiv{\p@enumiii\theenumiii}
+\newcommand\labelitemi{\normalfont\bfseries --}
+\newcommand\labelitemii{\normalfont\bfseries --}
+\newcommand\labelitemiii{$\m@th\bullet$}
+\newcommand\labelitemiv{$\m@th\cdot$}
+
+\if@spthms
+% definition of the "\spnewtheorem" command.
+%
+% Usage:
+%
+%     \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font}
+% or  \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font}
+% or  \spnewtheorem*{env_nam}{caption}{cap_font}{body_font}
+%
+% New is "cap_font" and "body_font". It stands for
+% fontdefinition of the caption and the text itself.
+%
+% "\spnewtheorem*" gives a theorem without number.
+%
+% A defined spnewthoerem environment is used as described
+% by Lamport.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\def\@thmcountersep{}
+\def\@thmcounterend{}
+\newdimen\spthmsep \spthmsep=3pt
+
+\def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}}
+
+% definition of \spnewtheorem with number
+
+\def\@spnthm#1#2{%
+  \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}}
+\def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}}
+
+\def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname
+   {\@definecounter{#1}\@addtoreset{#1}{#3}%
+   \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
+     \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}%
+   \expandafter\xdef\csname #1name\endcsname{#2}%
+   \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}%
+                              \global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
+   {\@definecounter{#1}%
+   \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
+   \expandafter\xdef\csname #1name\endcsname{#2}%
+   \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}%
+                               \global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@spothm#1[#2]#3#4#5{%
+  \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}%
+  {\expandafter\@ifdefinable\csname #1\endcsname
+  {\global\@namedef{the#1}{\@nameuse{the#2}}%
+  \expandafter\xdef\csname #1name\endcsname{#3}%
+  \global\@namedef{#1}{\@spthm{#2}{\csname #1name\endcsname}{#4}{#5}}%
+  \global\@namedef{end#1}{\@endtheorem}}}}
+
+\def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@
+\labelsep=\spthmsep\refstepcounter{#1}%
+\@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}}
+
+\def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}%
+                    \ignorespaces}
+
+\def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname
+       the#1\endcsname}{#5}{#3}{#4}\ignorespaces}
+
+\def\normalthmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist
+                 \item[\hskip\labelsep{##3##1\ ##2\@thmcounterend}]##4}
+\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
+      \item[\hskip\labelsep{##4##1\ ##2}]{##4(##3)\@thmcounterend\ }##5}}
+\normalthmheadings
+
+\def\reversethmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist
+                 \item[\hskip\labelsep{##3##2\ ##1\@thmcounterend}]##4}
+\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
+      \item[\hskip\labelsep{##4##2\ ##1}]{##4(##3)\@thmcounterend\ }##5}}
+
+% definition of \spnewtheorem* without number
+
+\def\@sthm#1#2{\@Ynthm{#1}{#2}}
+
+\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
+   {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}%
+    \expandafter\xdef\csname #1name\endcsname{#2}%
+    \global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@
+\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}}
+
+\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces}
+
+\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1}
+       {#4}{#2}{#3}\ignorespaces}
+
+\def\@Begintheorem#1#2#3{#3\trivlist
+                           \item[\hskip\labelsep{#2#1\@thmcounterend}]}
+
+\def\@Opargbegintheorem#1#2#3#4{#4\trivlist
+      \item[\hskip\labelsep{#3#1}]{#3(#2)\@thmcounterend\ }}
+
+\if@envcntsect
+   \def\@thmcountersep{.}
+   \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape}
+\else
+   \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape}
+   \if@envcntreset
+      \@addtoreset{theorem}{section}
+   \else
+      \@addtoreset{theorem}{chapter}
+   \fi
+\fi
+
+%definition of divers theorem environments
+\spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily}
+\spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily}
+\if@envcntsame % alle Umgebungen wie Theorem.
+   \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}}
+\else % alle Umgebungen mit eigenem Zaehler
+   \if@envcntsect % mit section numeriert
+      \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[section]{#3}{#4}}
+   \else % nicht mit section numeriert
+      \if@envcntreset
+         \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4}
+                                   \@addtoreset{#1}{section}}
+      \else
+         \let\spn@wtheorem=\@spynthm
+      \fi
+   \fi
+\fi
+\spn@wtheorem{case}{Case}{\itshape}{\rmfamily}
+\spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily}
+\spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape}
+\spn@wtheorem{definition}{Definition}{\bfseries}{\itshape}
+\spn@wtheorem{example}{Example}{\itshape}{\rmfamily}
+\spn@wtheorem{exercise}{Exercise}{\bfseries}{\rmfamily}
+\spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape}
+\spn@wtheorem{note}{Note}{\itshape}{\rmfamily}
+\spn@wtheorem{problem}{Problem}{\bfseries}{\rmfamily}
+\spn@wtheorem{property}{Property}{\itshape}{\rmfamily}
+\spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape}
+\spn@wtheorem{question}{Question}{\itshape}{\rmfamily}
+\spn@wtheorem{solution}{Solution}{\bfseries}{\rmfamily}
+\spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily}
+%
+\newenvironment{theopargself}
+    {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
+         \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5}
+     \def\@Opargbegintheorem##1##2##3##4{##4\trivlist
+         \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }}}{}
+\newenvironment{theopargself*}
+    {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
+         \item[\hskip\labelsep{##4##1\ ##2}]{\hspace*{-\labelsep}##4##3\@thmcounterend}##5}
+     \def\@Opargbegintheorem##1##2##3##4{##4\trivlist
+         \item[\hskip\labelsep{##3##1}]{\hspace*{-\labelsep}##3##2\@thmcounterend}}}{}
+\fi
+
+\def\@takefromreset#1#2{%
+    \def\@tempa{#1}%
+    \let\@tempd\@elt
+    \def\@elt##1{%
+        \def\@tempb{##1}%
+        \ifx\@tempa\@tempb\else
+            \@addtoreset{##1}{#2}%
+        \fi}%
+    \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname
+    \expandafter\def\csname cl@#2\endcsname{}%
+    \@tempc
+    \let\@elt\@tempd}
+
+\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}
+\def\qed{\ifmmode\else\unskip\quad\fi\squareforqed}
+\def\smartqed{\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil
+\penalty50\hskip1em\null\nobreak\hfil\squareforqed
+\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}}
+
+% Define `abstract' environment
+\def\abstract{\topsep=0pt\partopsep=0pt\parsep=0pt\itemsep=0pt\relax
+\trivlist\item[\hskip\labelsep
+{\bfseries\abstractname}]\if!\abstractname!\hskip-\labelsep\fi}
+\if@twocolumn
+   \def\endabstract{\endtrivlist\addvspace{5mm}\strich}
+   \def\strich{\hrule\vskip3ptplus12pt\null}
+\else
+   \def\endabstract{\endtrivlist\addvspace{3mm}}
+\fi
+%
+\newenvironment{verse}
+               {\let\\\@centercr
+                \list{}{\itemsep      \z@
+                        \itemindent   -1.5em%
+                        \listparindent\itemindent
+                        \rightmargin  \leftmargin
+                        \advance\leftmargin 1.5em}%
+                \item\relax}
+               {\endlist}
+\newenvironment{quotation}
+               {\list{}{\listparindent 1.5em%
+                        \itemindent    \listparindent
+                        \rightmargin   \leftmargin
+                        \parsep        \z@ \@plus\p@}%
+                \item\relax}
+               {\endlist}
+\newenvironment{quote}
+               {\list{}{\rightmargin\leftmargin}%
+                \item\relax}
+               {\endlist}
+\newcommand\appendix{\par
+  \setcounter{section}{0}%
+  \setcounter{subsection}{0}%
+  \renewcommand\thesection{\@Alph\c@section}}
+\setlength\arraycolsep{1.5\p@}
+\setlength\tabcolsep{6\p@}
+\setlength\arrayrulewidth{.4\p@}
+\setlength\doublerulesep{2\p@}
+\setlength\tabbingsep{\labelsep}
+\skip\@mpfootins = \skip\footins
+\setlength\fboxsep{3\p@}
+\setlength\fboxrule{.4\p@}
+\renewcommand\theequation{\@arabic\c@equation}
+\newcounter{figure}
+\renewcommand\thefigure{\@arabic\c@figure}
+\def\fps@figure{tbp}
+\def\ftype@figure{1}
+\def\ext@figure{lof}
+\def\fnum@figure{\figurename~\thefigure}
+\newenvironment{figure}
+               {\@float{figure}}
+               {\end@float}
+\newenvironment{figure*}
+               {\@dblfloat{figure}}
+               {\end@dblfloat}
+\newcounter{table}
+\renewcommand\thetable{\@arabic\c@table}
+\def\fps@table{tbp}
+\def\ftype@table{2}
+\def\ext@table{lot}
+\def\fnum@table{\tablename~\thetable}
+\newenvironment{table}
+               {\@float{table}}
+               {\end@float}
+\newenvironment{table*}
+               {\@dblfloat{table}}
+               {\end@dblfloat}
+
+\def \@floatboxreset {%
+        \reset@font
+        \small
+        \@setnobreak
+        \@setminipage
+}
+
+\newlength\abovecaptionskip
+\newlength\belowcaptionskip
+\setlength\abovecaptionskip{10\p@}
+\setlength\belowcaptionskip{0\p@}
+\newcommand\leftlegendglue{}
+
+\def\fig@type{figure}
+
+\newdimen\figcapgap\figcapgap=3pt
+\newdimen\tabcapgap\tabcapgap=5.5pt
+
+\@ifundefined{floatlegendstyle}{\def\floatlegendstyle{\bfseries}}{}
+
+\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname
+  ext@#1\endcsname}{#1}{\protect\numberline{\csname
+  the#1\endcsname}{\ignorespaces #2}}\begingroup
+    \@parboxrestore
+    \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
+  \endgroup}
+
+\def\capstrut{\vrule\@width\z@\@height\topskip}
+
+\@ifundefined{captionstyle}{\def\captionstyle{\normalfont\small}}{}
+
+\long\def\@makecaption#1#2{%
+ \captionstyle
+ \ifx\@captype\fig@type
+   \vskip\figcapgap
+ \fi
+ \setbox\@tempboxa\hbox{{\floatlegendstyle #1\floatcounterend}%
+ \capstrut #2}%
+ \ifdim \wd\@tempboxa >\hsize
+   {\floatlegendstyle #1\floatcounterend}\capstrut #2\par
+ \else
+   \hbox to\hsize{\leftlegendglue\unhbox\@tempboxa\hfil}%
+ \fi
+ \ifx\@captype\fig@type\else
+   \vskip\tabcapgap
+ \fi}
+
+\newdimen\figgap\figgap=1cc
+\long\def\@makesidecaption#1#2{%
+   \parbox[b]{\@tempdima}{\captionstyle{\floatlegendstyle
+                                         #1\floatcounterend}#2}}
+\def\sidecaption#1\caption{%
+\setbox\@tempboxa=\hbox{#1\unskip}%
+\if@twocolumn
+ \ifdim\hsize<\textwidth\else
+   \ifdim\wd\@tempboxa<\columnwidth
+      \typeout{Double column float fits into single column -
+            ^^Jyou'd better switch the environment. }%
+   \fi
+ \fi
+\fi
+\@tempdima=\hsize
+\advance\@tempdima by-\figgap
+\advance\@tempdima by-\wd\@tempboxa
+\ifdim\@tempdima<3cm
+    \typeout{\string\sidecaption: No sufficient room for the legend;
+             using normal \string\caption. }%
+   \unhbox\@tempboxa
+   \let\@capcommand=\@caption
+\else
+   \let\@capcommand=\@sidecaption
+   \leavevmode
+   \unhbox\@tempboxa
+   \hfill
+\fi
+\refstepcounter\@captype
+\@dblarg{\@capcommand\@captype}}
+
+\long\def\@sidecaption#1[#2]#3{\addcontentsline{\csname
+  ext@#1\endcsname}{#1}{\protect\numberline{\csname
+  the#1\endcsname}{\ignorespaces #2}}\begingroup
+    \@parboxrestore
+    \@makesidecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
+  \endgroup}
+
+% Define `acknowledgement' environment
+\def\acknowledgement{\par\addvspace{17pt}\small\rmfamily
+\trivlist\if!\ackname!\item[]\else
+\item[\hskip\labelsep
+{\it\ackname}]\fi}
+\def\endacknowledgement{\endtrivlist\addvspace{6pt}}
+% Define `noteadd' environment
+\def\noteadd{\par\addvspace{17pt}\small\rmfamily
+\trivlist\item[\hskip\labelsep
+{\itshape\noteaddname}]}
+\def\endnoteadd{\endtrivlist\addvspace{6pt}}
+
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
+\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
+\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}
+\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}
+\newcommand\@pnumwidth{1.55em}
+\newcommand\@tocrmarg{2.55em}
+\newcommand\@dotsep{4.5}
+\setcounter{tocdepth}{1}
+\newcommand\tableofcontents{%
+    \section*{\contentsname}%
+    \@starttoc{toc}%
+    \addtocontents{toc}{\begingroup\protect\small}%
+    \AtEndDocument{\addtocontents{toc}{\endgroup}}%
+    }
+\newcommand*\l@part[2]{%
+  \ifnum \c@tocdepth >-2\relax
+    \addpenalty\@secpenalty
+    \addvspace{2.25em \@plus\p@}%
+    \begingroup
+      \setlength\@tempdima{3em}%
+      \parindent \z@ \rightskip \@pnumwidth
+      \parfillskip -\@pnumwidth
+      {\leavevmode
+       \large \bfseries #1\hfil \hb@xt@\@pnumwidth{\hss #2}}\par
+       \nobreak
+       \if@compatibility
+         \global\@nobreaktrue
+         \everypar{\global\@nobreakfalse\everypar{}}%
+      \fi
+    \endgroup
+  \fi}
+\newcommand*\l@section{\@dottedtocline{1}{0pt}{1.5em}}
+\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
+\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
+\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
+\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
+\newcommand\listoffigures{%
+    \section*{\listfigurename
+      \@mkboth{\listfigurename}%
+              {\listfigurename}}%
+    \@starttoc{lof}%
+    }
+\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
+\newcommand\listoftables{%
+    \section*{\listtablename
+      \@mkboth{\listtablename}{\listtablename}}%
+    \@starttoc{lot}%
+    }
+\let\l@table\l@figure
+\newdimen\bibindent
+\setlength\bibindent{\parindent}
+\def\@biblabel#1{#1.}
+\def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw
+      {\let\protect\noexpand
+       \immediate
+       \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces}
+\newenvironment{thebibliography}[1]
+     {\section*{\refname
+        \@mkboth{\refname}{\refname}}\small
+      \list{\@biblabel{\@arabic\c@enumiv}}%
+           {\settowidth\labelwidth{\@biblabel{#1}}%
+            \leftmargin\labelwidth
+            \advance\leftmargin\labelsep
+            \@openbib@code
+            \usecounter{enumiv}%
+            \let\p@enumiv\@empty
+            \renewcommand\theenumiv{\@arabic\c@enumiv}}%
+      \sloppy\clubpenalty4000\widowpenalty4000%
+      \sfcode`\.\@m}
+     {\def\@noitemerr
+       {\@latex@warning{Empty `thebibliography' environment}}%
+      \endlist}
+%
+\newcount\@tempcntc
+\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
+  \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do
+    {\@ifundefined
+       {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries
+        ?}\@warning
+       {Citation `\@citeb' on page \thepage \space undefined}}%
+    {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}%
+     \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne
+       \@citea\def\@citea{,\hskip0.1em\ignorespaces}\hbox{\csname b@\@citeb\endcsname}%
+     \else
+      \advance\@tempcntb\@ne
+      \ifnum\@tempcntb=\@tempcntc
+      \else\advance\@tempcntb\m@ne\@citeo
+      \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}}
+\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else
+            \@citea\def\@citea{,\hskip0.1em\ignorespaces}%
+  \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else
+   {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else \def\@citea{--}\fi
+    \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi}
+%
+\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em}
+\let\@openbib@code\@empty
+\newenvironment{theindex}
+               {\if@twocolumn
+                  \@restonecolfalse
+                \else
+                  \@restonecoltrue
+                \fi
+                \columnseprule \z@
+                \columnsep 35\p@
+                \twocolumn[\section*{\indexname}]%
+                \@mkboth{\indexname}{\indexname}%
+                \thispagestyle{plain}\parindent\z@
+                \parskip\z@ \@plus .3\p@\relax
+                \let\item\@idxitem}
+               {\if@restonecol\onecolumn\else\clearpage\fi}
+\newcommand\@idxitem{\par\hangindent 40\p@}
+\newcommand\subitem{\@idxitem \hspace*{20\p@}}
+\newcommand\subsubitem{\@idxitem \hspace*{30\p@}}
+\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax}
+\renewcommand\footnoterule{%
+  \kern-3\p@
+  \hrule\@width.4\columnwidth
+  \kern2.6\p@}
+\newcommand\@makefntext[1]{%
+    \noindent
+    \hb@xt@\bibindent{\hss\@makefnmark\enspace}#1}
+%
+\newcommand\contentsname{Contents}
+\newcommand\listfigurename{List of Figures}
+\newcommand\listtablename{List of Tables}
+\newcommand\refname{References}
+\newcommand\indexname{Index}
+\newcommand\figurename{Fig.}
+\newcommand\tablename{Table}
+\newcommand\partname{Part}
+\newcommand\appendixname{Appendix}
+\newcommand\abstractname{Abstract\runinend}
+\newcommand\ackname{Acknowledgements\runinend}
+\newcommand\noteaddname{Note added in proof}
+% French section
+\def\ds@francais{%
+ \typeout{On parle francais.}%
+ \def\abstractname{R\'esum\'e\runinend}%
+ \def\ackname{Remerciements\runinend}%
+ \def\andname{et}%
+ \def\lastandname{ et}%
+ \def\appendixname{Appendice}
+ \def\chaptername{Chapitre}%
+ \def\claimname{Pr\'etention}%
+ \def\conjecturename{Hypoth\`ese}%
+ \def\contentsname{Table des mati\`eres}%
+ \def\corollaryname{Corollaire}%
+ \def\definitionname{D\'efinition}%
+ \def\examplename{Exemple}%
+ \def\exercisename{Exercice}%
+ \def\figurename{Fig.}%
+ \def\keywordname{{\bfseries Mots-cl\'e\runinend}}
+ \def\indexname{Index}
+ \def\lemmaname{Lemme}%
+ \def\contriblistname{Liste des contributeurs}
+ \def\listfigurename{Liste des figures}%
+ \def\listtablename{Liste des tables}%
+ \def\mailname{{\itshape Correspondence to\/}:}
+ \def\noteaddname{Note ajout\'ee \`a l'\'epreuve}%
+ \def\notename{Remarque}%
+ \def\partname{Partie}%
+ \def\problemname{Probl\`eme}%
+ \def\proofname{Preuve}%
+ \def\propertyname{Caract\'eristique}%
+%\def\propositionname{Proposition}%
+ \def\questionname{Question}%
+ \def\refname{Bibliographie}%
+ \def\remarkname{Remarque}%
+ \def\seename{voyez}
+ \def\solutionname{Solution}%
+%\def\subclassname{{\it Subject Classifications\/}:}
+ \def\tablename{Tableau}%
+ \def\theoremname{Th\'eor\`eme}%
+}
+%
+% German section
+\def\ds@deutsch{\typeout{Man spricht deutsch.}%
+ \def\abstractname{Zusammenfassung\runinend}%
+ \def\ackname{Danksagung\runinend}%
+ \def\andname{und}%
+ \def\lastandname{ und}%
+ \def\appendixname{Anhang}%
+ \def\chaptername{Kapitel}%
+ \def\claimname{Behauptung}%
+ \def\conjecturename{Hypothese}%
+ \def\contentsname{Inhaltsverzeichnis}%
+ \def\corollaryname{Korollar}%
+%\def\definitionname{Definition}%
+ \def\examplename{Beispiel}%
+ \def\exercisename{\"Ubung}%
+ \def\figurename{Abb.}%
+ \def\keywordname{{\bfseries Schl\"usselw\"orter\runinend}}
+ \def\indexname{Index}
+%\def\lemmaname{Lemma}%
+ \def\contriblistname{Mitarbeiter}
+ \def\listfigurename{Abbildungsverzeichnis}%
+ \def\listtablename{Tabellenverzeichnis}%
+ \def\mailname{{\itshape Correspondence to\/}:}
+ \def\noteaddname{Nachtrag}%
+ \def\notename{Anmerkung}%
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/CommentFromMaoraM.tex
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/CommentFromMaoraM.tex	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/CommentFromMaoraM.tex	(revision 392)
@@ -0,0 +1,8 @@
+1) Particle production yields are summarized in table 2. The pion energy spectra obtained at different energies and normalized to a 4MW SPL beam power, are presented in figure X.
+
+
+2) One notices that for $\epsilon_{syst} = 5\%$ there is no difference between a $3.5$~GeV or a $4.5$~GeV beam.  The inflance of the systematics is presented on figure 14 for a $4.5$~GeV beam.
+
+3) With a $3.5$~GeV SPL energy beam, in 5 years of focusing positive particles, one can reach a minimum value of $\sin^22\theta_{13} = 9.6\times 10^{-4}$ ($90\%$ CL, $\delta_{CP} = 0$) and realizes a $20\%$ gain compared to the up to now nominal $2.2$~GeV SPL energy beam. If one includes a mixed focusing scenario, to explore the ($\sin^22\theta_{13}$,$\delta_{CP}$) sensitivity, then the $\delta_{CP}$-independant $\sin^22\theta_{13} = 2.1\times 10^{-3}$ ($90\%$ CL) minimum value that may be reached with a $3.5$~GeV energy beam is $12.5\%$ better than the value that may be reached with a $2.2$~GeV beam. 
+
+This may be the sign that a $3.5$~GeV SPL beam energy design is to be investigated from the machine development and cost implication point of view.
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.aux
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.aux	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.aux	(revision 392)
@@ -0,0 +1,173 @@
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+\newlabel{tab:nbPart}{{2}{4}}
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+\@writefile{toc}{\contentsline {subsection}{\numberline {Appendix B.1}Pion neutrino probability computation}{18}}
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+\bibcite{Gaisser}{41}
+\bibcite{picasso}{42}
+\bibcite{pdg}{43}
+\bibcite{GEANT4}{44}
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.aux.sav
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.aux.sav	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.aux.sav	(revision 392)
@@ -0,0 +1,157 @@
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+\newlabel{tab:nbvsE}{{7}{16}}
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+\newlabel{eq:significance}{{1}{16}}
+\newlabel{fig:sensi45}{{13}{17}}
+\newlabel{fig:compSensi}{{14}{18}}
+\newlabel{fig:compEpsSyst}{{15}{19}}
+\newlabel{tab:thvseps}{{9}{20}}
+\newlabel{tab:sign}{{10}{20}}
+\@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{20}}
+\@writefile{toc}{\contentsline {section}{\numberline {Appendix B}Decay probability computations}{20}}
+\newlabel{fig:compDelta5pos}{{16}{21}}
+\citation{donega}
+\newlabel{fig:pionDecay}{{B1}{22}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {Appendix B.1}Pion neutrino probability computation}{22}}
+\newlabel{sec:Ppi}{{Appendix B.1}{22}}
+\newlabel{probaPi}{{B.1}{22}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {Appendix B.2}Muon neutrino probability computation}{22}}
+\newlabel{sec:Pmu}{{Appendix B.2}{22}}
+\newlabel{probaMu}{{B.2}{22}}
+\citation{Gaisser}
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+\newlabel{tab:Function}{{B1}{23}}
+\newlabel{pola}{{B.3}{23}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {Appendix B.3}The treatment of the kaons}{23}}
+\newlabel{sec:kaons}{{Appendix B.3}{23}}
+\newlabel{probaL}{{B.4}{23}}
+\citation{pdg}
+\bibcite{PMNS}{1}
+\bibcite{LSND}{2}
+\bibcite{MINIBOONE}{3}
+\bibcite{UNO}{4}
+\bibcite{SKNU04}{5}
+\bibcite{K2KNU04}{6}
+\bibcite{MINOS}{7}
+\bibcite{KAMLAND}{8}
+\bibcite{OPERA}{9}
+\bibcite{ICARUS}{10}
+\bibcite{CNGS}{11}
+\bibcite{CHOOZ}{12}
+\bibcite{DOUBLE-CHOOZ}{13}
+\bibcite{Wpaper}{14}
+\newlabel{tab:BRKP0SL}{{B2}{24}}
+\bibcite{SPL}{15}
+\bibcite{CERN}{16}
+\bibcite{nuFact134}{17}
+\bibcite{Meer}{18}
+\bibcite{fluka}{19}
+\bibcite{MARS}{20}
+\bibcite{harp}{21}
+\bibcite{minerva}{22}
+\bibcite{MMWPSGaroby}{23}
+\bibcite{MMWPSCazes}{24}
+\bibcite{FLUKAprivate}{25}
+\bibcite{geant}{26}
+\bibcite{SIMONE1}{27}
+\bibcite{nuFact138}{28}
+\bibcite{donega}{29}
+\bibcite{Gaisser}{30}
+\bibcite{picasso}{31}
+\bibcite{pdg}{32}
+\bibcite{Mezzetto}{33}
+\bibcite{JJG}{34}
+\bibcite{DONINI}{35}
+\bibcite{DONINI-2}{36}
+\bibcite{mosca}{37}
+\bibcite{NUANCE}{38}
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.blg
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.blg	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.blg	(revision 392)
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.log
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.log	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.log	(revision 392)
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+\documentclass{iopart}
+%
+%----------------------------------------------------------------------------
+%
+\usepackage{slashbox}
+\usepackage[T1]{fontenc}
+\usepackage[latin1]{inputenc}
+\usepackage{graphicx}
+\usepackage{epsfig}
+%\usepackage{vmargin}
+%\usepackage{multicol}
+%\usepackage[footnotesize,normal,up]{caption}
+%\usepackage{subeqnarray}
+%\usepackage[francais,american]{babel}
+\usepackage{amssymb}
+%\usepackage{amsmath}
+\usepackage{setstack}
+\usepackage{latexsym}
+
+
+%\newcommand{\beq}[1]{\begin{equation}\label{eq:#1}}
+%\newcommand{\enq}{\end{equation}}
+%\newcommand{\refeq}[1]{\ref{eq:#1}}
+%\newcommand{\biz}{\begin{itemize}}
+%\newcommand{\eiz}{\end{itemize}}
+%\newcommand{\beqa}{\begin{eqnarray}}
+%\newcommand{\enqa}{\end{eqnarray}}
+%\newcommand{\ol}{\overline}
+%\newcommand{\virg}{\mbox{,}}
+%\newcommand{\pt}{\mbox{.}}
+
+
+
+%
+%
+%----------------------------------------------------------------------------
+%----------------------------------------------------------------------------
+%
+
+\begin{document}
+%
+\title{The $\theta_{13}$ and $\delta_{CP}$ sensitivities of the SPL-Fréjus project revisited}
+\author{Jean Eric Campagne, Antoine Cazes}
+\address{ Laboratoire de l'Accélérateur Linéaire -
+Université Paris-Sud - B\^at. 200 - BP 34 -
+91898 Orsay Cedex, France}
+\eads{\mailto{campagne@lal.in2p3.fr}, \mailto{cazes@lal.in2p3.fr}}
+%\date{\today}
+%
+%
+%
+%\selectlanguage{francais}
+%
+\begin{abstract}
+An optimization of the CERN SPL beam line has been performed guided by the sensitivity to the $\theta_{13}$ mixing angle and to the $\delta_{CP}$ Dirac CP violating phase performances. A UNO-like 440 ktons water \v{C}erenkov detector located at 130~km from the target in a new foreseen Fréjus laboratory has been used as a generic detector. Concerning $\theta_{13}$ sensitivity, a gain of about $24\%$ may be reached using a $4.5$~GeV proton beam compared to the up to now considered $2.2$~GeV beam energy. This may motivate new machine developments to upgrade the nominal SPL proton beam energy.
+\end{abstract}
+\pacs{14.60.Pq, 14.60.Lm}
+
+\maketitle
+
+
+\section{Introduction}
+The very near future of the neutrino long baseline experiments is devoted to the study of the oscillation mechanism in the range of $\Delta m^2 = \Delta m^2_{atm} \approx 2.7\,10^{-3}\mathrm{eV}^2$ \cite{SKNU04,K2KNU04} using conventional $\nu_\mu$ beams. The current K2K experiment in Japan \cite{K2KNU04}, and the forthcoming MINOS in the USA \cite{MINOS} take benefit of low energy beam to measure the $\Delta m^2$ parameter using the disappearance mode $\nu_\mu\rightarrow\nu_\mu$, while OPERA/ICARUS experiments \cite{OPERA,ICARUS} using the high energy CNGS beam \cite{CNGS} will be able to detect $\nu_\tau$ appearance. If we do not consider the LSND anomaly \cite{LSND} that will be further studied soon by MiniBooNE experiment \cite{MINIBOONE}, the three flavor family scenario will be confirmed and accommodated by a $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix \cite{PMNS} with three angles ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase $\delta_{CP}$.  
+
+Beyond this medium term plan, two of the next future tasks of neutrino physics are to improve the sensitivity of the last unknown mixing angle parameter, the so-called $\theta_{13}$, and to explore the CP violation mechanism in the leptonic sector. The present upper bound on $\theta_{13}$ is $\sin^22\theta_{13}<0.1$ for large $\Delta m^2$ at $90\%$~CL \cite{CHOOZ}. This sensitivity can be improved using reactor and accelerator experiments. In reactor experiments, one uses $\bar{\nu}_e$ in disappearance mode and may reach $\sin^22\theta_{13}<0.03$ \cite{Wpaper}. In accelerator experiments, one can use $\nu_e$ and $\bar{\nu}_e$ from $\beta$ beams \cite{BETABEAM} in both  disappearance and appearance modes (\textsl{i.e} $\stackrel{\scriptscriptstyle (-)}{\nu}_e\rightarrow \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$), and also $\nu_\mu$ in appearance mode (\textsl{i.e} $\nu_\mu\rightarrow\nu_e$) with conventional beams either with sub-mega watt proton drivers \cite{NOVA,T2K} or with multi-mega watt proton drivers \cite{T2K,BNLHS,CERN}. The later neutrino beam type, called Superbeam, is foreseen to be extended to produce $\nu_\mu$ beam and $\bar{\nu}_\mu$ beam from muon decays, the so-called Neutrino Factory, in order to study the eventual leptonic CP violation. Such Neutrino Complex is under study in Japan, in USA and also in Europe at CERN and details may be found in reference \cite{CERN}. A comparison of the performances of $\beta$ beam and Superbeam may be found for instance in reference \cite{DONINI}.  The reactor experiment result on $\theta_{13}$ is straight forward as compared to Superbeam and Neutrino Factory results that are on one hand reacher but in an other hand more complex to analyse due to the interplay between the different physics factors $\theta_{13}$, $\delta_{CP}$, sign$(\Delta m^2_{23})$, sign$(\tan(2\theta_{23}))$ \cite{DONINI,DOUBLE-CHOOZ}. 
+
+This paper presents results of a new simulation of the SPL (Super Proton Linac) Superbeam that could take place at CERN \cite{SPL}, using for definitiveness a UNO-like 440kT fiducial water \v{C}erenkov detector \cite{UNO} located in a new enlarged underground laboratory under study in the Fréjus tunnel, $130$~km away from CERN \cite{mosca}. The SPL neutrino beam is created by  decays of pions, muons and kaons produced by the interactions of a $4$~MW proton beam impinging a liquid mercury jet \cite{CERN}. Pions, muons and kaons are collected using two concentric electromagnetic lenses (horns), the inner one and the outer one are hereafter called "Horn" and "Reflector" respectively \cite{Meer}. Horns are followed by a decay tunnel where most of the neutrinos are produced. A sketch of the beam line is shown on figure~\ref{fig:Sbeam}.  
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.2]{../picts/cernmeg3_6-02.eps}
+\caption{\label{fig:Sbeam}Sketch of the SPL neutrino Superbeam from CERN to the Fréjus tunnel.}	
+\end{figure}
+
+The analysis chain consists of different stages: the simulation of the interactions between the proton beam and the mercury target, the propagation of the resulting secondary particles through the magnetic field and the materials of the horns, the tracking of $\pi^\pm$, $K^{\pm,0}$ and $\mu^\pm$ until they decay, the computation of the neutrino flux at the detector site, and finally the statistical analysis. A part of the simulation chain has already been described in reference \cite{nuFact134,MMWPSCazes}. 
+
+
+Compared to recent papers on the same subject \cite{DONINI,JJG,Mezzetto}, we have reoptimized the Horn and Reflector shapes \cite{nuFact138}, and introduced the kaon background simulation which allows us to update the SPL beam energy. The organization of this document follows the simulation chain: the interaction between the proton beam and the mercury target is presented in the second section. The kaon production is detailed in the third section. The simulation of the horns is described in the forth section, while the algorithms used to compute the neutrino fluxes are explained in the fifth section. Then, the sensitivities to $\theta_{13}$ and $\delta_{CP}$ are revisited with new studies about the optimization of the proton beam energy, the pion collection and the decay tunnel geometry.
+
+\section{Target simulation}
+\label{sec:target}
+Since hadronic processes are crucial to describe the interactions of the proton beam on the target, the FLUKA simulator \cite{fluka} has been chosen for this first step of the simulation. 
+
+\Table{\label{tab:targ}Liquid mercury jet parameters.}
+    \br
+     \centre{2}{Hg target}\\
+     \mr
+      Hg jet speed & $20$~m/s \\
+      density & $13.546$ \\
+      Length, radius & $30$~cm, $7.5$~mm \\
+      \br
+\endTable
+The target used in the present study is a mercury liquid jet \cite{CERN} simulated by a cylinder $30$~cm long (representing two hadronic lengths) and $1.5$~cm diameter (see table~\ref{tab:targ}). The pencil like simulated proton beam is composed with  $10^6$ mono-energetic protons. The beam axis is also the symmetry axis of the target and the horns and the decay tunnel. Simulations have been performed for $2.2$~GeV proton kinetic energy, the up to now nominal design \cite{SPL}, as well as for $3.5$~GeV, $4.5$~GeV, $6.5$~GeV and $8$~GeV according to possible new designs \cite{MMWPSGaroby}.
+
+
+Particle production yields are summarized in table~\ref{tab:nbPart}. The secondary proton and neutron rates induce important radiation damages and power dissipation in the horns which have been addressed in reference \cite{nuFact134}, and which will require specific R\&D effort. At $2.2$~GeV, kaon yields are very low, but it has a dramatic energy dependence as further studied in section~\ref{sec:kaon}. It is worth to mention that the numbers in table~\ref{tab:nbPart} are not to be taken as face values, because the cross sections of pion and kaon productions using proton beam are still under studies as for instance by the HARP experiment \cite{harp} and in the future by the MINERVA experiment \cite{minerva}.
+
+\fulltable{\label{tab:nbPart}Average number of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA). The $\mu^+/\mu^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}
+\br
+$E_k$ (GeV) & p & n & $\gamma$ & $e^-$ & $e^+$ & $\pi^+$ & $\pi^-$ & $\mu^+$ & $\mu^-$ & $K^+$ & $K^0$ \\
+\mr
+2.2 & $1.4$     &  $17$   & $5.0$  &  $0.17$   &  $0.08$    &  $0.24$   &  $0.18$ & $4$ & $1$ & $7$ & $6$ \\
+
+3.5 &$1.8$    &  $17$  & 7.0  &  0.28   &  0.15    &  0.41   &  0.37 & $10$ & $3$ & $35$ & $30$ \\
+
+$4.5$ &  $2.3$  &  $17$ & $7.7$ &  $0.35$  & $0.21$   &  $0.57$ & $0.39$&  $11$ & $3.3$  &  $93$ &  $68$       \\
+
+$8$   &  $3.1$  &  $17$ & $11.0$ & $0.63$  & $0.41$   &  $1.00$  &  $0.85$ &  $30$ &  $9.5$ &  $413$ &    $340$         \\
+
+\br
+\endfulltable
+
+The cross section uncertainties are the main source of discrepancy between simulator programs. Some comparisons between FLUKA and MARS \cite{MARS} have already been presented in the same context \cite{nuFact134}. The energy distribution of the pions exiting the target, computed with the two simulator programs FLUKA and MARS, is shown on figure~\ref{fig:compFlukaMars}a. Pions come from $\Delta$ decays which in turn are originated from two different sources. At low energy ($P<200$~MeV/c), $\Delta$ are produced by protons of the target excited by the beam interactions, while the highest energy part of the spectrum is due to transformation of protons of the beam into $\Delta$. The discrepancy is quite large for the low energy part. However, the horns are designed to focus the high energy part of the spectrum (see section~\ref{sec:horn}), and therefore, MARS and FLUKA are in better agreement for the energy spectrum computed at the entrance of the decay tunnel (figure~\ref{fig:compFlukaMars}b). So,  the discrepancy  at low energy between MARS and FLUKA does not matter too much for the present application.
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/compMarsFluka.eps}
+\caption{\label{fig:compFlukaMars}Pion momentum distribution at the exit the target (a) and at the exit of the horns (b), simulated by FLUKA (\dashed) and by MARS (\full).}
+\end{figure}
+%
+\section{Kaon production}
+\label{sec:kaon}
+The possibility to increase the SPL energy in order to study the optimization of the physics program has been recently pointed out \cite{MMWPSGaroby}. Then, the kaon production should be clearly addressed because it is a source of $\nu_e$ and $\bar{\nu}_e$ background events. The kaon decay channels and branching ratios are presented in table~\ref{tab:BRKP0SL} in \ref{sec:kaons}.
+
+The target simulation described in section~\ref{sec:target} has been used with $500,000$ p.o.t with kinetic energy uniformly distributed between $2.2$~GeV and $5$~GeV. The momentum of outgoing pions and kaons are recorded when they exit the target. The number of produced $K^{o,\pm}$ at different proton beam energies are presented on figure~\ref{fig:KaonsPions}a. In one hand the $K^o$ production rate is similar to the $K^+$ production rate, but in an other hand the $K^-$ production rate is almost forty times smaller. For comparison, the numbers of $\pi^+$ and $\pi^-$  produced in the same conditions are presented on figure~\ref{fig:KaonsPions}b. Pion production rate is about two orders of magnitude greater than the kaon production rate.
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/KaonProd.eps}
+\caption{\label{fig:KaonsPions}Kaon production (a) as a function of the incident proton beam energy ($E_p$) for $500~000$ incident protons with (\full) curve for $K^+$, (\dashed) curve for $K^-$ and (\dotted) curve for $K^o$. Pion production (b) in the same conditions with (\full) curve for $\pi^+$ and (\dashed) curve for $\pi^-$.}
+\end{figure}
+
+The behavior of the two pion and kaon production rates are quite different. The pion yield grows smoothly with the proton energy while the production of kaons seams to have two origins, which has been confirmed by FLUKA's authors \cite{FLUKAprivate}. For beam energy below approximatively $4$~GeV, the resonance production model is used, and one notices a low production rate with a maximum at about $3.4$~GeV. For beam energy above  $4$~GeV, the dual parton model is used, and the production rate experiences a threshold effect with a rapid rise. The ratio between positive kaon and pion production rates is about $0.5\%$ between $2.2$~GeV and $4$~GeV and grow up to $2.5\%$ at $5$~GeV. One notices that the maching between the two kaon production models may not be optimal.
+%
+\section{Horn simulation}
+\label{sec:horn}
+The simulation code of the electromagnetic horns is written using GEANT 3.2.1 \cite{geant} for convenience and since electromagnetic processes are dominant, FLUKA has not been considered as mandatory, but this may be revised in a future work. The geometry of the horns has been inspired by an existing CERN prototype and a Reflector design proposed in reference \cite{SIMONE1}. Depending of the current injection, only positive secondary particles or negative secondary particles are focused. The relevant parameters are detailed in table~\ref{tab:specif}.
+
+The mercury target is localized inside the Horn because of the low energy and the large emittance of the secondary pions produced: $<P_{\pi T}>/<P_\pi> \approx 240$~MeV$/400$~MeV ($2.2$~GeV proton beam energy). This explains the Horn design (figure~\ref{fig:plan}), with a cylindrical part around the target, called the neck, which is larger than the transversal size of the target to simulate the room for target handling, and a conic part designed such that the relevant pions are focused as much as possible to exit the magnetic field parallel to the beam axis.
+
+\Table{\label{tab:specif}Relevant parameters of horns. The shapes of the conductors are not changed by proton beam energy changes, as the focusing has been optimized for a defined pion momentum.}
+\br
+\centre{2}{inner horn} & \centre{2}{reflector} \\
+\mr
+  neck inner radius & $3.7$~cm              & neck inner radius & $20.3$~cm \\
+  neck length & $40$~cm                     & end cone inner radius & $35.7$~cm \\
+  end cone inner radius & $15.7$~cm         & outer radius & $40$~cm \\
+  outer radius & $20.3$~cm                  & total length & $200$~cm \\
+  total length & $180$~cm                   & Peak current & $600$~kA \\
+  Alu thickness  & $3$~mm                   & Frequency & $50$~Hz \\
+  Peak current & $300$~kA                   & & \\
+  Frequency & $50$~Hz                       & & \\
+\br
+\endTable
+
+The shape of the horns conductors is a crucial point since it determines the energy spectrum of the neutrino at the detector site. The details of the conductor shape optimization for the present context may be found in reference \cite{nuFact138}. We just recall here some ingredients. For a $\theta_{13}$ driven $\nu_\mu \rightarrow \nu_e$ oscillation, a $\Delta m^2_{23}$ parameter value of $2.5\ 10^{-3}\mathrm{eV}^2$, and a baseline distance of $130$~km, the first oscillation maximum occurs for a neutrino energy of $260$~MeV\footnote{If one includes an energy spectral shape of the neutrino beam with a typical $\sigma_E/E \approx 1/3$, then a 10\% increase of the average neutrino energy is expected. But, the induced change on the $\theta_{13}$ sensitivity is negligeable.}. The   optimization of the physics potential depends at first approximation on the pion neutrino characteristics, which energy is fully determined by the pion 2-body decay and boost. To reach an energy of $260$~MeV, the pion needs a $\beta=0.97$, which in turn induces a pion momentum of $600$~MeV/c. Then, the shape of the conic part of the horns is determined such that these $600$~MeV/c pions exit parallel to the beam axis.
+
+\begin{figure}
+\centering
+\includegraphics[width=0.75\textwidth]{../picts/corneSchema.eps}
+\caption{\label{fig:plan}Design of the Horn and the Reflector conductor shapes implemented in the GEANT simulation. The Hg target is located inside the cylindrical part of the Horn.}
+\end{figure}
+
+Before closing this section, it is worth to quote that the Horn/Reflector conductor shapes optimized in the present study to focus a given pion momentum value, is not affected by a proton beam energy change. What is affected is the production rate of the relevant pions. This Horn/Reflector design consideration would be different if one wishes to focus as much as possible all the pions produced for which the mean energy is of course affected by a proton beam energy change.    
+%
+\section{Particle decay treatment and flux calculation}
+%
+The decay tunnel representation is a simple cylinder with variable length ($L_T$) and radius ($R_T$) filled with "vacuum". The base line design is a $20$~m long and $1$~m radius cylinder, but simulations have also been conducted with lengths of $10$~m and $40$~m, and radius of $1.5$~m in the spirit of reference \cite{donega}. In the GEANT simulation, to gain in CPU time, only pions, muons and kaons are tracked in the volume of the tunnel, and all particles exiting this volume are discarded. 
+
+
+Beyond the $1/L^2$ solid angle factor due to the source-detector distance ($L$) which decreases dramatically the fluxes, the neutrino beam focusing is very limited due to the small pion boost factor ($\approx 4$). Therefore, computational algorithms have been used to avoid a too prohibitive CPU time resulting from the simulation of each secondary particle decay. Otherwise, about $10^{15}$ p.o.t would have been necessary to obtain reliable statistics for the estimation of the $\bar{\nu}_e$ flux for instance.
+
+It is worth to mention that the particle decays occurring before the entrance of the decay tunnel are also taken into account and treated in the same manner, which is not the case in reference \cite{donega}. 
+
+\subsection{Algorithm description}
+\label{sec:algo}
+
+The decay code has been included in the GEANT code. The basic idea of this algorithm is to compute the neutrino fluxes using the probability of reaching the detector for each neutrino produced by a $\pi$ or a $K$ or a $\mu$ particle (on-axis neutrino beam). This method has already been used in reference \cite{donega} and has been modified and extended to the kaon decay chain for the present study. 
+
+Muon neutrino comes mostly from pion decay. In a first stage, each pion is tracked by GEANT until it decays. Then, the probability for the produced muon neutrino to reach the detector is computed. The flux is obtained applying the probability as a weight for each neutrino. All the pions produced in the simulation are therefore useful to compute the flux, and this allows to reduce the number of events in the simulation to $10^6$ p.o.t. In this computation, the decay region (horns and tunnel) is considered as point like compared to the source-detector distance. 
+
+The same method is applied for neutrino coming from muons and kaons with some modifications  because most of the muons do not decay, and there are very few kaons produced (see table~\ref{tab:nbPart}).
+The probability computation is presented in \ref{sec:decayprobcomp}. 
+
+\Table{\label{tab:proton}Number of protons on target for different beam energy at 4~MW constant power.}
+\br
+			Beam energy  & number of proton \\
+			  (GeV)      & per year ($10^{23}$ p.o.t/y) \\
+\mr
+			2.2 & 1.10 \\
+			3.5 & 0.70 \\
+			4.5 & 0.56 \\
+			6.5 & 0.40 \\
+			8.0 & 0.30 \\
+\br
+\endTable
+\subsection{Validation of the algorithm}
+The validity of the method presented in the previous section have been tested against a straight forward  algorithm consisting of decaying each pion $N$ times ($N \approx 10^6$) in a full GEANT simulation of the event (decays included). Such method presents the advantage to keep all the information of the neutrino available for further studies. It can be a good approach to compute the muon neutrino flux coming from pion decays. It can also provide the beam profile, but it shows its limits for the muon induced fluxes, especially the $\bar{\nu}_e$ flux. Indeed, this means that each muon is duplicated $N$ times and when a muon decays, it must decay $N$ times again. For $N\approx 10^6$, this is a prohibitive CPU time consuming.
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/compGeantDonega.eps}
+\caption{\label{fig:compGeantDonega}Comparison between the probability method, (\full) curve, and the full GEANT simulation method, (\dashed) curve, for the $\nu_\mu$ from $\pi^+$ flux (left) and the $\bar{\nu}_\mu$ from $\pi^-$ flux  (right). The horns are set to focus positive particles.}
+\end{figure}
+
+The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are displayed on figure~\ref{fig:compGeantDonega} for both methods. The two spectra shows a clear agreement, and this makes confidence on the probability method.
+%
+\subsection{Simulated fluxes}
+The fluxes are computed at a distance of $100$~km from the source by convention and can be rescaled at any desired distance. They provide the number of the four neutrino species ($\nu_\mu$, $\bar{\nu}_\mu$, $\nu_e$, $\bar{\nu}_e$) passing through a $100$~m$^2$ fiducial area during $1$~year.
+
+In practice, the fluxes are given as a function of the neutrino energy via histograms composed of $20$~MeV bin width.  These histograms are filled with the energy of each neutrino weighted by the probability to reach the detector (section~\ref{sec:algo}). To obtain the fluxes, the histograms are rescaled to the number of p.o.t per year depending on the beam energy. Table~\ref{tab:proton} reports on the number of p.o.t per year for the different energies studied using the definition of one year being $10^7$~s and keeping the beam power constant (\textsl{i.e} $4$~MW).
+
+Three origins are identified in the composition of each neutrino flux:
+\begin{itemize}
+	\item neutrinos from pions, which includes neutrinos created by primary pion decays and neutrinos coming from the muons produced by pion decays or muons directly exiting the target. This is the component studied in reference \cite{donega} but with different settings and event generator;
+	\item neutrinos emitted during the decay chain of the charged kaons, either by direct production, or produced by the daughter pions and muons;
+	\item neutrinos coming from the decay chain of the neutral kaons.
+\end{itemize}
+
+The three components of the fluxes for the four neutrino species are presented on figure~\ref{fig:flux22p} for positive particle focusing and a proton beam kinetic energy of $2.2$~GeV. The $\nu_\mu$ flux is dominated by the neutrinos of pion decays, but a tail above $500$~MeV (zoom on the top left part) is created by the $K^+\rightarrow \mu^+\nu_\mu$ channel, which is anyway at least three order of magnitude below the flux maximum. The $\bar{\nu}_\mu$ flux is mostly due to the decays of $\pi^-$ that are not unfocused by the horns, but the higher energy part comes from $\mu^+$ decays. It is noticable that the $\nu_e$ and $\bar{\nu}_e$ fluxes are respectively more than $200$ and more than $7000$ times smaller than the $\nu_\mu$ flux. The $\bar{\nu}_e$ are produced in a large part by the $K^0_L\rightarrow\pi^+e^-\bar{\nu}_e$ decay channel and by $\mu^-$ decays, while the  $\nu_e$ flux is dominated by the $\mu^+$ decays.
+
+On figure~\ref{fig:flux22m}, the horns are set to focus negative particles keeping other parameters identical. By comparison with positive focusing, one can at first approximation translate the results by exchanging particles and anti-particles, except that the $K^+/K^-$ ratio is about 100  in the beam-target interactions (see table~\ref{tab:nbPart}).
+
+On figures~\ref{fig:flux45p} and \ref{fig:flux8p}, one observes the evolution of figure~\ref{fig:flux22p} when the proton beam kinetic energy increases to $4.5$~GeV and $8$~GeV, respectively. Correspondingly, the results for negative particle focusing are presented on figures~\ref{fig:flux45m} and \ref{fig:flux8m}. One clearly notices the increase of the kaon induced neutrino contents as the beam energy grows.
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux22p.eps}
+\caption{	\label{fig:flux22p}Neutrino fluxes $100$~km from the decay region and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$~GeV (4~MW), a decay tunnel with a length of $20$~m and a radius of $1$~m. The (\full) curve is the contribution from primary pions and the daughter muons, the (\dashed) curve is the contribution from the charged kaon decay chain, and the (\dotted) curve is the contribution from the $K^0$ decay chain.}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux22m.eps}
+\caption{\label{fig:flux22m}Same legend as for figure~\ref{fig:flux22p} but the horns are focusing negative particles.}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux45p.eps}
+\caption{\label{fig:flux45p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $4.5$~GeV (4~MW).}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux45m.eps}
+\caption{\label{fig:flux45m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $4.5$~GeV (4~MW).}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux8p.eps}
+\caption{\label{fig:flux8p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux8m.eps}
+\caption{\label{fig:flux8m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure}
+
+\fulltable{\label{tab:speciesfluxes}Integral of the different species fluxes with different settings. The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are expressed in $10^{13}/100\mathrm{m}^2/y$ unit while the $\nu_e$ and $\bar{\nu}_e$ fluxes are expressed in $10^{11}/100\mathrm{m}^2/y$ unit. The positive focusing  and negative focusing  are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. Setting (1) is the baseline option and means $L_T = 20$~m and $R_T = 1$~m, while setting (2) means $L_T = 10$~m and $R_T = 1$~m and setting (3) means $L_T = 40$~m and $R_T = 1$~m, and finally the setting (4) means $L_T = 20$~m and $R_T = 1.5$~m.}
+
+\br
+
+			Settings  & \centre{2}{$\nu_\mu$} & \centre{2}{$\nu_e$} 
+								&	\centre{2}{$\bar{\nu}_\mu$} & \centre{2}{$\bar{\nu}_e$} \\
+								\cline{2-9}
+								& $+$ & $-$ & $+$ & $-$ & $+$ & $-$ 
+								& $+$ & $-$ \\ 
+\mr
+
+(1): $2.2$~GeV  
+	& $7.6$         & $0.4$ 
+	& $3.2$ 				& $0.2$
+	& $0.3$ 				& $5.8$  
+	& $0.1$ 				& $1.6$ \\		  
+
+(1): $3.5$~GeV  
+	& $10.0$          & $0.9$ 
+	& $4.4$           & $0.6$
+	& $0.7$ 					& $8.5$  
+	& $0.3$ 					& $2.2$ \\		  
+
+(1): $4.5$~GeV  
+	& $10.9$          & $1.1$ 
+	& $5.1$           & $1.0$
+	& $0.7$ 					& $6.7$  
+	& $0.4$ 					& $1.8$ \\		  
+
+(1): $6.5$~GeV  
+	& $10.4$          & $1.4$ 
+	& $6.4$           & $2.0$
+	& $1.0$           & $7.1$  
+	& $0.9$ 					& $2.5$ \\	
+
+(1): $8.0$~GeV  
+	& $9.7$          & $1.5$ 
+	& $6.7$           & $2.3$
+	& $1.2$           & $7.1$  
+	& $1.1$ 					& $2.8$ \\
+
+
+(2): $4.5$~GeV  
+	& $7.1$          & $1.0$ 
+	& $2.8$          & $0.9$
+	& $0.5$          & $5.2$  
+	& $0.3$ 				  & $1.1$ \\		  
+
+(3): $4.5$~GeV  
+	& $12.3$          & $1.2$ 
+	& $7.2$           & $1.0$
+	& $0.8$           & $7.5$  
+	& $0.4$ 					& $2.6$ \\	
+
+(4): $4.5$~GeV  
+	& $13.2$          & $1.5$ 
+	& $6.9$           & $1.4$
+	& $0.9$           & $8.1$  
+	& $0.6$  					& $2.7$ \\
+	
+\br
+\endfulltable
+
+On table~\ref{tab:speciesfluxes} are reported the integral of the fluxes when one modifies the decay tunnel length and radius, as well as the beam kinetic energy.  Switching the radius from $1$~m to $1.5$~m has increased the $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes by $20\%$ but also in paralell the $\nu_e$ and $\bar{\nu}_e$ fluxes by $38\%$. Increasing the decay tunnel length from $10$~m up to $40$~m yields an increase of the signal like flux by $75\%$ and also in paralell an increase of the background like flux by a factor $1.7$. Notice that the $\nu_\mu/\bar{\nu}_\mu$ flux ratio is rather insensitive to the decay tunnel length. The feeling that $L_T = 20$~m and $R_T = 1$~m is a good signal over background compromise is confirmed by sensitivity quantitative studies reported in section~\ref{sec:results}.  
+
+Looking at the evolution of $\nu_\mu$ flux with respect to the beam energy, one notices that a maximum is reached around $4.5$~GeV. This is due to the competition between the cross section rise with respect to the energy and the decrease of the number of p.o.t due to the constant SPL power ($4$~MW).
+%
+\section{Sensitivity computation ingredients}
+%
+The sensitivity to $\theta_{13}$ and $\delta_{CP}$ is computed for an $\nu_\mu\rightarrow\nu_e$ appearance experiment. An analysis program described in reference \cite{MEZZETTONUFACT060} has been used for such sensitivity computation. See table~\ref{tab:param} for the default user parameter values used in this paper. We just remind here some key points of the program. 
+
+It is included a full 3-flavors oscillation probability computation with matter effects, but no ambiguities are taken into account. This latest point may be revisited in a future work using reference \cite{DONINI-2}. Concerning the background events, the $\nu_e/\bar{\nu}_e$ from the beam, the $\nu_\mu e^-$ elastic scattering process, the $\pi^o$ production as well as the $\mu/e$ misidentification are taken into account. The cross-sections from the NUANCE program are used \cite{NUANCE}. The systematics error is a user parameter and we have used the $2\%$ value considered as a final goal, but also $5\%$ and $10\%$ \cite{MEZZETTONUFACT060}. The detector considered for definitiveness is similar to the UNO detector, i.e. a $440$~kt fiducial water \v{C}erenkov detector \cite{UNO}. It is located at $L = 130$~km from CERN, in the foreseen new Fréjus laboratory \cite{mosca}. It is worth to mention that if one wants to evaluate the influence of $L$ on the sensitivity, it would mean a re-optimization of the horns for each $L$ envisaged (see section~\ref{sec:horn}).  
+
+\Table{\label{tab:param}Default user parameters used to compute the sensitivity curves \cite{MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masses and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite{KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite{JJG}.}
+\br
+			$\Delta m^2_{12} = 8.2 (0.5)\times 10^{-5}~\mathrm{eV}^2$ & $\sin^22\theta_{12} = 0.82 (9\%)$ \\
+			$\Delta m^2_{23} = 2.5 (0.1)\times 10^{-3}~\mathrm{eV}^2$ & $\sin^22\theta_{23} = 1.0 (1\%)$ \\
+\mr
+		  $L_T = 20$~m & $R_T = 1$~m \\ 
+		  $M=440$~kT   & $\epsilon_{syst}=2\%$ \\
+\br
+\endTable
+
+The running time scenario has been fixed to 5 years focusing positive particles for the $\theta_{13}$ sensitivity studies. This scenario gives comparable $\theta_{13}$ sensitivity than a mixed focusing scenario defined as 2 years focusing positive particles and 8 years focusing negative particles which is more appropriate for $\delta_{CP}$ sensitivity studies.
+%
+\section{Results}
+\label{sec:results}
+The $\theta_{13}$ and $\delta_{CP}$ sensitivities are computed with $\theta_{13} = 0^\circ$ and $\delta_{CP} = 0^\circ$ if not explicitly mentioned. 
+
+Table~\ref{tab:nbvsE} presents the number of signal and background events for a $5$ years positive focusing experiment, but with different beam energy settings. The significance parameter is defined in reference \cite{MEZZETTONUFACT060} as:
+\begin{equation}
+\mathcal{S} = \frac{N^{osc}_{\nu_e}}{\sqrt{N^{osc}_{\nu_e} + N^{beam}_{\nu_e} + N^{oth. bkg} + \left(\left(N^{osc}_{\nu_e}+N^{beam}_{\nu_e}\right)\times\epsilon_{syst}\right)^2}}
+\label{eq:significance}
+\end{equation}
+with $N^{osc}_{\nu_e}$ the number of $\nu_e/\bar{\nu}_e$ events due to $\nu_\mu/\bar{\nu}_\mu$ oscillations, $N^{beam}_{\nu_e}$ the number of background events coming from the $\nu_e/\bar{\nu}_e$ contamination of the beam, $N^{oth. bkg}$ the other kinds of background events and $\epsilon_{syst}$ the systematical factor. One can appreciate that $4.5$~GeV beam energy presents better results and may become the new base line energy.
+%
+
+\Table{\label{tab:nbvsE}Number of events for 5 years positive focusing scenario with default parameters of table~\ref{tab:param}. : $\pi^0$, $\nu_\mu$-elast., $\mu/e$-missId. The significance parameter is defined by equation~\ref{eq:significance}.}
+\br
+
+			 & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\mr
+			non oscillated $\nu_\mu$       & $36917$  & $60969$  & $73202$  & $78024$ & $76068$ \\ 
+			oscillated $\nu_e$             & $31$  & $44$  & $47$  & $44$ & $41$ \\
+			beam $\nu_e$                   & $165$ & $222$ & $241$ & $287$ & $299$ \\
+			other background & $70$  & $104$ & $126$ & $147$ & $152$ \\
+\mr
+			Significance                  &  $1.87$ & $2.18$  & $2.20$  & $1.92$ & $1.74$ \\
+\br
+\endTable
+
+The contours at $90\%$, $95\%$ and $99\%$~CL of the $\theta_{13}$ sensitivity are presented in the $(\sin^22\theta_{13}, \Delta m^2_{23})$ plane on figure~\ref{fig:sensi45} for $4.5$~GeV proton beam kinetic energy. The comparison between the contours at $90\%$~CL with $2.2$~GeV, $3.5$~GeV, $4.5$~GeV and $8$~GeV beam energies is shown on figure~\ref{fig:compSensi}. One notices a better perfomence reached with a $4.5$~GeV energy beam as a confirmation of significance parameter value. But, in fact there is not much visual difference between a sensitivity obtained with $3.5$~GeV and $4.5$~GeV, even if one should keep in mind that kaon production models are different at these two energies (see section~\ref{sec:kaon}). Quantitative studies of the minimum $\sin^22\theta_{13}$ with respect to the kinetic beam energy $E_k(proton)$, and the decay length $L_T$, and the systematics $\epsilon_{syst}$ are presented in tables~\ref{tab:thvsE} and \ref{tab:thvseps}. The influance of the systematical level is presented on figure~\ref{fig:compEpsSyst}.
+%
+\begin{figure}
+\centering
+\includegraphics[scale=0.4]{../picts/sensi45.eps}
+\caption{\label{fig:sensi45}Sensitivity contours obtained with a SPL energy of $4.5$~GeV and default parameters of table~\ref{tab:param}.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[scale=0.4]{../picts/compSensi.eps}
+\caption{\label{fig:compSensi}Comparison of 90\% sensitivity contours obtained with SPL energies of ($2.2$, $3.5$, $4.5$, $8$)~GeV and default parameters of table~\ref{tab:param}.}
+\end{figure}
+
+\Table{\label{tab:thvsE}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for diferent decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$). Other parameters are fixed to default values (table~\ref{tab:param}).}
+\br
+		        & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV  \\
+\mr
+			$10$~m & $1.10$ & $0.96$ & $1.05$ & $1.10$ & $1.20$ \\
+			$20$~m & $1.20$ & $0.96$ & $0.91$ & $1.05$ & $1.15$ \\
+			$40$~m & $1.26$ & $1.00$ & $1.00$ & $1.10$ & $1.20$ \\
+\br
+\endTable
+
+\Table{\label{tab:thvseps}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for different level of systematics ($\epsilon_{syst}$) and kinetic beam energy ($E_k(proton)$). Other parameters are fixed to default values (table~\ref{tab:param}).}
+\br			
+			      & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\mr			
+			$2\%$ & $1.20$ & $0.96$ & $0.91$ & $1.10$ & $1.20$ \\
+			$5\%$ & $1.51$ & $1.26$ & $1.26$ & $1.51$ & $1.66$ \\
+			$10\%$ & $2.40$ & $2.19$ & $2.29$ & $2.75$ & $3.16$ \\
+\br			
+\endTable
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.4]{../picts/compEpsSyst.eps}
+\caption{\label{fig:compEpsSyst}$90\%$ CL sensitivity contours obtained with a SPL energy of $4.5$~GeV and default parameters of table~\ref{tab:param} but for different $\epsilon_{syst}$ values.}
+\end{figure}
+
+There are also variations on the minimum $\sin^22\theta_{13}$ value that may be reached in a $\nu_\mu \rightarrow \nu_e$ experiment which are due to the $\mathrm{sign}(\Delta m^2_{23})$ ambiguity and the $\delta_{CP}$ value. On table~\ref{tab:sign} are presented these kind of variations. Other ambiguities coming from the sign$(\tan(2\theta_{23}))$ ignorance also take place as studied in reference \cite{DONINI}. From figure~9 of this reference, we estimate a 30\% effect on $\sin^2(2\theta_{13})$ sensivity due to these ambiguities.
+
+%\begin{figure}[htb]
+%	\centering
+%		\includegraphics{../picts/compDelta_thVSdm.eps}
+%	\caption{$\theta_{13}$-sensitivity dependence up on the $\delta_CP$ phase obtained for a $4.5$~GeV SPL beam and 5 years running with a positive focusing scenario.}
+%	\label{fig:compDelta_thVSdm}
+%\end{figure}
+ 
+\Table{\label{tab:sign}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for different values of sign$(\Delta m^2_{23})$ and $\delta_{CP}$. Other parameters are fixed to default values (table~\ref{tab:param}).}
+\br
+			    & $-180^\circ$ & $-90^\circ$ & $0^\circ$ & $90^\circ$ & $180^\circ$\\
+\mr
+			$+$ & $1.45$ & $0.43$ & $1.20$ & $11.48$ & $1.45$\\
+			$-$ & $1.45$ & $12.02$& $1.15$ & $0.44$  & $1.45$ \\
+\br
+\endTable
+
+The combined $\sin^22\theta_{13}$ and $\delta_{CP}$ sensitivity is presented on figure~\ref{fig:compDeltaTheta}a for the 5 years positive focusing scenario to appreciate in an other way the above mentioned $\delta_{CP}$ ambiguity. 
+%
+\begin{figure}
+\centering
+\includegraphics[scale=0.4]{../picts/compDeltaTheta.eps}
+\caption{\label{fig:compDeltaTheta}Sensitivity contours obtained with SPL beam energy of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) at $90\%$ CL. Default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}
+\end{figure}
+%
+To improve the $\delta_{CP}$-independent limit on $\sin^22\theta_{13}$, one may envisaged a combination of 2 years with positive focusing and 8 years negative focusing as in references \cite{DONINI,JJG,Mezzetto}. The corresponding combined sensitivity contours are presented in figure~\ref{fig:compDeltaTheta}b. With this kind of mixed focusing scenario, one gets a limit $\sin^22\theta_{13} < 2.4 \times 10^{-3}$ ($90\%$ CL) independently of $\delta_{CP}$ with a $3.5$~GeV kinetic energy beam. Note that with a $2.2$~GeV beam or a $4.5$~GeV beam, one gets $\sin^22\theta_{13} < 2.7 \times 10^{-3}$ which is just a bit worse, but it is better than the limit of $\sin^22\theta_{13} < 3.2 \times 10^{-3}$ that may be reached with a $8$~GeV beam.
+%
+\section{Summary and outlook}
+A complete chain of simulation has been set up for the SPL-Fréjus project. The neutrino production has been extended to the kaon decay contribution, which is important to test SPL energy scenario above $2.2$~GeV.
+
+The beam line optimization has been performed using the sensitivity to $\sin^22\theta_{13}$. The shape of the focusing system has been updated and we have confirmed that the decay tunnel parameters $20$~m long and $1$~m radius may still be conserved as baseline values. 
+
+With a $4.5$~GeV SPL energy beam, in 5 years of focusing positive particles, one can reach a minimum value of $\sin^22\theta_{13} = 9.1\times 10^{-4}$ ($90\%$ CL, $\delta_{CP} = 0$) and realizes a $24\%$ gain compared to the up to now nominal $2.2$~GeV SPL energy beam. This may be the sign that a $4.5$~GeV SPL beam energy design is to be investigated from the machine development implication point of view. If one includes  a mixed focusing scenario to explore the ($\sin^22\theta_{13}$,$\delta_{CP}$) sensitivity, then their is no much difference between the $\delta_{CP}$-independant $\sin^22\theta_{13}$ minimum value that may be reached with a $2.2$~GeV energy beam and a $4.5$~GeV energy beam.
+
+The authors think that the present study may be extended in two directions. The beam line simulation part may be performed with a single simulator as FLUKA (or GEANT4 \cite{GEANT4} for comparison). The sensitivity analysis may be deeper investigated using the complete set of possible ambiguities as in reference \cite{DONINI}, and the $\theta_{13}$ or $\delta_{CP}$ measurement accuracy with new beam energy scenario may be investigated too.    
+%
+\ack
+The authors would like to thank M.~Mezzetto to have expressed his interest at early stage of this work and to have provided us his sensitivity computation program. Also the authors thank S.~Gilardoni for fruitful discussions.
+%
+\appendix
+\setcounter{section}{1}
+\section{Decay probability computations}
+\label{sec:decayprobcomp}
+This appendix contains the probability formulas and the algorithms used in the flux computation (see section~\ref{sec:algo}).
+
+\subsection{Pion neutrino probability computation}
+\label{sec:Ppi}
+Pions decay only as $\pi^+\rightarrow \mu^+ + \nu_\mu$ or $\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$ and the neutrinos are emitted isotropically in the pion rest frame, with an energy of about $30$~MeV given by the 2-body decay kinematics. Applying a Lorentz boost knowing the pion momentum and direction, it is possible to compute the probability to reach the detector for the neutrinos. Only neutrino parallel to the beam axis are supposed to pass through the detector fiducial area, and therefore, the neutrino must be emitted by the pion with an angle opposite to the angle between the pion and the beam axis (see figure~\ref{fig:pionDecay}). This gives:
+\begin{equation}
+\mathcal{P}_\pi = \frac{1}{4\pi}\frac{A}{L^2}\frac{1-\beta^2}{(\beta\cos\alpha-1)^2}
+\label{probaPi}
+\end{equation}
+where $\beta$ is the velocity of the pion in the tunnel frame, $A$ is the fiducial detector surface, $L$ the distance between the neutrino source and the detector, and $\alpha$ the angle between the pion direction and the beam axis in the laboratory frame.
+
+\begin{figure}
+\centering
+\includegraphics{../picts/pionDecay.eps}
+\caption{\label{fig:pionDecay}Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha$ is needed.}
+\end{figure}
+
+\subsection{Muon neutrino probability computation}
+\label{sec:Pmu}
+Muons decay only as $\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_\mu$ or $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$, and will produce background events. The mean decay length of the muons is $2$~km, therefore, most of them do not decay in the tunnel. This induces a lake of statistics to estimate the corresponding level of background. This problem has been solved using each muon appearing in the simulation in the following steps:
+\begin{enumerate}
+	\item the probability for the muon to decay into the tunnel has been computed using a straight line propagation;
+	\item the available energy for the neutrino in the tunnel frame has been divided in $20$~MeV energy bins; 
+	% (the number of bin depending of the muon energy).
+	\item one $\nu_e$ and one $\nu_\mu$ have been simulated in each of the energy bins (step 2). Then, the probability to reach the detector has been computed, and multiplied by the probability computed at step 1.%the neutrino energy is stored in an histogram, weighted with this probability and 
+\end{enumerate}
+After the probability computation, the non useful muon is discarded by GEANT to gain in CPU time. 
+
+The probability for the muon neutrino and the electron neutrino to be emitted parallel to the beam axis is \cite{donega}:
+\begin{equation}
+\fl \frac{d\mathcal{P}_\mu}{dE_\nu} = \frac{1}{4\pi}\frac{A}{L^2}\frac{2}{m_\mu}\frac{1}{\gamma_\mu(1+\beta_\mu\cos\theta^*)}\frac{1-\beta_\mu^2}{(\beta_\mu\cos\rho-1)^2}\left[f_0(x)\mp \Pi_\mu^T f_1(x)\cos\theta^*\right]
+\label{probaMu}
+\end{equation}
+where $\beta_\mu$ and $\gamma_\mu$ are the velocity and the Lorentz boost of the muon in the tunnel frame, $\theta^*$ is the angle with respect to the beam axis of the muon in the muon rest frame, $\rho$ is the corresponding angle in the tunnel frame. Like in the pion case, this angle appears because the neutrino must be parallel to the beam axis. $\Pi_\mu^T$ is the muon transverse polarization, the parameter $x$ is defined as $x=2E_\nu^*/m_\mu$ where $E_\nu^*$ is the neutrino energy in the muon rest frame, and the function $f_0(x)$ and $f_1(x)$ coming from the matrix element of the muon decay are given in table~\ref{tab:Function}. The sign in front of $\Pi_\mu^T$ in equation~\ref{probaMu} is $(-)$ for the $\nu_\mu$ and $(+)$ for the $\bar{\nu}_\mu$, respectively.
+
+\Table{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+\br
+		      &  $f_0(x)$ & $f_1(x)$ \\
+\mr
+		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+\br
+\endTable
+
+Muon polarization is computed using the conservation of the transverse component of the velocity four-vector $\gamma(1,\beta)$ between the muon rest frame (where the polarization is computed) and the pion rest frame, where the muon helicity is $-1$, due to the parity non conservation. It yields \cite{picasso}:
+\begin{equation}
+\Pi_\mu^T = \frac{\gamma_\pi\beta_\pi}{\gamma_\mu\beta_\mu}\sin\theta^*
+%\mbox{ and }\Pi_\mu^L = \sqrt{1-\Pi_\mu^{T2}}\virg 
+\label{pola}
+\end{equation}
+where $\gamma_\pi$, $\beta_\pi$, $\gamma_\mu$, and $\beta_\mu$ are the Lorentz boost and velocity of the pion and of the muon in the tunnel frame, and $\theta^*$ the angle with respect to the beam axis of the muon in the pion rest frame.
+
+\subsection{The treatment of the kaons}
+\label{sec:kaons}
+Contrary to pions and muons, kaons have many decay channels. They are summarized in table~\ref{tab:BRKP0SL}.
+
+\Table{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+\br
+\centre{2}{$K^\pm$}         & \centre{2}{$K^0_L$}     & \centre{2}{$K^0_S$}\\
+\mr
+$\mu^\pm\nu_\mu$ & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+$\pi^\pm\pi^0$ & $21.17\%$   & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+$\pi^\pm\pi^+\pi^-$ & $5.59\%$ & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+$e^\pm\nu_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+$\mu^\pm\nu_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+$\pi^\pm\pi^0\pi^0$ & $1.73\%$ & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+\br
+\endTable
+
+There is a very small amount of kaons produced (section~\ref{sec:algo}), and this number has been artificially increased in order to obtain statistically satisfactory results.  The multiplicity of decay channels makes impossible the method used for the muon case (\ref{sec:Pmu}). The method chosen for the good compromise between the gain in CPU and the statistical uncertaincy of the results, is to duplicate 300 times each kaon exiting the target. 
+
+All the kaons daughter particles are tracked by GEANT until they decay. Three different types of daughter particles are identified in the kaon decays. The first type corresponds to primary neutrinos, the second type concerns charged pions and muons, and the neutral pions are left for the last type.
+
+In the $K^\pm\rightarrow\mu^\pm \nu_\mu(\bar{\nu}_\mu)$ decay modes, the computation of the probability for a neutrino to reach the detector is the same than the 2-body decay formula used to in the pion decay (equation~\ref{probaPi}), where $\beta$ is now the kaon velocity, and $\alpha$ the angle of the kaon with respect to the beam axis. 
+
+When a neutrino is produced by a kaon 3-body decay, the probability to reach the detector is computed using a pure phase space formula. It yields:
+\begin{equation}
+\mathcal{P}_K = \frac{1}{4\pi}\frac{A}{L^2}\frac{1}{m_K-m_\pi-m_l}\frac{1}{\gamma_K(1+\beta_K\cos\theta^*)}\frac{1-\beta_K^2}{(\beta_K\cos\delta-1)^2}
+\label{probaL}
+\end{equation}
+where $m_K$ is the kaon mass (charged or neutral), $m_\pi$ is the pion mass ($\pi^0$ mass in $K^\pm$ decays and $\pi^\pm$ mass in $K_L^0$ decays), and $m_l$ is the mass of the lepton associated with the neutrino. The $\beta_K$ and $\gamma_K$ are the velocity and the Lorentz boost of the kaon, $\theta^*$ is the angle between the neutrino direction and the kaon direction, in the kaon rest frame. Finally, $\delta$ is the angle between the kaon direction and the beam axis in the tunnel frame.
+
+When a $\pi^\pm$ is produced in the kaon decay chain, it is tracked by GEANT until it decays, and the probability of equation~\ref{probaPi} is applied to the produced neutrino. In case of a muon, it is treated as explained in \ref{sec:Pmu}. The muon polarization is computed this time using the kaon decay informations. Finally, when a $\pi^0$ is produced, as it cannot create neutrinos, it is simply discarded.
+
+%
+\section*{References}
+\begin{thebibliography}{99}
+%
+\bibitem{SKNU04}
+Kearns E [SuperKamiokande Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+
+\bibitem{K2KNU04}
+Nakaya T [K2K Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+
+\bibitem{MINOS}
+Thomson T [MINOS Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement) \\
+Adamson P \etal NuMi-L-337
+
+\bibitem{OPERA}
+Autiero D [OPERA Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)\\
+Guler M \etal \textsl{ Experiment proposal} CERN/SPSC 2000-028 SPSC/P318 LNGS P25/2000 
+
+\bibitem{ICARUS}
+Guler M \etal [ICARUS Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement) \\
+Aprili P \etal CERN-SPSC-2002-027
+
+\bibitem{CNGS}
+Acquistapace G \etal CERN-98-02
+
+\bibitem{LSND}
+Athanassopoulos A \etal [LSND Collaboration] 1998 \PRL {\bf 81} 1774\\
+Aguilar A \etal [LSND Collaboration] 2001 \PR D {\bf 64} 112007
+
+\bibitem{MINIBOONE}
+Stancu I \etal [MiniBooNE Collaboration] FERMILAB-TM-2207
+
+\bibitem{PMNS}
+Pontecorvo B  1957 \textsl{Sov. Phys.--JETP} {\bf 6} 429 [1957 \textsl{Zh. Eksp. Teor. Fiz.} \textbf{33} 549]\\
+Maki Z, Nakagawa M and Sakata S 1962 \textsl{Prog. Theor. Phys.} \textbf{28} 870\\
+Pontecorvo B 1968 \textsl{Sov. Phys.--JETP} \textbf{26}  984 [1967 \textsl{Zh. Eksp. Teor. Fiz.} \textbf{53} 1717]\\
+Gribov V N and Pontecorvo B 1969 \PL B \textbf{28} 493
+
+\bibitem{CHOOZ}
+Apollonio M \etal  [CHOOZ Collaboration] 1999 \PL B {\bf 466} 415\\
+Apollonio M \etal  [CHOOZ Collaboration] 2003 \EJP C {\bf 27}  331
+
+\bibitem{Wpaper}
+Anderson K \etal 2004 \textsl{White paper report on using nuclear reactors to search for a value of $\theta_{13}$} http://www.hep.anl.gov/minos/reactor13/reactor13.pdf
+
+\bibitem{BETABEAM}
+Zucchelli P 2002 \PL B \textbf{532} 166
+
+\bibitem{NOVA}
+Ambats I \etal 2004 NO$\nu$A proposal FNAL P929
+
+\bibitem{T2K}
+Itow Y 2001 KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05\\
+see also arXiv:hep-ex/0106019
+
+\bibitem{BNLHS}
+Diwan M V 2003 \PR D {\bf 68} 012002
+
+\bibitem{CERN}
+Blondel A \etal CERN-2004-002
+
+\bibitem{DONINI}
+Donini A \etal 2004 IFT-UAM/CSIC-04-30\\
+see also arXiv:hep-ph/0406132.
+
+\bibitem{DOUBLE-CHOOZ}
+Dalnoki-Veress F for the Double-CHOOZ project arXiv:hep-ex/0406070
+
+\bibitem{SPL}
+Autin B \etal CERN-2000-12
+
+\bibitem{UNO} 
+The UNO whitepaper \textsl{Physics Potential and Feasibility of UNO} (preprint SBHEP01-3) (see also http://ale.physics.sunysb.edu/uno/)
+
+\bibitem{mosca}
+Mosca L 2004 Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Meer}
+van der Meer S 1961 CERN-Report No 61-7
+
+\bibitem{nuFact134} 
+Campagne J E and Cazes A 2003 CERN-NUFACT-Note-134\\ http://slac.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+
+\bibitem{MMWPSCazes} 
+Campagne J E and Cazes 2004 Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 \\
+http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{JJG}
+G\'omez Gadenas J J \etal 2001 IFIC/01-31 \\
+see also arXiv:hep-ph/0105297
+
+\bibitem{Mezzetto}
+Mezzetto M 2003 \jpg {\bf 29} 1781-1784\\
+see also arXiv:hep-ex/0302005
+
+
+\bibitem{nuFact138} 
+Campagne J E 2004 CERN-NUFACT-Note-138\\
+ http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+
+\bibitem{fluka}
+Fasso A \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, Kling A \etal - eds., Springer-Verlag Berlin, p159-164 (2001);\\
+Fasso A \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, Kling A \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+
+\bibitem{MMWPSGaroby} 
+Garoby R 2004 Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{harp}
+Catanesi C \etal [HARP Collaboration] CERN-SPSC 2002/019
+
+\bibitem{minerva} 
+Drakoulakos D \etal [Minerva Collaboration] Fermilab P-938\\
+see also arXiv:hep-ex/405002
+
+\bibitem{MARS}
+Mokhov N V \etal 1995 The MARS Code System User Guide, Version 13(95), Fermilab-FN-628 \\
+Mokhov N V \etal 1998 MARS oed Develepments; LANL Report LA-UR-98-5716, nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+
+\bibitem{FLUKAprivate}
+Battistoni G and Ferrari A \textsl{private communication}
+
+\bibitem{geant}
+Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+
+\bibitem{SIMONE1}
+Gilardoni S 2003 Talk at NuFact03 http://www.cap.bnl.gov/nufact03/
+
+\bibitem{donega}
+Blondel A \etal 2001 CERN-NUFACT-Note-78\\
+ http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+
+\bibitem{DONINI-2}
+Donini A, Meloni D and Rigolin S 2004 J. High Energy Phys. \textbf{0406} 011\\
+see also arXiv:hep-ph/0312072
+
+\bibitem{NUANCE}
+Casper D  2002\textsl{ Nucl. Phys. Proc. Suppl.} \textbf{112} 161-170\\
+see also arXiv:hep-ph/0208030
+
+\bibitem{MEZZETTONUFACT060}
+Mezzetto M 2000 CERN-NUFACT-Note-60\\
+ http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+
+
+\bibitem{KAMLAND}
+Gratta G [KamLAND Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+
+\bibitem{Gaisser}
+Gaisser T K 1990 \textsl{Cosmic Rays and Particle Physics} Cambridge University Press 
+
+\bibitem{picasso}
+Combley F and Picasso E 1974 \textsl{Phys. Rept.} {\bf 14} 1
+
+\bibitem{pdg}
+Hagiwara K \etal 2002 \PR D {\bf 66}  010001
+
+\bibitem{GEANT4}
+Agostinelli A \etal [GEANT4 Collaboration] 2003 \NIM A \textbf{506} 250-503
+\end{thebibliography}
+
+
+
+
+
+
+
+\end{document}
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/SPLFrejus.tps
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+\begin{document}
+%
+% mefiance : le begin{document} fait bien des choses...
+%
+% \def\figurename{\textrm{Figure}}%
+% \def\tablename{\textrm{Table}}%
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+%\selectlanguage{francais} 
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+%
+%%
+% Titre et resume...
+%
+\title{The $\theta_{13}$ sensitivity of the SPL-Fréjus project revisited}
+\author{Jean Eric Campagne, Antoine Cazes\\
+~\\
+Laboratoire de l'Accélérateur Lineaire\\
+Université Paris-Sud - B\^at. 200 - BP 34\\
+91898 Orsay Cedex	}
+\date{\today}
+%
+\maketitle
+%
+%
+%\selectlanguage{francais}
+%
+\begin{abstract}
+  \medskip 
+
+  One of the possible tool for the search of $\theta_{13}$ is a conventional neutrino beam with a high intensity. There is a project of such a beam at CERN using the Super Proton Linac with a 4~MW beam intensity. The presented posted described the simulation of the beam as well as the computation of the neutrino flux at the Fréjus laboratory. Sensitivity is computed for the nominal energy of the SPL ($2.2$~GeV) and the gain in sensitivity is shown in the case of an increase of the SPL energy up to $8$~GeV.
+  
+\end{abstract}
+
+\section{Introduction}
+The very near future of the neutrino long baseline experiments is devoted to the study of the oscillation mechanism in the range of $\Delta m^2 = \Delta m^2_{atm} \approx 2.7\,10^{-3}\mathrm{eV}^2$ \cite{SKNU04,K2KNU04} using conventional $\nu_\mu$ beams. The current K2K experiment in Japan \cite{K2KNU04}, and the forthcoming MINOS in the USA \cite{MINOS} takes benefit of low energy beam to measure the $\Delta m^2$ using the disappearance mode $\nu_\mu\rightarrow\nu_\mu$, while OPERA/ICARUS experiments \cite{OPERA,ICARUS} using the high energy CNGS beam \cite{CNGS} will be able to detect $\nu_\tau$ appearance. If we do not consider the LSND anomaly \cite{LSND} that will be further studied soon by MiniBooNE experiment \cite{MINIBOONE}, the three flavor family scenario will be confirmed and accommodated by a $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix \cite{PMNS} with three angles ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase $\delta_{CP}$.  
+
+Beyond this medium term plan, two of the next future tasks of neutrino physics are to improve the sensitivity of the last unknown mixing angle parameter, the so-called $\theta_{13}$, and to explore the CP violation mechanism in the leptonic sector. The present upper bound on $\theta_{13}$ is $\sin^22\theta_{13}<0.1$ for large $\Delta m^2$ at $90\%$~CL \cite{CHOOZ}. This sensitivity can be improved using reactor experiments in a $\bar{\nu}_e$ disappearance mode ($\sin^22\theta_{13}<0.03$) \cite{Wpaper}, and conventionnal high intensity $\nu_\mu$ beams, called Superbeam, by using the potentiality of $\nu_\mu\rightarrow\nu_e$ oscillations in the appearance mode. Ultimately, Superbeam facilities are foreseen to be extended to produce $\nu_\mu$ beams and $\bar{\nu}_\mu$ beams from muon decays, the so-called Neutrino Factory, in order to study the eventual leptonic CP violation. One of such Neutrino Complex is under study at CERN and details may be found in reference \cite{CERN}. The reactor experiment result on $\theta_{13}$ is straight forward as compared to Superbeam and Neutrino Factory results that are on one hand reacher but in an other hand more complicated to analyse due to the interplay between the different physics factors as for instance $\theta_{13}$, $\delta_{CP}$, sign$(\Delta m^2_{23})$, sign$\tan(2\theta_{23})$ \cite{DOUBLE-CHOOZ}. 
+
+This paper presents results of a new simulation of the SPL (Super Proton Linac) Superbeam that could take place at CERN \cite{SPL}, using for definitiveness a UNO-like 440kT fiducial water \v{C}erenkov detector \cite{UNO} located in a new enlarged underground laboratory under study in the Fréjus tunnel, $130$~km away from CERN \cite{mosca}. The SPL neutrino beam is created by  decays of pions, muons and kaons produced by the interactions of a $4$~MW proton beam impinging a liquid mercury jet \cite{CERN}. Pions, muons and kaons are collected using two concentric electromagnetic lenses (horns), the inner one and the outer one are hereafter called "Horn" and "Reflector" respectively \cite{Meer}. Horns are followed by a decay tunnel where most of the neutrinos are produced. A sketch of the beam line is shown on Fig.~\ref{fig:Sbeam}.  
+
+\begin{figure}[htb]
+	\centering
+		\includegraphics[scale=0.4]{../picts/cernmeg3_6-02.eps}
+	\caption{Sketch of the SPL neutrino Superbeam from CERN to the Fréjus tunnel.}
+	\label{fig:Sbeam}
+\end{figure}
+
+The analysis chain consists of different stages: the simulation of the interactions between the proton beam and the mercury target, the propagation of the resulting secondary particles through the magnetic field and the materials of the horns, the tracking of the $\pi^\pm$, $K^{\pm,0}$ and $\mu^\pm$ particles until they decay in the tunnel, the computation of the neutrino flux at the detector site, and finally the $\theta_{13}$ statistical analysis. A part of the simulation chain has already been described in reference \cite{nuFact134,MMWPSCazes}. 
+
+
+Compared to recent papers on the same subject \cite{JJG,Mezzetto,DONINI}, we have reoptimized the Horn and Reflector shapes \cite{nuFact138}, and introduced the kaon background simulation which allows us to update the SPL beam energy. The organization of this document follows the simulation chain: the interaction between the proton beam and the mercury target is presented in the second section. The kaon production is detailed in the third section. The simulation of the horns is described in the forth section, while the algorithms used to compute the neutrino fluxes are explained in the fifth section. Then, the sensitivities to $\theta_{13}$ and $\delta_{CP}$ are revisited with new studies about the optimization of the proton beam energy, the pion collection, the decay tunnel geometry.
+
+\section{Target simulation}
+\label{sec:target}
+Since hadronic processes are crucial to describe the interactions of the proton beam on the target, the FLUKA simulator \cite{fluka} has been chosen for this first step of the simulation. 
+
+\begin{table}[htb]
+	\centering
+		\begin{tabular}{|l|c|}
+    \hline
+     \multicolumn{2}{|c|}{Hg target}\\
+     \hline
+%  Materials & Liquid Hg jet \\
+      Hg jet speed & $20~m/s$ \\
+      density & $13.546$ \\
+      Length, radius & $30~cm\mbox{, }7.5~mm$ \\
+      \hline			
+		  \end{tabular}
+	\caption{Liquid mercury jet parameter}
+	\label{tab:targ}
+\end{table}
+
+The target used in the present study is a mercury liquid jet \cite{CERN} simulated by a cylinder $30$~cm long (representing two hadronic lengths) and $1.5$~cm diameter (see Tab.~\ref{tab:targ}). The pencil like simulated proton beam is composed with  $10^6$ mono energetic protons, and the beam axis is also the symmetry axis of the target, and the horns, and the decay tunnel. Simulations have been performed for $2.2$~GeV proton kinetic energy, the up to now nominal design \cite{SPL}, as well as for $3.5$~GeV, $4.5$~GeV, $6.5$~GeV and $8$~GeV according to possible new designs \cite{MMWPSGaroby}.
+
+\bet{|c||c|c|c|c|c|c|c|c|c|c|c|}
+\hline
+$E_k$ (GeV) & p & n & $\gamma$ & $e^-$ & $e^+$ & $\pi^+$ & $\pi^-$ & $\mu^+$ & $\mu^-$ & $K^+$ & $K^0$ \\
+\hline
+\hline
+2.2 & $1.4$     &  $17$   & $5.0$  &  $0.17$   &  $0.08$    &  $0.24$   &  $0.18$ & $4.~10^{-4}$ & $1.~10^{-4}$ & $7.~10^{-4}$ & $6.~10^{-4}$ \\
+\hline
+3.5 &$1.8$    &  $17$  & 7.0  &  0.28   &  0.15    &  0.41   &  0.37 & $10.~10^{-4}$ & $3.~10^{-4}$ & $35.~10^{-4}$ & $30.~10^{-4}$ \\
+\hline
+$4.5$ &  $2.3$  &  $17$ & $7.7$ &  $0.35$  & $0.21$   &  $0.57$ & $0.39$&  $11.~10^{-4}$ & $3.3~10^{-4}$  &  $93.~10^{-4}$ &  $68.~10^{-4}$       \\
+\hline
+$8$   &  $3.1$  &  $17$ & $11$ & $0.63$  & $0.41$   &  $1.0$  &  $0.85$ &  $30.~10^{-4}$ &  $9.5~10^{-4}$ &  $413.~10^{-4}$ &    $340.~10^{-4}$         \\
+\hline
+\ent{Average number of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA). Note that the $K^-$ are at the level of $10^{-5}$ per proton.}{nbPart}
+
+Particle production yields are summarized in Tab.~\ref{tab:nbPart}. The level of the secondary proton and neutron emissions induces important radiation damages and power dissipation problems on the horns which have been addressed in reference \cite{nuFact134}, and which will require specific R\&D effort \cite{nuFact134}. At $2.2$~GeV, kaon yields are very low, but it has a dramatic energy dependence as further studied in Sec.~\ref{sec:kaon}. It is worth to mention that the numbers in Tab.~\ref{tab:nbPart} are not to be taken at face value, because the cross sections of pion and kaon productions using proton beam are still under studies as for instance by the HARP experiment \cite{harp} and in the future by the MINERVA experiment \cite{minerva}.
+
+The cross section uncertainties are the main source of discrepancy between simulator programs. Some comparisons between FLUKA and MARS \cite{MARS} have allready been presented in the same context \cite{nuFact134}. The energy distribution of the pions exiting the target, computed with the two simulator programs (FLUKA in blue dashed line and MARS in red full line), is shown on Fig.~\ref{fig:comp1}. Pions come from $\Delta$ decays which in turn are originated from two different sources. At low energy ($P<200$~MeV/c), $\Delta$ are produced by protons of the target excited by the beam interactions, while the highest energy part of the spectrum is due to transformation of protons of the beam into $\Delta$. The discrepancy is quite large for the low energy part. However, MARS and FLUKA are in better agreement for the energy spectrum computed at the entrance of the decay tunnel (Fig.~\ref{fig:comp2}). Moreover, the horns are designed to focus the high energy part of the spectrum (see Sec.~\ref{sec:horn}), and therefore, the discrepancy  at low energy between MARS and FLUKA does not matter too much for the present application.
+
+\DBLFIG{ht}{compMARSmom_NB}{Momentum distribution of the pion exiting the target simulated by FLUKA (in blue dashed line) and by MARS (in red full line).}{comp1}{compCorneMARS_NB}{Same as figure \ref{fig:comp1} but after pions have been tracked through the magnetic fields of the horns.}{comp2}
+%
+\section{Kaon production}
+\label{sec:kaon}
+
+The possibility to increase the SPL energy in order to study the optimization of the physics program has been recently pointed out \cite{MMWPSGaroby}. Then, the kaon production should be clearly addressed because it is a source of $\nu_e$ and $\bar{\nu}_e$ background events. The kaon decay channels and branching ratios are presented in Tabs.~\ref{tab:BRkp}, \ref{tab:BRk0S} and \ref{tab:BRk0L} in appendix~\ref{sec:kaons}.
+
+The target simulation described in Sec.~\ref{sec:target} has been used with $500,000$ p.o.t with kinetic energy uniformly distributed between $2.2$~GeV and $5$~GeV. The momentum of outgoing pions and kaons are recorded when they exit the target. Numbers of produced $K^+$ at different proton beam energies are presented on Fig.~\ref{fig:kaons}. Numbers of $K^-$ is also plotted on the same figure (dashed line) but they are almost 40 times less numerous than the $K^+$. For comparison,  the numbers of $\pi^+$ (solid line) and $\pi^-$ (dashed line) produced in the same conditions are presented on Fig.~\ref{fig:pions}. Pion production rate is about two orders of magnitude greater than the kaon production rate.
+% ET LES KO???? J.E 25/7/04
+\DBLFIG{h}{kaons}{kaon production as a function of the incident proton beam energy for $500~000$ incident protons}{kaons}{piplus}{Same as figure \ref{fig:kaons} for the $\pi^\pm$ production}{pions}
+
+The behavior of the two pion and kaon production rates are quite different. The pion yield grows smoothly with the proton energy while the production of kaons seams to have two origins, which has been confirmed by FLUKA's authors \cite{FLUKAprivate}. For beam energy below approximatively $4$~GeV, the resonance production model is used, and one notices a low production rate with a maximum at about $3.4$~GeV. For beam energy above  $4$~GeV, the dual parton model is used, and the production rate experience a threshold effect with a rapid rise. The ratio between positive kaon and pion production rates is about $0.5\%$ between $2.2$~GeV and $4$~GeV and grow up to $2.5\%$ at $5$~GeV. One notices that the maching between the two kaon production models may not be optimal.
+%
+\section{Horn simulation}
+\label{sec:horn}
+The simulation code of the electromagnetic horns is written using GEANT 3.2.1 \cite{geant} for convenience and since electromagnetic processes are dominant, FLUKA has not been considered as mandatory, but this may be revised in a future work. The geometry of the horns has been inspired by an existing CERN prototype and a reflector design proposed in reference \cite{SIMONE1}. Depending of the current injection, only positive secondary particles or negative secondary particles are focused. The relevant parameters are detailed in Tab.~\ref{tab:specif}.
+
+\begin{figure}[htb]
+	\centering
+		\includegraphics[width=0.75\textwidth]{../picts/corneSchema.eps}
+	\caption{Design of the Horn (in blue) and the Reflector (in red). The target is located inside the cylindrical part of the Horn (in grey).}
+	\label{fig:plan}
+\end{figure}
+
+%\FIG{corne}{}{fig:plan}{9}
+
+The mercury target is localized inside the Horn because of the low energy and the large emittance of the secondary pions produced: $<P_{\pi T}>/<P_\pi>=240$~MeV$/400$~MeV. This explains the Horn design (Fig.~\ref{fig:plan}), with a cylindrical part around the target, called the neck, which is larger than the transversal size of the target to simulate the room for a cooling system, and a conic part designed such that the relevant pions are focused as much as possible to exit the magnetic field parallel to the beam axis.
+\begin{table}[ht]
+\begin{center}
+\begin{sloppypar}
+\parbox{8.0cm}{
+\begin{center}
+  \begin{tabular}{|l|c|}
+  \hline
+  \multicolumn{2}{|c|}{inner horn}\\
+  \hline
+  neck inner radius & $3.7$~cm \\
+  neck length & $40$~cm \\
+  end cone inner radius & $15.7$~cm \\
+  outer radius & $20.3$~cm \\
+  total length & $180$~cm \\
+  Alu thickness  & $3$~mm \\
+  %cooling water thickness & $2~mm$ \\
+  %double skin thickness & $2~mm$ \\
+  Peak current & $300$~kA \\
+  Frequency & $50$~Hz \\
+  \hline
+  \end{tabular}
+\end{center} }
+%\hspace{0.5cm}
+\parbox{8.0cm}{
+\begin{center}
+  \begin{tabular}{|l|c|}
+  \hline
+  \multicolumn{2}{|c|}{reflector}\\
+  \hline
+  neck inner radius & $20.3$~cm \\
+  end cone inner radius & $35.7$~cm \\
+  outer radius & $40$~cm \\
+  total length & $200$~cm \\
+  Peak current & $600$~kA \\
+  Frequency & $50$~Hz \\
+  \hline
+  \end{tabular}
+\end{center} }
+\end{sloppypar}
+\caption{Relevant parameters of horns. The shapes of the conductors are not changed by proton beam energy changes, as the focusing has been optimized for a defined pion momentum.}
+\label{tab:specif}
+\end{center}
+\end{table}
+
+%\subsection{Study of the horns designs in function of the energy}
+
+The shape of the horns conductors is a crucial point since it determines the energy spectrum of the neutrino at the detector site. For a $\theta_{13}$ driven oscillation $\nu_\mu \rightarrow \nu_e$, a $\Delta m^2_{23}$ parameter value of $2.5\ 10^{-3}\mathrm{eV}^2$, and a baseline distance of $130$~km, the first oscillation maximum occurs for a neutrino energy of $260$~MeV\footnote{If one includes an energy spectral shape of the neutrino beam with a typical $\sigma_E/E \approx 1/3$, then a 10\% increase of the average neutrino energy is expected. But, the induced change on the $\theta_{13}$ sensitivity is negligeable.}. The optimization of the physics potential depends at first approximation on the pion neutrino characteristics, which energy is fully determined by the pion 2-body decay and boost. To reach an energy of $260$~MeV, the pion needs a $\beta=0.97$, which in turn induces a pion momentum of $600$~MeV/c. 
+
+Figure \ref{fig:focusing} represents, in the $r-z$ plane, the trajectories of pions emitted at $z=r=0$ with different zenith angles. Particles are deviated\footnote{The magnetic field inside the aluminum conductors themselves is neglected as the material thickness is of the order of 3~mm.} by a toroidal magnetic field for $r>4$~cm:
+$$
+B_\phi(r) = \frac{\mu_0 I}{2\pi r}
+$$
+where $I$ is the peak current, which is set to $300$~kA for the Horn ($4~\mathrm{cm}<r<20~\mathrm{cm}$) and to $600$~kA for the Reflector ($20~\mathrm{cm}<r<40~\mathrm{cm}$). The exact profile of the conic part of the horns is determined such that the relevant pions exit parallel to the beam axis \cite{nuFact138}. The Horn cylindrical part is $40$~cm long while the conic part is $80$~cm long with an opening angle of $8.4^\circ$. The Reflector cylindrical part is adjusted to the Horn external cylinder, and the conic part is $80$~cm long with an opening angle of $12.8^\circ$. Another design have been studied with a Reflector having a $60$~cm radius. It shows an improvement by $35\%$ of the fluxes, but no improvement in the $\theta_{13}$ sensitivity, therefore, it is no longer used.
+
+It is worth to quote that the Horn/Reflector conductor shapes optimized in the present study to focus a given pion momentum value, is not affected by a proton beam energy change. What is affected is the production rate of the relevant pions. This Horn/Reflector design consideration would be different if one wishes to focus as much as possible all the pions produced with an energy spectrum which of course is affected by a proton beam energy change.    
+
+\begin{figure}[htb]
+	\centering
+		\includegraphics[width=0.6\textwidth]{../picts/corne600hr.eps}
+	  \caption{Pion focusing optimization. Lines represent different trajectories of pion having a $600$~MeV momentum emitted at $r=0$, $z=0$ with different angles. The red line joins the points where the trajectories are parallel to the $z$ axis and the dashed line represents the chosen design of the horn, and two possible design of the reflector($20~cm<r-1<40~cm$ and $20~cm<r-1<60~cm$}
+	  	\label{fig:focusing}
+\end{figure}
+%
+\section{Particle decay treatment and flux calculation}
+%
+The decay tunnel representation is a simple cylinder with variable length ($L_T$) and radius ($R_T$) filled with "vacuum". The base line design used in reference \cite{donega} is a $20$~m long and $1$~m radius cylinder, but simulations have also been conducted with lengths of $10$~m and $40$~m, and radius of $1.5$~m. In the GEANT simulation to gain in CPU time, only pions, muons and kaons are tracked in the volume of the tunnel, and all particles exiting this volume are discarded. 
+
+
+Beyond the $1/L^2$ solid angle factor due to the source-detector distance ($L$) which decreases dramatically the fluxes, the neutrino beam focusing is very limited due to the small pion boost factor ($\approx 4$). Therefore, computational algorithms have been used to avoid a too prohibitive CPU time resulting from the simulation of each secondary particle decay. Otherwise, about $10^{15}$ p.o.t would have been necessary to obtain reliable statistics for the estimation of the $\bar{\nu}_e$ flux for instance.
+
+It is worth to mention that the particle decays occurring before the entrance of the decay tunnel are also taken into account and treated in the same manner, which is not the case in reference \cite{donega}. 
+
+\subsection{Algorithm description}
+\label{sec:algo}
+
+The decay code has been included in the GEANT code. The basic idea of this algorithm is to compute the neutrino fluxes using the probability of reaching the detector for each neutrino produced by a $\pi/K/\mu$ particle. This method has already been used in reference \cite{donega} and has been modified and extended to the kaon decay chain for the present study. 
+
+Muon neutrino comes mostly from pion decay. In a first stage, each pion is tracked by GEANT until it decays. Then, the probability for the produced muon neutrino to reach the detector is computed. The flux is obtained applying the probability as a weight for each neutrino. All the pions produced in the simulation are therefore useful to compute the flux, and this allows to reduce the number of events in the simulation to $10^6$ p.o.t. In this computation, the decay region (horns and tunnel) is considered as point like compare to the source-detector distance. 
+
+The same method is applied for neutrino coming from muons and kaons with some modifications  because most of the muons do not decay, and there are very few kaons produced (see Tab.~\ref{tab:nbPart}).
+
+The probability computation is presented in the appendix. 
+
+\begin{table}[htb]
+	\centering
+		\begin{tabular}{|c|c|}
+			\hline
+			Beam energy  & number of proton \\
+			  (GeV)      & per year ($10^{23}$ p.o.t/y) \\
+			\hline
+			2.2 & 1.1 \\
+			3.5 & 0.7 \\
+			4.5 & 0.56 \\
+			6.5 & 0.4 \\
+			8   & 0.3 \\
+		  \hline
+		\end{tabular}
+	\caption{Number of protons on target for different beam energy at 4~MW constant power.}
+	\label{tab:proton}
+\end{table}
+
+\subsection{Validation of the algorithms}
+
+The validity of the method presented in the previous section have been tested against a straight forward  algorithm consisting of decaying each pion $N$ times ($N \approx 10^6$). A full GEANT simulation of the event (decays included) is performed and presents the advantage to keep all the informations of the neutrino available for further studies. Such method can be a good approach to compute the muon neutrino flux coming from pion decays. It can also provide the beam profile, but it shows its limits for the muon induced fluxes, especially the $\bar{\nu}_e$ flux. Indeed, this means that each muon is duplicated $N$ times and when a muon decays, it must decay $N$ times again. For $N\approx 10^6$, this is prohibitive CPU time consuming.
+\begin{figure}[htb]
+	\centering
+		\includegraphics[width=0.50\textwidth]{../picts/compGeantDonega_NB.eps}
+	\caption{Comparison between the probability method (see Sec.~\ref{sec:algo}) and the full GEANT simulation method for the $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes.}
+	\label{fig:compGeantDonega}
+\end{figure}
+
+The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are displayed on Fig.~\ref{fig:compGeantDonega} for both methods. The two spectra shows a clear agreement, and this makes confidence on the probability method.
+%
+\subsection{Simulated fluxes}
+The fluxes are computed at a distance of $100$~km from the source by convention, but can be rescaled at any desired distance. They provide the number of the four neutrino species ($\nu_\mu$, $\bar{\nu}_\mu$, $\nu_e$, $\bar{\nu}_e$) passing through a $100$~m$^2$ fiducial area during $1$~year.
+
+In practice, the fluxes are given as a function of the neutrino energy via histograms composed of $20$~MeV bin width.  These histograms are filled with the energy of each neutrino weighted by the probability to reach the detector (Sec.~\ref{sec:algo}). To obtain the fluxes, the histograms are rescaled to the number of p.o.t per year depending on the beam energy. For a $2.2$~GeV beam of $4$~MW, the number of protons is $1.1~10^{16}$~p.o.t/s. Table \ref{tab:proton} reports on the number of p.o.t per year for the different energies studied using the definition of one year being $10^7$~s. In the following, the up to now nominal $2.2$~GeV proton beam is used, if it is not otherwise mentioned.
+
+Three origins are identified in the composition of each neutrino flux (see Tab.~\ref{tab:BRkp}-\ref{tab:BRk0L} in appendix \ref{sec:kaons} for the kaon cases):
+\begin{itemize}
+	\item neutrinos from pions, which includes neutrinos created by primary pion decays and neutrinos coming from the muons produced by pion decays or muons directly exiting the target. This is the component studied in reference \cite{donega} but with different settings and event generator;
+	\item neutrinos emitted during the decay chain of the charged kaons, either by direct production, or produced by the daughter pions and muons;
+	\item neutrinos coming from the decay chain of the neutral kaons.
+\end{itemize}
+
+The three components of the fluxes as well as the total neutrino fluxes for the four neutrino species are presented on Fig.~\ref{fig:flux22p} for positive particle focusing and a proton beam kinetic energy of $2.2$~GeV. The $\nu_\mu$ flux is dominated by the neutrino of pion decays, but a tail at high energy (above $500$~MeV) is created by the $K^+\rightarrow \mu^+\nu_\mu$ channel, which is anyway at least three order of magnitude below the flux maximum. The $\bar{\nu}_\mu$ flux is mostly due to the decays of $\pi^-$ that are not unfocused by the horns, but the higher energy part comes from $\mu^+$ decays. It is noticable that the $\nu_e$ and $\bar{\nu}_e$ fluxes are respectively more than $200$ and more than $7000$ times less numerous than the muon neutrino. The $\bar{\nu}_e$ are produced in a large part by the $K^0_L\rightarrow\pi^+e^-\bar{\nu}_e$ decay channel and by $\mu^-$ decay, while the  $\nu_e$ flux is dominated by the $\mu^+$ decays.
+
+On Fig.~\ref{fig:flux22m}, the horns are set to focus negative particles keeping other parameters identical. By comparison with positive focusing, one can at first approximation translate the results by exchanging particles and anti-particles, except that the $K^+/K^-$ ratio is about 100  in the beam-target interactions (see Tab.~\ref{tab:nbPart}).
+
+On Figs.~\ref{fig:flux45p} and \ref{fig:flux80p}, one observes the evolution of Fig.~\ref{fig:flux22p} when the proton beam kinetic energy increases to $4.5$~GeV and $8$~GeV, respectively. Correspondingly, the results for negative particle focusing are presented on Figs.\ref{fig:flux45m} and \ref{fig:flux80m}. One clearly notices the increase of the kaon induced neutrino contents as the beam energy grows.
+
+\begin{figure}[p]
+	\centering
+	\includegraphics[scale=0.6]{../picts/flux22p.eps}
+	\caption{Neutrino fluxes $100$~km from the decay region and with the collection elements focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$~GeV (4~MW), a decay tunnel with a length of $20$~m and a radius of $1$~m. Solid line is the 	total flux. Dashed line is the contribution from primary pions and their muons. Dotted line are the neutrino from the charged kaon decay chains, and dotted-dashed line are for the $K^0$ decay chain contribution.}
+	\label{fig:flux22p}
+\end{figure}
+
+\begin{figure}[p]
+	\centering
+	\includegraphics[scale=0.6]{../picts/flux22m.eps}
+	\caption{Same remarks as for Fig.~\ref{fig:flux22p} but the collection elements are  focusing negative charges.}
+	\label{fig:flux22m}
+\end{figure}
+
+\begin{figure}[p]
+	\centering
+	\includegraphics[scale=0.6]{../picts/flux45p.eps}
+	\caption{Same as for Fig.~\ref{fig:flux22p} but for proton beam kinetic energy of $4.5$~GeV (4~MW).}
+	\label{fig:flux45p}
+\end{figure}
+
+\begin{figure}[p]
+	\centering
+	\includegraphics[scale=0.6]{../picts/flux45m.eps}
+	\caption{Same as for Fig.~\ref{fig:flux22m} but for proton beam kinetic energy of $4.5$~GeV (4~MW).}
+	\label{fig:flux45m}
+\end{figure}
+
+\begin{figure}[p]
+	\centering
+	\includegraphics[scale=0.6]{../picts/flux80p.eps}
+	\caption{Same as for Fig.~\ref{fig:flux22p} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+	\label{fig:flux80p}
+\end{figure}
+
+
+\begin{figure}[p]
+	\centering
+	\includegraphics[scale=0.6]{../picts/flux80m.eps}
+	\caption{Same as for Fig.~\ref{fig:flux22m} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+	\label{fig:flux80m}
+\end{figure}
+
+\begin{table}[htb]
+	\centering
+		\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
+			\hline
+			Settings  & \multicolumn{2}{c|}{$\nu_\mu$} & \multicolumn{2}{c|}{$\nu_e$} 
+								&	\multicolumn{2}{c|}{$\bar{\nu}_\mu$} & \multicolumn{2}{c|}{$\bar{\nu}_e$} \\
+								\cline{2-9}
+								& $+$ & $-$ & $+$ & $-$ & $+$ & $-$ & $+$ & $-$ \\ \hline
+(1): $2.2$~GeV  
+	& $7.6$          & $4.5\,10^{-1}$ 
+	& $3.2\,10^{-2}$ & $2.4\,10^{-3}$
+	& $3.1\,10^{-1}$ & $5.8$  
+	& $1.1\,10^{-3}$ & $1.6\,10^{-2}$ \\		  \hline
+
+(1): $3.5$~GeV  
+	& $10.0$          & $8.7\,10^{-1}$ 
+	& $4.4\,10^{-2}$  & $6.1\,10^{-3}$
+	& $7.0\,10^{-1}$ & $8.5$  
+	& $2.8\,10^{-3}$ & $2.2\,10^{-2}$ \\		  \hline
+
+(1): $4.5$~GeV  
+	& $10.9$          & $1.1$ 
+	& $5.0\,10^{-2}$  & $9.6\,10^{-3}$
+	& $6.8\,10^{-1}$ & $6.7$  
+	& $3.9\,10^{-3}$ & $1.8\,10^{-2}$ \\		  \hline
+
+(1): $6.5$~GeV  
+	& $10.4$          & $1.4$ 
+	& $6.4\,10^{-2}$  & $2.0\,10^{-2}$
+	& $9.6\,10^{-1}$ & $7.0$  
+	& $9.2\,10^{-3}$ & $2.5\,10^{-2}$ \\		  \hline
+
+(1): $8.0$~GeV  
+	& $9.7$          & $1.5$ 
+	& $6.6\,10^{-2}$  & $2.3\,10^{-2}$
+	& $1.1$           & $7.1$  
+	& $1.1\,10^{-2}$ & $2.8\,10^{-2}$ \\
+		  \hline\hline
+
+(2): $4.5$~GeV  
+	& $7.0$          & $1.0$ 
+	& $2.7\,10^{-2}$  & $9.1\,10^{-3}$
+	& $5.0\,10^{-1}$ & $5.2$  
+	& $3.4\,10^{-3}$ & $1.1\,10^{-2}$ \\		  \hline
+
+(3): $4.5$~GeV  
+	& $12.3$          & $1.2$ 
+	& $7.2\,10^{-2}$  & $1.0\,10^{-2}$
+	& $7.6\,10^{-1}$ & $7.5$  
+	& $4.1\,10^{-3}$ & $2.6\,10^{-2}$ \\		  \hline\hline
+
+(4): $4.5$~GeV  
+	& $13.2$          & $1.5$ 
+	& $6.9\,10^{-2}$  & $1.4\,10^{-2}$
+	& $9.0\,10^{-1}$  & $8.1$  
+	& $5.6\,10^{-3}$  & $2.7\,10^{-2}$ \\		  \hline
+
+		\end{tabular}
+	\caption{Integral of the different species fluxes with different settings. Numbers are in $10^{13}/100\mathrm{m}^2/y$ for positive focusing ($+$) and negative focusing ($-$). The settings used  corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. Setting (1) is the baseline option and means $L_T = 20$~m and $R_T = 1$~m, while setting (2) means $L_T = 10$~m and $R_T = 1$~m and setting (3) means $L_T = 40$~m and $R_T = 1$~m, and finally the setting (4) means $L_T = 20$~m and $R_T = 1.5$~m.}
+	\label{tab:speciesfluxes}
+\end{table}
+
+On Tab.~\ref{tab:speciesfluxes} are reported the integral of the fluxes when one modifies the decay tunnel geometry as for instance the length or the radius, as well as the beam kinetic energy (keeping the beam power constant).  Switching the radius from $1$~m to $1.5$~m (doubling the surface basically) has increased the signal like fluxes ($\nu_\mu$, $\bar{\nu}_\mu$) by a factor $20\%$ but also in paralell the background like fluxes ($\nu_e$, $\bar{\nu}_e$) by a factor $38\%$. Increasing the length from $10$~m up to $40$~m yields an increase of the signal like flux by $75\%$ and also in paralell an increase of the background like flux by a factor $1.7$. The feeling that $L_T = 20$~m and $R_T = 1$~m is a good signal over background compromise is confirmed by sensitivity quantitative studies reported in Sec.~\ref{sec:results}.  
+
+Looking at the evolution of $\nu_\mu$ flux with respect to the beam energy, one notices that a maximum is reached around $4.5$~GeV. This is due to the competition between the cross section rise with respect to the energy and the decrease of the number of p.o.t due to the constant SPL power ($4$~MW). The indication that a new beam energy base line arround $4.5$~GeV may be proposed, replacing the previous $2.2$~GeV base line design. This proposal will be reenforced in Sec.~\ref{sec:results}.
+%
+\section{Sensitivity computation ingredients}
+%
+The sensitivity to $\theta_{13}$ is computed for an $\nu_\mu\rightarrow\nu_e$ appearance experiment. An analysis program described in reference \cite{Mezzetto} has been used for such sensitivity computation. See Tab.~\ref{tab:param} for the default user parameter values used in this paper. We just remind here some key points of the program. 
+
+It is included a full 3-flavors oscillation probability computation with matter effects, but no ambiguities are taken into account. This latest point may be revisited in a future work using reference \cite{DONINI-2}. Concerning the background events, the $\nu_e/\bar{\nu}_e$ from the beam, the $\nu_\mu e^-$ elastic scattering process, the $\pi^0$ production as well as the $\mu/e$ misidentification are taken into account. The cross-sections from the NUANCE program are used \cite{NUANCE}. The systematics error is a user parameter and we have used the default $2\%$ value and also $5\%$ and $10\%$. The detector considered for definitiveness is similar to the UNO detector, i.e. a $440$~kt fiducial water \v{C}erenkov detector \cite{UNO}. It is located at $L = 130$~km from CERN, in the foreseen new Fréjus laboratory \cite{mosca}. It is worth to mention that if one wants to evaluate the influence of $L$ on the sensitivity, it would mean a re-optimization of the horns for each $L$ envisaged (see Sec.~\ref{sec:horn} for discussion on Horn conductor shape determination).  
+
+\begin{table}[htb]
+	\centering
+		\begin{tabular}{|l|l|}
+			\hline
+			$\Delta m^2_{12} = 8.2 10^{-5}~\mathrm{eV}^2$ & $\sin^22\theta_{12} = 0.82$ \\
+			$\sigma(\Delta m^2_{12}) = 0.5 10^{-5}~\mathrm{eV}^2$ & $\sigma(\sin^22\theta_{12}) = 9\%$ \\ \hline
+			$\Delta m^2_{23} = 2.5 10^{-3}~\mathrm{eV}^2$ & $\sin^22\theta_{23} = 1.$ \\
+			$\sigma(\Delta m^2_{23}) = 10^{-4}~\mathrm{eV}^2$ & $\sigma(\sin^22\theta_{23}) = 1\%$ \\
+		  \hline
+		  \hline
+		  $L_T = 20$~m & $R_T = 1$~m \\ \hline
+		  $M=440$~kT   & $\epsilon_{syst}=2\%$ \\
+		  \hline 
+		\end{tabular}
+	\caption{Default user parameters used to compute the sensitivity curves \cite{Mezzetto}. The quoted errors for the $(12)$ and the $(23)$ parameters are coming respectively from the up to date combined Solar and KamLAND results \cite{KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite{JJG}.}
+	\label{tab:param}
+\end{table}
+
+The running time scenario has been fixed to 5 years focusing $\pi^+$ for the $\theta_{13}$ sensitivity studies. This scenario gives comparable $\theta_{13}$ sensitivity than a scenario defined as 2 years focusing $\pi^+$ followed by 8 years focusing $\pi^-$, which is more appropriate for $\delta_{CP}$ sensitivity studies.
+%
+\section{Results}
+\label{sec:results}
+The $\theta_{13}$-sensitivity is computed for $\theta_{13} = 0^\circ$ and $\delta_{CP} = 0^\circ$ if not explicitly mentioned. The other default parameters are listed in Tab.~\ref{tab:param}.
+
+Tab.~\ref{tab:nbvsE} presents the number of signal and background events for a $5$ years positive focusing experiment, but with different beam energy settings. The significance parameter is defined in reference \cite{Mezzetto} as:
+\begin{equation}
+\mathcal{S} = \frac{N^{osc}_{\nu_e}}{\sqrt{N^{osc}_{\nu_e} + N^{beam}_{\nu_e} + N^{oth. bkg} + \left(\left(N^{osc}_{\nu_e}+N^{beam}_{\nu_e}\right)\times\epsilon_{syst}\right)^2}}
+\label{eq:significance}
+\end{equation}
+with $N^{osc}_{\nu_e}$ the number of $\nu_e/\bar{\nu}_e$ events due to $\nu_\mu/\bar{\nu}_\mu$ oscillations, $N^{beam}_{\nu_e}$ the number of background events coming from the prompt $\nu_e/\bar{\nu}_e$ contamination of the beam, $N^{oth. bkg}$ the other kinds of background events and $\epsilon_{syst}$ the systematical factor. One can appreciate that $4.5$~GeV beam energy presents better results and may become the new base line energy.
+%
+\begin{table}[htb]
+	\centering
+		\begin{tabular}{|p{4cm}|c|c|c|c|c|}
+			\cline{2-6}
+			\multicolumn{1}{c|}{} & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+			\hline
+			non oscillated $\nu_\mu$       & $36917.2$  & $60968.6$  & $73202.4$  & $78023.9$ & $76068.2$ \\
+			\hline
+			oscillated $\nu_e$             & $43.0$  & $59.7$  & $63.7$  & $60.6$ & $55.9$ \\
+			\hline
+			beam $\nu_e$, $\bar{\nu}_e$     & $165.9$ & $225.2$ & $244.9$ & $299.8$ & $309.7$ \\
+			\hline
+			other background: $\pi^0$, $\nu_\mu$-elast., $\mu/e$-missId. & $70.3$  & $104.7$ & $126.6$ & $147.6$ & $151.3$ \\
+			\hline
+			Significance                  &  $2.50$ & $2.91$  & $2.93$  & $2.57$ & $2.34$ \\
+			\hline
+		\end{tabular}
+	\caption{Number of events for 5 years positive focusing scenario with default parameters of Tab.~\ref{tab:param}. The significance parameter is defined by Eq.~\ref{eq:significance}.}
+	\label{tab:nbvsE}		
+\end{table}
+
+The contours at $90\%$, $95\%$ and $99\%$~CL of the $\theta_{13}$ sensitivity are presented in the $(\sin^22\theta_{13}, \Delta m^2_{23})$ plane on Fig.\ref{fig:sensi45} for $4.5$~GeV proton beam kinetic energy. The comparison between the contours at $90\%$~CL but with $2.2$~GeV, $3.5$~GeV, $4.5$~GeV and $8$~GeV is shown on Fig.~\ref{fig:compSensi}. One notices a better perfomence reached with a $4.5$~GeV energy beam as a confirmation of significance parameter value. But, in fact there is not much visual difference between a sensitivity obtained with $3.5$~GeV and $4.5$~GeV, even if one should keep in mind that kaon production models are different at these two energies (see Sec.~\ref{sec:kaon}. Quantitative studies of the minimum $\sin^22\theta_{13}$ with respect to the kinetic beam energy $E_k(proton)$, and the decay length $L_T$, and the systematics $\epsilon_{syst}$ are presented in Tabs.~\ref{tab:thvsE}, \ref{tab:thvseps}. The influance of the systematical level is presented on Fig.~\ref{fig:compEpsSyst}. One should keep in mind that $\epsilon_{syst}$ is considered as an ultimate goal.     
+%
+\begin{figure}[htb]
+	\centering
+		\includegraphics{../picts/sensi45.eps}
+	\caption{Sensitivity contours obtained with a SPL energy of $4.5$~GeV and default parameters of Tab.~\ref{tab:param}.}
+	\label{fig:sensi45}
+\end{figure}
+%
+\begin{figure}[htb]
+	\centering
+		\includegraphics{../picts/compSensi.eps}
+	\caption{Comparison of 90\% sensitivity contours obtained with SPL energies of ($2.2$, $3.5$, $4.5$, $8$)~GeV and default parameters of Tab.~\ref{tab:param}.}
+	\label{fig:compSensi}
+\end{figure}
+
+
+\begin{table}[htb]
+	\centering
+		\begin{tabular}{|l|c|c|c|c|c|}
+			\hline
+			\backslashbox{$L_T$}{$E_k(proton)$} & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV  \\
+			\hline
+			$10$m & $1.10$ & $0.96$ & $1.05$ & $1.10$ & $1.20$ \\
+			\hline
+			$20$m & $1.20$ & $0.96$ & $0.91$ & $1.05$ & $1.15$ \\
+			\hline
+			$40$m & $1.26$ & $1.00$ & $1.00$ & $1.10$ & $1.20$ \\
+			\hline
+		\end{tabular}
+	\caption{Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL. Other parameters are fixed to default values (Tab.~\ref{tab:param}).}
+	\label{tab:thvsE}
+\end{table}
+
+
+
+\begin{table}[htb]
+	\centering
+		\begin{tabular}{|l|c|c|c|c|c|}
+			\hline
+			\backslashbox{$\epsilon_{syst}$}{$E_k(proton)$} & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+			\hline
+			$2\%$ & $1.20$ & $0.96$ & $0.91$ & $1.10$ & $1.20$ \\
+			\hline
+			$5\%$ & $1.51$ & $1.26$ & $1.26$ & $1.51$ & $1.66$ \\
+			\hline
+			$10\%$ & $2.40$ & $2.19$ & $2.29$ & $2.75$ & $3.16$ \\
+			\hline
+		\end{tabular}
+	\caption{minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL. Other parameters are fixed to default values (Tab.~\ref{tab:param}).}
+	\label{tab:thvseps}		
+\end{table}
+
+\begin{figure}[htb]
+	\centering
+		\includegraphics{../picts/compEpsSyst.eps}
+	\caption{$90\%$ CL sensitivity contours obtained with a SPL energy of $4.5$~GeV and default parameters of Tab.~\ref{tab:param} but $\epsilon_{syst}$.}
+	\label{fig:compEpsSyst}
+\end{figure}
+
+
+There are also uncertainties on the minimum $\sin^22\theta_{13}$ value that might be reached in a $\nu_\mu \rightarrow \nu_e$ experiment which are due to the $\mathrm{sign}(\Delta m^2_{23})$ and the $\delta_{CP}$ ambiguities. On Fig.~\ref{fig:compDelta_thVSdm} and Tab.~\ref{tab:sign} are presented the results of these ambiguities making use of the oscillation probability symmetry $P(\Delta m^2_{23},\delta_{CP}) =  P(-\Delta m^2_{23},\pi - \delta_{CP})$. Other ambiguities coming from the sign$(\tan(2\theta_{23}))$ ignorance also take place as studied in reference \cite{DONINI}. From Fig.~9 of this reference, we estimate a 30\% effect on $\sin^2(2\theta_{13})$ sentivity due to these ambiguities.
+\begin{figure}[htb]
+	\centering
+		\includegraphics{../picts/compDelta_thVSdm.eps}
+	\caption{$\theta_{13}$-sensitivity dependence up on the $\delta_CP$ phase obtained for a $4.5$~GeV SPL beam and 5 years running with a positive focusing scenario.}
+	\label{fig:compDelta_thVSdm}
+\end{figure}
+ 
+\begin{table}[htb]
+	\centering
+		\begin{tabular}{|c|c|c|}
+			\hline
+			\backslashbox{sign$(\Delta m^2_{23})$}{$\delta_{CP}$} & $0^\circ$ & $90^\circ$ \\
+			\hline
+			$+$ & $1.20$ & $11.48$ \\
+			\hline
+			$-$ & $1.15$ & $0.44$ \\
+			\hline
+		\end{tabular}
+	\caption{Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL. Other parameters are fixed to default values (Tab.~\ref{tab:param}).}
+	\label{tab:sign}		
+\end{table}
+
+
+The combined $\sin^22\theta_{13}$ and $\delta_{CP}$ sensibility is presented on Fig.~\ref{fig:delta45} for the 5 years positive focusing scenario to appreciate in an other way the above mentioned $\delta_{CP}$ ambiguity. 
+\begin{figure}[htb]
+	\centering
+		\includegraphics{../picts/delta45.eps}
+	\caption{Sensitivity contours obtained with a SPL energy of $4.5$~GeV and default parameters of Tab.~\ref{tab:param} and 5 years positive focusing scenario.}
+	\label{fig:delta45}
+\end{figure}
+To improve the $\delta_{CP}$-independent limit on $\sin^22\theta_{13}$, one may envisaged a combination of 2 years with positive focusing and 8 years negative focusing as in references \cite{JJG,Mezzetto,DONINI}. The corresponding combined sensitivity contours are presented in Fig.~\ref{fig:delta45FocPM}. With this kind of mixed focusing scenario, $\sin^22\theta_{13} < 10^{-3}$ independently of $\delta_{CP}$.
+\begin{figure}[htb]
+	\centering
+		\includegraphics{../picts/delta45FocPM.eps}
+	\caption{Same as Fig.~\ref{fig:delta45} but for 2 years positive focusing and 8 years negative focusing scenario.}
+	\label{fig:delta45FocPM}
+\end{figure}
+The comparison of the two scenarios modifying the SPL beam energy is presented on Figs.~\ref{fig:compDelta5pos}, \ref{fig:compDeltaFocPM}. It is noticeable that for $\delta_{CP}\approx 50^\circ$ ($\Delta m^2_{23}>0$) one gets better sensitivity with a $2.2$~GeV SPL beam than a $4.5$~GeV SPL beam. This is due to 
+\begin{figure}[htb]
+	\centering
+		\includegraphics{../picts/compDelta5pos.eps}
+	\caption{Same conditions as Fig.~\ref{fig:delta45} but at different SPL beam energy.}
+	\label{fig:compDelta5pos}
+\end{figure}
+\begin{figure}[htb]
+	\centering
+		\includegraphics{../picts/compDeltaFocPM.eps}
+	\caption{Same conditions as Fig.~\ref{fig:delta45FocPM} but at different SPL beam energy.}
+	\label{fig:compDeltaFocPM}
+\end{figure}
+ 
+%
+\section{Summary and outlook}
+A complete chain of simulation has been set up for the SPL super beam project. It includes neutrino production from kaon decay, which is important to test higher SPL energy scenario.
+A simulation has been performed with the nominal energy of the SPL and also for an kinetic energy of $3.5$~GeV. The gain in the sensitivity is $30\%$ in this last scenario with a moderate change  in the horn profiles, which leads to a potential sensitivity to $\sin^22\theta_{13} = 2.10^{-3}$ at $90\%$ CL. But, it could be improved since many parameters have not yet been optimized: reflector/horn design, decay tunnel length, $\pi^+$/$\pi^-$ focusing time...
+%
+\section*{Acknoledgments}
+The authors are very grateful to thanks M. Mezzetto to have express his interest at early stage of this work and to have provided us his sensitivity computation program. Also the authors thank S. Gilardoni for fruitful discussions.
+%
+\appendix
+\section{Decay probability computations}
+This appendix contains the probability formulas and the algorithms used in the flux computation (see Sec.~\ref{sec:algo}).
+
+\subsection{Pion neutrino probability computation}
+\label{sec:Ppi}
+Pions decay only as $\pi^+\rightarrow \mu^+ + \nu_\mu$ or $\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$ and the neutrinos are emitted isotropically in the pion rest frame, with an energy of about $30$~MeV given by the 2-body decay kinematics. Applying a Lorentz boost knowing the pion momentum and direction, it is possible to compute the probability to reach the detector for the neutrinos. Only neutrino parallel to the beam axis are supposed to pass through the detector fiducial area, and therefore, the neutrino must be emitted by the pion with an angle opposite to the angle between the pion and the beam axis (see Fig.~\ref{fig:pionDecay}). This gives:
+\beq{probaPi}
+\mathcal{P}_\pi = \frac{1}{4\pi}\frac{A}{L^2}\frac{1-\beta^2}{(\beta\cos\alpha-1)^2}
+\enq
+where $\beta$ is the velocity of the pion in the tunnel frame, $A$ is the fiducial detector surface, $L$ the distance between the neutrino source and the detector, and $\alpha$ the angle between the pion direction and the beam axis in the laboratory frame.
+
+\begin{figure}[htb]
+	\centering
+		\includegraphics{../picts/pionDecay.eps}
+	\caption{Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha$ is needed.}
+	\label{fig:pionDecay}
+\end{figure}
+
+\subsection{Muon neutrino probability computation}
+\label{sec:Pmu}
+Muons decay only as $\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_\mu$ or $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$, and will produce background events. The mean decay length of the muons is $2$~km , therefore, most of them do not decay in the tunnel. This induces a lake of statistics to estimate the corresponding level of background. This problem has been solved using each muon appearing in the simulation in the following steps:
+\begin{enumerate}
+	\item the probability for the muon to decay into the tunnel has been computed using a straight line propagation;
+	\item the available energy for the neutrino in the tunnel frame has been divided in $20$~MeV energy bins; 
+	% (the number of bin depending of the muon energy).
+	\item one $\nu_e$ and one $\nu_\mu$ have been simulated in each of the energy bins (step 2). Then, the probability to reach the detector has been computed, and multiplied by the probability computed at step 1.%the neutrino energy is stored in an histogram, weighted with this probability and 
+\end{enumerate}
+After the probability computation, the non useful muon is discarded by GEANT to gain in CPU time. 
+
+The probability for the muon neutrino and the electron neutrino to be emitted parallel to the beam axis is \cite{donega}:
+\beq{probaMu}
+\frac{d\mathcal{P}_\mu}{dE_\nu} = \frac{1}{4\pi}\frac{A}{L^2}\frac{2}{m_\mu}\frac{1}{\gamma_\mu(1+\beta_\mu\cos\theta^*)}\frac{1-\beta_\mu^2}{(\beta_\mu\cos\rho-1)^2}\left[f_0(x)\mp \Pi_\mu^T f_1(x)\cos\theta^*\right]
+\enq 
+where $\beta_\mu$ and $\gamma_\mu$ are the velocity and the Lorentz boost of the muon in the tunnel frame, $\theta^*$ is the angle with respect to the beam axis of the muon in the muon rest frame, $\rho$ is the corresponding angle in the tunnel frame. Like in the pion case, this angle appears because the neutrino must be parallel to the beam axis. $\Pi_\mu^T$ is the muon transverse polarization, the parameter $x$ is defined as $x=2E_\nu^*/m_\mu$ where $E_\nu^*$ is the neutrino energy in the muon rest frame, and the function $f_0(x)$ and $f_1(x)$ coming from the matrix element of the muon decay are given in Tab.~\ref{tab:Function}. The sign in front of $\Pi_\mu^T$ in Eq.~\refeq{probaMu} is $(-)$ for the $\nu_\mu$ and $(+)$ for the $\bar{\nu}_\mu$, respectively.
+
+\begin{table}[htb]
+	\begin{center}
+		\begin{tabular}{|c||c|c|}
+		\hline
+		      &  $f_0(x)$ & $f_1(x)$ \\
+		\hline
+		\hline
+		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+		\hline
+		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+		\hline
+		\end{tabular}
+	\end{center}
+	\caption{Flux function in the muon rest frame \cite{Gaisser}.}
+	\label{tab:Function}
+\end{table}
+
+Muon polarization is computed using the conservation of the transverse component of the velocity four-vector $\gamma(1,\beta)$ between the muon rest frame (where the polarization is computed) and the pion rest frame, where the muon helicity is $-1$, due to the parity non conservation. It yields \cite{picasso}:
+\beq{pola}
+\Pi_\mu^T = \frac{\gamma_\pi\beta_\pi}{\gamma_\mu\beta_\mu}\sin\theta^*
+%\mbox{ and }\Pi_\mu^L = \sqrt{1-\Pi_\mu^{T2}}\virg 
+\enq
+where $\gamma_\pi$, $\beta_\pi$, $\gamma_\mu$, and $\beta_\mu$ are the Lorentz boost and velocity of the pion and of the muon in the tunnel frame, and $\theta^*$ the angle with respect to the beam axis of the muon in the pion rest frame.
+
+\subsection{The treatment of the kaons}
+\label{sec:kaons}
+Contrary to pions and muons, kaons have many decay channels. They are summarized in tables \ref{tab:BRkp}, \ref{tab:BRk0S} and \ref{tab:BRk0L}.
+
+There is a very small amount of kaons produced (Sec.~\ref{sec:algo}), and this number has been artificially increased in order to obtain statistically satisfactory results.  The multiplicity of decay channels makes impossible the method used for the muon case (Sec.~\ref{sec:Pmu}). The method chosen for the good compromise between the gain in CPU and the statistical uncertaincy of the results, is to duplicate 300 times each kaon exiting the target. 
+
+All the kaons daughter particles are tracked by GEANT until they decay. Three different types of daughter particles are identified in the kaon decays. The first type corresponds to primary neutrinos, the second type concerns charged pions and muons, and the neutral pions are left for the last type.
+
+In the $K^\pm\rightarrow\mu^\pm \nu_\mu(\bar{\nu}_\mu)$ decay modes, the computation of the probability for a neutrino to reach the detector is the same than the 2-body decay formula used to in the pion decay (Eq.~\refeq{probaPi}), where $\beta$ is now the kaon velocity, and $\alpha$ the angle of the kaon with respect to the beam axis. 
+
+When a neutrino is produced by a kaon 3-body decay, the probability to reach the detector is computed using a pure phase space formula. It yields:
+\beq{probaL}
+\mathcal{P}_K = \frac{1}{4\pi}\frac{A}{L^2}\frac{1}{m_K-m_\pi-m_l}\frac{1}{\gamma_K(1+\beta_K\cos\theta^*)}\frac{1-\beta_K^2}{(\beta_K\cos\delta-1)^2}\virg
+\enq 
+where $m_K$ is the kaon mass (charged or neutral), $m_\pi$ is the pion mass ($\pi^0$ mass in $K^\pm$ decays and $\pi^\pm$ mass in $K_L^0$ decays), and $m_l$ is the mass of the lepton associated with the neutrino. The $\beta_K$ and $\gamma_K$ are the velocity and the Lorentz boost of the kaon, $\theta^*$ is the angle between the neutrino direction and the kaon direction, in the kaon rest frame. Finally, $\delta$ is the angle between the kaon direction and the beam axis in the tunnel frame. \\
+
+When a $\pi^\pm$ is produced in the kaon decay chain, it is tracked by GEANT until it decays, and the probability of Eq.~\refeq{probaPi} is applied to the produced neutrino. In case of a muon, it is treated as explained in Sec.~\ref{sec:Pmu}. The muon polarization is computed this time using the kaon decay informations. Finally, when a $\pi^0$ is produced, as it cannot create neutrinos, it is simply discarded.
+
+\begin{table}
+\begin{center}
+\begin{sloppypar}
+\parbox{5.cm}{
+\begin{center}
+\mbox{
+\begin{tabular}{|c|c|}
+\hline
+\multicolumn{2}{|c|}{$K^\pm$} \\
+\hline
+$\mu^\pm\nu_\mu$ & $63,51\%$ \\
+\hline
+$\pi^\pm\pi^0$ & $21,17\%$ \\  			
+\hline
+$\pi^\pm\pi^+\pi^-$ & $5,59\%$ \\
+\hline
+$e^\pm\nu_e\pi^0$ & $4,82\%$ \\  			
+\hline	
+$\mu^\pm\nu_\mu\pi^0$ & $3,18\%$ \\
+\hline
+$\pi^\pm\pi^0\pi^0$ & $1,73\%$ \\ 			
+\hline
+\end{tabular}
+}
+\end{center}
+}
+\hspace{0.5cm}
+\parbox{4cm}{
+\begin{center}
+\mbox{
+\begin{tabular}{|c|c|}
+\hline
+\multicolumn{2}{|c|}{$K^0$ short} \\
+\hline
+$\pi^+\pi^-$ & $68,61\%$ \\
+\hline
+$\pi^0\pi^0$ &  $31.39\%$\\
+\hline
+\end{tabular}
+}
+\end{center}
+}
+\hspace{0.5cm}
+\parbox{5.cm}{
+\begin{center}
+\mbox{
+\begin{tabular}{|c|c|}
+\hline
+\multicolumn{2}{|c|}{$K^0$ long} \\
+\hline
+$\pi^-e^+\nu_e$ & $19,35\%$ \\
+\hline
+$\pi^+e^-\bar{\nu}_e$ & $19,35\%$ \\  			
+\hline
+$\pi^-\mu^+\nu_\mu$ & $13,5\%$ \\
+\hline
+$\pi^+\mu^-\bar{\nu}_\mu$ & $13,5\%$ \\  			
+\hline	
+$\pi^0\pi^0\pi^0$ & $21,5\%$ \\
+\hline
+$\pi^+\pi^-\pi^0$ & $12,38\%$ \\
+\hline
+\end{tabular}
+}
+\end{center}
+}
+%\end{sloppypar}
+%    \begin{sloppypar}
+      \parbox{5.cm}{
+      	\caption{Charged kaons decay channels and branching ratios \cite{pdg}}
+	      \label{tab:BRkp}
+      }
+      \hspace{0.5cm}
+      \parbox{5.cm}{
+      	\caption{$K^0_S$ decay channels and branching ratios \cite{pdg}}
+      	\label{tab:BRk0S}
+      }
+      \hspace{0.5cm}
+      \parbox{5.cm}{
+      	\caption{$K^0_L$ decay channels and branching ratios \cite{pdg}}
+      	\label{tab:BRk0L}
+      }
+\end{sloppypar}
+\end{center}
+\end{table}
+
+
+
+\begin{thebibliography}{9}
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+B. Pontecorvo, Sov. Phys. JETP {\bf 6} (1957) 429 [Zh. Eksp. Teor. Fiz. \textbf{33} (1957) 549];\\
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+B. Pontecorvo, Sov. Phys. JETP \textbf{26} (1968) 984 [Zh. Eksp. Teor. Fiz. \textbf{53} (1967) 1717];\\
+V. N. Gribov and B. Pontecorvo, Phys. Lett. B \textbf{28} (1969) 493.
+
+\bibitem{LSND}
+A. Athanassopoulos at al. [LSND Collaboration], Phys. Rev. Lett. {\bf 81} (1998) 1774;\\
+A. Aguilar et al. [LSND Collaboration], Phys. Rev. D {\bf 64} (2001) 112007.
+
+\bibitem{MINIBOONE}
+I. Stancu et al. [MiniBooNE Collaboration], FERMILAB-TM-2207.
+
+\bibitem{UNO} 
+The UNO whitepaper, "Physics Potential and Feasibility of UNO" (preprint SBHEP01-3) (see also http://ale.physics.sunysb.edu/uno/)
+
+\bibitem{SKNU04}
+E.~Kearns [SuperKamiokande Collaboration], Talk at Neutrino 2004, 14-19 June 2004 Paris, to be published in Nuclear Physics B (Proceedings Supplement).
+
+\bibitem{K2KNU04}
+T.~Nakaya [K2K Collaboration], Talk at Neutrino 2004, 14-19 June 2004 Paris, Nuclear Physics B (Proceedings Supplement). 
+
+\bibitem{MINOS}
+M.~Thomson  [MINOS Collaboration], Talk at Neutrino 2004, 14-19 June 2004 Paris, Nuclear Physics B (Proceedings Supplement); \\
+P.~Adamson et al., NuMi-L-337.
+
+\bibitem{KAMLAND}
+G. Gratta [KamLAND Collaboration], Talk at Neutrino 2004, 14-19 June 2004 Paris, Nuclear Physics B (Proceedings Supplement).
+
+\bibitem{OPERA}
+D.~Autiero [OPERA Collaboration], Talk at Neutrino 2004, 14-19 June 2004 Paris, Nuclear Physics B (Proceedings Supplement); \\
+M.~Guler et al., Experiment proposal, CERN/SPSC 2000-028, SPSC/P318, LNGS P25/2000 
+
+\bibitem{ICARUS}
+M.~Guler et al. [ICARUS Collaboration], Talk at Neutrino 2004, 14-19 June 2004 Paris, Nuclear Physics B (Proceedings Supplement); \\
+P.~Aprili et al.  , CERN-SPSC-2002-027.
+
+\bibitem{CNGS}
+G.~Acquistapace et al., CERN-98-02.
+
+\bibitem{CHOOZ}
+M.~Apollonio et al.  [CHOOZ Collaboration], Phys.\ Lett.\ B {\bf 466} (1999) 415;\\
+M.~Apollonio et al.  [CHOOZ Collaboration], Eur. Phys. J. C {\bf 27} (2003) 331.
+
+\bibitem{DOUBLE-CHOOZ}
+F. Dalnoki-Veress  for the Double-CHOOZ project, arXiv:hep-ex/0406070.
+
+
+\bibitem{Wpaper}
+K. Anderson et al., White paper report on using nuclear reactors to search for a value of $\theta_{13}$. (2004) \\ http://www.hep.anl.gov/minos/reactor13/reactor13.pdf
+
+\bibitem{SPL}
+B. Autin et al, CERN 2000-12.
+
+\bibitem{CERN}
+A. Blondel et al., CERN-2004-002.
+
+\bibitem{nuFact134} 
+J.E. Campagne, A. Cazes, CERN-NUFACT-Note-134, http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html.
+
+\bibitem{Meer}
+S. van der Meer. CERN-Report No 61-7 (1961).
+
+\bibitem{fluka}
+A. Fasso et al., Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A.Kling et al. - eds., Springer-Verlag Berlin, p159-164 (2001)
+A. Fasso et al., Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A.Kling et al. - eds., Springer-Verlag Berlin, p955-960 (2001)
+
+\bibitem{MARS}
+N.V. Mokhov et al., The MARS Code System User Guide, Version 13(95), Fermilab-FN-628, 1995
+N.V. Mokhov et al., MARS oed Develepments; LANL Report LA-UR-98-5716, 1998, nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/.
+
+\bibitem{harp}
+G. Catanesi et al. [HARP Collaboration], CERN-SPSC 2002/019.
+
+\bibitem{minerva} 
+D. Drakoulakos et al. [Minerva Collaboration], Fermilab P-938, arXiv:hep-ex/405002.
+
+\bibitem{MMWPSGaroby} 
+R. Garoby, Talk in the Physics with a Multi MegaWatt Proton Source Workshop held at CERN, 25-27 May 2004, (http://physicsatmwatt.web.cern.ch/physicsatmwatt/)
+
+\bibitem{MMWPSCazes} 
+J.E. Campagne, A. Cazes, poster session at the Physics with a Multi MegaWatt Proton Source Workshop held at CERN, 25-27 May 2004. 
+
+\bibitem{FLUKAprivate}
+G. Battistoni and A. Ferrari, private communication.
+
+\bibitem{geant}
+Application Software group, Computing and Network Division \& al. --
+\newblock GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+
+\bibitem{SIMONE1}
+S. Gilardoni, Talk at NuFact03, http://www.cap.bnl.gov/nufact03/.
+
+\bibitem{nuFact138}
+J.E.~Campagne, CERN-NUFACT-Note-138 (2004), http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html.
+
+\bibitem{donega}
+M. Donegà, CERN-NUFACT-Note-78 (2001).
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+\bibitem{Gaisser}
+T.K. Gaisser, Cosmic Rays and Particle Physics, Cambridge University Press (1990) 
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+\bibitem{picasso}
+F. Combley and E. Picasso, Phys. Rept. {\bf 14} (1974).
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+\bibitem{pdg}
+K.~Hagiwara et al., Phys. Rev. D {\bf 66} (2002)  010001.
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+\bibitem{Mezzetto}
+M.~Mezzetto, J. Phys. G {\bf 29} (2003) 1781-1784;\\
+arXiv:hep-ex/0302005.
+
+\bibitem{JJG}
+J. J. G\'omez Gadenas et al., IFIC/01-31, arXiv:hep-ph/0105297.
+
+\bibitem{DONINI}
+A. Donini et al., IFT-UAM/CSIC-04-30, arXiv:hep-ph/0406132.
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+\bibitem{DONINI-2}
+A. Donini, D. Meloni and S. Rigolin, JHEP \textbf{0406} (2004) 011; arXiv:hep-ph/0312072.
+ 
+\bibitem{mosca}
+L.~Mosca, Talk in the Physics with a Multi MegaWatt Proton Source Workshop held at CERN, 25-27 May 2004, (http://physicsatmwatt.web.cern.ch/physicsatmwatt/)
+
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+D.~Casper, Nucl. Phys. Proc. Suppl. \textbf{112} (2002) 161-170;\\
+arXiv:hep-ph/0208030.
+
+\end{thebibliography}
+
+
+
+
+
+
+
+\end{document}
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopams.sty
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopams.sty	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopams.sty	(revision 392)
@@ -0,0 +1,87 @@
+%% 
+%% This is file `iopams.sty'
+%% File to include AMS fonts and extra definitions for bold greek 
+%% characters for use with iopart.cls
+%%
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{iopams}[1997/02/13 v1.0]
+\RequirePackage{amsgen}[1995/01/01]
+\RequirePackage{amsfonts}[1995/01/01]
+\RequirePackage{amssymb}[1995/01/01]
+\RequirePackage{amsbsy}[1995/01/01]
+%
+\iopamstrue   % \newif\ifiopams in iopart.cls & iopbk2e.cls
+%             % allows optional text to be in author guidelines
+%
+% Bold lower case Greek letters
+%
+\newcommand{\balpha}{\boldsymbol{\alpha}}
+\newcommand{\bbeta}{\boldsymbol{\beta}}
+\newcommand{\bgamma}{\boldsymbol{\gamma}}
+\newcommand{\bdelta}{\boldsymbol{\delta}}
+\newcommand{\bepsilon}{\boldsymbol{\epsilon}}
+\newcommand{\bzeta}{\boldsymbol{\zeta}}
+\newcommand{\bfeta}{\boldsymbol{\eta}}
+\newcommand{\btheta}{\boldsymbol{\theta}}
+\newcommand{\biota}{\boldsymbol{\iota}}
+\newcommand{\bkappa}{\boldsymbol{\kappa}}
+\newcommand{\blambda}{\boldsymbol{\lambda}}
+\newcommand{\bmu}{\boldsymbol{\mu}}
+\newcommand{\bnu}{\boldsymbol{\nu}}
+\newcommand{\bxi}{\boldsymbol{\xi}}
+\newcommand{\bpi}{\boldsymbol{\pi}}
+\newcommand{\brho}{\boldsymbol{\rho}}
+\newcommand{\bsigma}{\boldsymbol{\sigma}}
+\newcommand{\btau}{\boldsymbol{\tau}}
+\newcommand{\bupsilon}{\boldsymbol{\upsilon}}
+\newcommand{\bphi}{\boldsymbol{\phi}}
+\newcommand{\bchi}{\boldsymbol{\chi}}
+\newcommand{\bpsi}{\boldsymbol{\psi}}
+\newcommand{\bomega}{\boldsymbol{\omega}}
+\newcommand{\bvarepsilon}{\boldsymbol{\varepsilon}}
+\newcommand{\bvartheta}{\boldsymbol{\vartheta}}
+\newcommand{\bvaromega}{\boldsymbol{\varomega}}
+\newcommand{\bvarrho}{\boldsymbol{\varrho}}
+\newcommand{\bvarzeta}{\boldsymbol{\varsigma}}  %NB really sigma
+\newcommand{\bvarsigma}{\boldsymbol{\varsigma}}
+\newcommand{\bvarphi}{\boldsymbol{\varphi}}
+%
+% Bold upright capital Greek letters
+%
+\newcommand{\bGamma}{\boldsymbol{\Gamma}}
+\newcommand{\bDelta}{\boldsymbol{\Delta}}
+\newcommand{\bTheta}{\boldsymbol{\Theta}}
+\newcommand{\bLambda}{\boldsymbol{\Lambda}}
+\newcommand{\bXi}{\boldsymbol{\Xi}}
+\newcommand{\bPi}{\boldsymbol{\Pi}}
+\newcommand{\bSigma}{\boldsymbol{\Sigma}}
+\newcommand{\bUpsilon}{\boldsymbol{\Upsilon}}
+\newcommand{\bPhi}{\boldsymbol{\Phi}}
+\newcommand{\bPsi}{\boldsymbol{\Psi}}
+\newcommand{\bOmega}{\boldsymbol{\Omega}}
+%
+% Bold versions of miscellaneous symbols
+%
+\newcommand{\bpartial}{\boldsymbol{\partial}}
+\newcommand{\bell}{\boldsymbol{\ell}}
+\newcommand{\bimath}{\boldsymbol{\imath}}
+\newcommand{\bjmath}{\boldsymbol{\jmath}}
+\newcommand{\binfty}{\boldsymbol{\infty}}
+\newcommand{\bnabla}{\boldsymbol{\nabla}}
+\newcommand{\bdot}{\boldsymbol{\cdot}}
+%
+% Symbols for caption
+%
+\renewcommand{\opensquare}{\mbox{$\square$}}
+\renewcommand{\opentriangle}{\mbox{$\vartriangle$}}
+\renewcommand{\opentriangledown}{\mbox{$\triangledown$}}
+\renewcommand{\opendiamond}{\mbox{$\lozenge$}}
+\renewcommand{\fullsquare}{\mbox{$\blacksquare$}}
+\newcommand{\fulldiamond}{\mbox{$\blacklozenge$}}
+\newcommand{\fullstar}{\mbox{$\bigstar$}}
+\newcommand{\fulltriangle}{\mbox{$\blacktriangle$}}
+\newcommand{\fulltriangledown}{\mbox{$\blacktriangledown$}}
+
+\endinput
+%% 
+%% End of file `iopams.sty'.
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopart.cls
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopart.cls	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopart.cls	(revision 392)
@@ -0,0 +1,1007 @@
+%% 
+%% This is file `iopart.cls'
+%% 
+%% This file is distributed in the hope that it will be useful, 
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
+%% 
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
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+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+%
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesClass{iopart}[1996/06/10 v0.0 IOP Journals LaTeX article class]
+\newcommand\@ptsize{0}
+\newif\if@restonecol
+\newif\if@titlepage
+\newif\ifiopams
+\@titlepagefalse
+\DeclareOption{a4paper}
+   {\setlength\paperheight {297mm}%
+    \setlength\paperwidth  {210mm}}
+\DeclareOption{letterpaper}
+   {\setlength\paperheight {11in}%
+    \setlength\paperwidth  {8.5in}}
+\DeclareOption{landscape}
+   {\setlength\@tempdima   {\paperheight}%
+    \setlength\paperheight {\paperwidth}%
+    \setlength\paperwidth  {\@tempdima}}
+\DeclareOption{10pt}{\renewcommand\@ptsize{0}}
+\DeclareOption{11pt}{\renewcommand\@ptsize{2}} % No 11pt version
+\DeclareOption{12pt}{\renewcommand\@ptsize{2}}
+\DeclareOption{draft}{\setlength\overfullrule{5pt}}
+\DeclareOption{final}{\setlength\overfullrule{0pt}}
+\DeclareOption{titlepage}{\@titlepagetrue}
+\DeclareOption{notitlepage}{\@titlepagefalse}
+\ExecuteOptions{letterpaper,final}
+\ProcessOptions
+\DeclareMathAlphabet{\bi}{OML}{cmm}{b}{it}
+\DeclareMathAlphabet{\bcal}{OMS}{cmsy}{b}{n}
+\input{iopart1\@ptsize.clo}
+\setlength\lineskip{1\p@}
+\setlength\normallineskip{1\p@}
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+\renewcommand\dblfloatpagefraction{.8}
+%
+\pretolerance=5000
+\tolerance=8000
+%
+% Headings for all pages apart from first
+%
+\def\ps@headings{\let\@oddfoot\@empty
+      \let\@evenfoot\@empty
+      \def\@evenhead{\thepage\hfil\itshape\rightmark}%
+      \def\@oddhead{{\itshape\leftmark}\hfil\thepage}%
+      \let\@mkboth\markboth
+      \let\sectionmark\@gobble
+      \let\subsectionmark\@gobble}
+%
+% Headings for first page
+%
+\def\ps@myheadings{\let\@oddfoot\@empty\let\@evenfoot\@empty
+    \let\@oddhead\@empty\let\@evenhead\@empty
+    \let\@mkboth\@gobbletwo
+    \let\sectionmark\@gobble
+    \let\subsectionmark\@gobble}
+%
+% \maketitle just ends page
+%
+\newcommand\maketitle{\newpage}
+%
+% Article titles
+%
+% Usage: \title[Short title]{Full title}
+% [Short title] is optional; use where title is too long
+% or contains footnotes, 50 characters maximum 
+%
+\renewcommand{\title}{\@ifnextchar[{\@stitle}{\@ftitle}}
+\def\@stitle[#1]#2{\markboth{#1}{#1}%
+    \thispagestyle{myheadings}%
+    \vspace*{3pc}{\exhyphenpenalty=10000\hyphenpenalty=10000 
+    \Large\raggedright\noindent
+    \bf#2\par}}
+\def\@ftitle#1{\markboth{#1}{#1}%
+    \thispagestyle{myheadings}%
+    \vspace*{3pc}{\exhyphenpenalty=10000\hyphenpenalty=10000 
+    \Large\raggedright\noindent
+    \bf#1\par}}
+%
+% Can use \paper instead of \title
+%
+\let\paper=\title
+%
+% Generic title command for articles other than papers
+%
+% Usage: \article[Short title]{ARTICLE TYPE}{Full title}
+% [Short title] is optional; use where title is too long
+% or contains footnotes, 50 characters maximum 
+%
+\newcommand{\article}{\@ifnextchar[{\@sarticle}{\@farticle}}
+\def\@sarticle[#1]#2#3{\markboth{#1}{#1}%
+    \thispagestyle{myheadings}%
+     \vspace*{.5pc}%
+    {\parindent=\mathindent \bf #2\par}%
+     \vspace*{1.5pc}%
+    {\exhyphenpenalty=10000\hyphenpenalty=10000
+     \Large\raggedright\noindent
+     \bf#3\par}}%
+\def\@farticle#1#2{\markboth{#2}{#2}%
+    \thispagestyle{myheadings}%
+     \vspace*{.5pc}%
+    {\parindent=\mathindent \bf #1\par}%
+     \vspace*{1.5pc}%
+    {\exhyphenpenalty=10000\hyphenpenalty=10000
+     \Large\raggedright\noindent
+     \bf#2\par}}%
+%
+% Letters to the Editor
+%
+% Usage \letter{Full title}
+% No short title is required for Letters
+%
+\def\letter#1{\article[Letter to the Editor]{LETTER TO THE EDITOR}{#1}}
+%
+% Review articles
+%
+% Usage: \review[Short title]{Full title}
+% [Short title] is optional; use where title is too long
+% or contains footnotes, 50 characters maximum 
+%
+\def\review{\@ifnextchar[{\@sreview}{\@freview}}
+\def\@sreview[#1]#2{\@sarticle[#1]{REVIEW ARTICLE}{#2}}
+\def\@freview#1{\@farticle{REVIEW ARTICLE}{#1}}
+%
+% Topical Review
+%
+% Usage: \topical[Short title]{Full title}
+% [Short title] is optional; use where title is too long
+% or contains footnotes, 50 characters maximum 
+%
+\def\topical{\@ifnextchar[{\@stopical}{\@ftopical}}
+\def\@stopical[#1]#2{\@sarticle[#1]{TOPICAL REVIEW}{#2}}
+\def\@ftopical#1{\@farticle{TOPICAL REVIEW}{#1}}
+%
+% Comments
+%
+% Usage: \comment[Short title]{Full title}
+% [Short title] is optional; use where title is too long
+% or contains footnotes, 50 characters maximum 
+%
+\def\comment{\@ifnextchar[{\@scomment}{\@fcomment}}
+\def\@scomment[#1]#2{\@sarticle[#1]{COMMENT}{#2}}
+\def\@fcomment#1{\@farticle{COMMENT}{#1}}
+%
+% Rapid Communications
+%
+% Usage: \rapid[Short title]{Full title}
+% [Short title] is optional; use where title is too long
+% or contains footnotes, 50 characters maximum 
+%
+\def\rapid{\@ifnextchar[{\@srapid}{\@frapid}}
+\def\@srapid[#1]#2{\@sarticle[#1]{RAPID COMMUNICATION}{#2}}
+\def\@frapid#1{\@farticle{RAPID COMMUNICATION}{#1}}
+%
+% Notes
+%
+% Usage: \note[Short title]{Full title}
+% [Short title] is optional; use where title is too long
+% or contains footnotes, 50 characters maximum 
+%
+\def\note{\@ifnextchar[{\@snote}{\@fnote}}
+\def\@snote[#1]#2{\@sarticle[#1]{NOTE}{#2}}
+\def\@fnote#1{\@farticle{NOTE}{#1}}
+%
+% Preliminary Communications
+%
+% Usage: \prelim[Short title]{Full title}
+% [Short title] is optional; use where title is too long
+% or contains footnotes, 50 characters maximum 
+%
+\def\prelim{\@ifnextchar[{\@sprelim}{\@fprelim}}
+\def\@sprelim[#1]#2{\@sarticle[#1]{PRELIMINARY COMMUNICATION}{#2}}
+\def\@fprelim#1{\@farticle{PRELIMINARY COMMUNICATION}{#1}}
+%
+% List of authors
+%
+% Usage \author[Short form]{List of all authors}
+% The short form excludes footnote symbols linking authors to addresses 
+% and is used for running heads in printed version (but not on preprints)
+%
+\renewcommand{\author}{\@ifnextchar[{\@sauthor}{\@fauthor}}
+\def\@sauthor[#1]#2{\markright{#1}    % for production only
+   \vspace*{1.5pc}%
+   \begin{indented}%
+   \item[]\normalsize\bf\raggedright#2
+   \end{indented}%
+   \smallskip}
+\def\@fauthor#1{%\markright{#1}         for production only
+   \vspace*{1.5pc}%
+   \begin{indented}%
+   \item[]\normalsize\bf\raggedright#1
+   \end{indented}%
+   \smallskip}
+%
+% Affiliation (authors address)
+%
+% Usage: \address{Address of first author}
+%        \address{Address of second author}
+% Use once for each address, use symbols \dag \ddag \S \P $\|$
+% to connect authors with addresses
+%
+\newcommand{\address}[1]{\begin{indented}
+   \item[]\rm\raggedright #1
+   \end{indented}}
+%
+% American Mathematical Society Classification Numbers
+% Usage: \ams{57.XX, 58.XX}
+%
+\def\ams#1{\vspace{10pt}
+     \begin{indented}
+     \item[]\rm AMS classification scheme numbers: #1\par
+     \end{indented}}
+%
+% A single Physics & Astronomy Classification Number
+% Usage \pacno{31.10}
+%
+\def\pacno#1{\vspace{10pt}
+     \begin{indented}
+     \item[]\rm PACS number: #1\par
+     \end{indented}}
+%
+% Physics & Astronomy Classification Numbers (more than one)
+% Usage \pacs{31.10, 31.20T}
+%
+\def\pacs#1{\vspace{10pt}
+     \begin{indented}
+     \item[]\rm PACS numbers: #1\par
+     \end{indented}}
+%
+% Submission details. If \jl command used journals name printed
+% otherwise Institute of Physics Publishing 
+%
+\def\submitted{\vspace{28pt plus 10pt minus 18pt}
+     \noindent{\small\rm Submitted to: {\it \journal}\par}}
+%
+\def\submitto#1{\vspace{28pt plus 10pt minus 18pt}
+     \noindent{\small\rm Submitted to: {\it #1}\par}}
+%
+% For articles (other than Letters) not divided into sections
+% Usage \nosections Start of text
+%
+\def\nosections{\vspace{30\p@ plus12\p@ minus12\p@}
+    \noindent\ignorespaces}
+%
+% Acknowledgments (no heading if letter)
+% Usage \ack for Acknowledgments, \ackn for Acknowledgement
+%
+\def\ack{\ifletter\bigskip\noindent\ignorespaces\else
+    \section*{Acknowledgments}\fi}
+\def\ackn{\ifletter\bigskip\noindent\ignorespaces\else
+    \section*{Acknowledgment}\fi}
+%
+% Footnotes: symbols selected in order \dag (1), \ddag (2), \S (3), 
+% $\|$ (4), $\P$ (5), $^+$ (6), $^*$ (7), \sharp (8), \dagger\dagger (9)
+% unless optional argument of [<num>] use to specify required symbol, 
+% 1=\dag, 2=\ddag, etc
+% Usage: \footnote{Text of footnote}
+%        \footnote[3]{Text of footnote}
+%
+\def\footnoterule{}%
+\setcounter{footnote}{1}
+\long\def\@makefntext#1{\parindent 1em\noindent 
+ \makebox[1em][l]{\footnotesize\rm$\m@th{\fnsymbol{footnote}}$}%
+ \footnotesize\rm #1}
+\def\@makefnmark{\hbox{${\fnsymbol{footnote}}\m@th$}}
+\def\@thefnmark{\fnsymbol{footnote}}
+\def\footnote{\@ifnextchar[{\@xfootnote}{\stepcounter{\@mpfn}%
+       \begingroup\let\protect\noexpand
+       \xdef\@thefnmark{\thempfn}\endgroup
+     \@footnotemark\@footnotetext}}
+\def\@xfootnote[#1]{\setcounter{footnote}{#1}%
+   \addtocounter{footnote}{-1}\footnote}
+\def\@fnsymbol#1{\ifcase#1\or \dagger\or \ddagger\or \S\or
+   \|\or \P\or ^{+}\or ^{\tsty *}\or \sharp
+   \or \dagger\dagger \else\@ctrerr\fi\relax}
+%
+% IOP Journals
+%
+\newcounter{jnl}
+\newcommand{\jl}[1]{\setcounter{jnl}{#1}}
+\def\journal{\ifnum\thejnl=0 Institute of Physics Publishing\fi
+        \ifnum\thejnl=1 J. Phys.\ A: Math.\ Gen.\ \fi
+        \ifnum\thejnl=2 J. Phys.\ B: At.\ Mol.\ Opt.\ Phys.\ \fi
+        \ifnum\thejnl=3 J. Phys.:\ Condens. Matter\ \fi
+        \ifnum\thejnl=4 J. Phys.\ G: Nucl.\ Part.\ Phys.\ \fi
+        \ifnum\thejnl=5 Inverse Problems\ \fi
+        \ifnum\thejnl=6 Class. Quantum Grav.\ \fi
+        \ifnum\thejnl=7 Network: Comput.\ Neural Syst.\ \fi
+        \ifnum\thejnl=8 Nonlinearity\ \fi
+        \ifnum\thejnl=9 J. Opt. B: Quantum Semiclass. Opt.\ \fi
+        \ifnum\thejnl=10 Waves Random Media\ \fi
+        \ifnum\thejnl=11 J. Opt. A: Pure Appl. Opt.\ \fi
+        \ifnum\thejnl=12 Phys. Med. Biol.\ \fi
+        \ifnum\thejnl=13 Modelling Simul.\ Mater.\ Sci.\ Eng.\ \fi
+        \ifnum\thejnl=14 Plasma Phys. Control. Fusion\ \fi
+        \ifnum\thejnl=15 Physiol. Meas.\ \fi
+        \ifnum\thejnl=16 Combust. Theory Modelling\ \fi
+        \ifnum\thejnl=17 High Perform.\ Polym.\ \fi
+        \ifnum\thejnl=18 Public Understand. Sci.\ \fi
+        \ifnum\thejnl=19 Rep.\ Prog.\ Phys.\ \fi
+        \ifnum\thejnl=20 J.\ Phys.\ D: Appl.\ Phys.\ \fi
+        \ifnum\thejnl=21 Supercond.\ Sci.\ Technol.\ \fi
+        \ifnum\thejnl=22 Semicond.\ Sci.\ Technol.\ \fi
+        \ifnum\thejnl=23 Nanotechnology\ \fi
+        \ifnum\thejnl=24 Measur.\ Sci.\ Technol.\ \fi
+        \ifnum\thejnl=25 Plasma.\ Sources\ Sci.\ Technol.\ \fi
+        \ifnum\thejnl=26 Smart\ Mater.\ Struct.\ \fi
+        \ifnum\thejnl=27 J.\ Micromech.\ Microeng.\ \fi
+        \ifnum\thejnl=28 Distrib.\ Syst.\ Engng\ \fi
+        \ifnum\thejnl=29 Bioimaging\ \fi
+        \ifnum\thejnl=30 J.\ Radiol. Prot.\ \fi
+        \ifnum\thejnl=31 Europ. J. Phys.\ \fi
+        \ifnum\thejnl=32 J. Opt. A: Pure Appl. Opt.\ \fi
+        \ifnum\thejnl=33 New. J. Phys.\ \fi}
+%
+% E-mail addresses (to provide links from headers)
+%
+\def\eads#1{\vspace*{5pt}\address{E-mail: #1}}
+\def\ead#1{\vspace*{5pt}\address{E-mail: \mailto{#1}}}
+\def\mailto#1{{\tt #1}}
+%
+% Switches
+%
+\newif\ifletter
+%
+\setcounter{secnumdepth}{3}
+\newcounter {section}
+\newcounter {subsection}[section]
+\newcounter {subsubsection}[subsection]
+\newcounter {paragraph}[subsubsection]
+\newcounter {subparagraph}[paragraph]
+\renewcommand\thesection       {\arabic{section}}
+\renewcommand\thesubsection    {\thesection.\arabic{subsection}}
+\renewcommand\thesubsubsection {\thesubsection.\arabic{subsubsection}}
+\renewcommand\theparagraph     {\thesubsubsection.\arabic{paragraph}}
+\renewcommand\thesubparagraph  {\theparagraph.\arabic{subparagraph}}
+\def\@chapapp{Section}
+
+\newcommand\section{\@startsection {section}{1}{\z@}%
+                   {-3.5ex \@plus -1ex \@minus -.2ex}%
+                   {2.3ex \@plus.2ex}%
+                   {\reset@font\normalsize\bfseries\raggedright}}
+\newcommand\subsection{\@startsection{subsection}{2}{\z@}%
+                   {-3.25ex\@plus -1ex \@minus -.2ex}%
+                   {1.5ex \@plus .2ex}%
+                   {\reset@font\normalsize\itshape\raggedright}}
+\newcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
+                                     {-3.25ex\@plus -1ex \@minus -.2ex}%
+                                     {-1em \@plus .2em}%
+                                     {\reset@font\normalsize\itshape}}
+\newcommand\paragraph{\@startsection{paragraph}{4}{\z@}%
+                                    {3.25ex \@plus1ex \@minus.2ex}%
+                                    {-1em}%
+                                    {\reset@font\normalsize\itshape}}
+\newcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}%
+                                       {3.25ex \@plus1ex \@minus .2ex}%
+                                       {-1em}%
+                                      {\reset@font\normalsize\itshape}}
+\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
+     \let\@svsec\@empty\else
+     \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname. }\fi
+     \@tempskipa #5\relax
+      \ifdim \@tempskipa>\z@
+        \begingroup #6\relax
+          \noindent{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%
+        \endgroup
+       \csname #1mark\endcsname{#7}\addcontentsline
+         {toc}{#1}{\ifnum #2>\c@secnumdepth \else
+                      \protect\numberline{\csname the#1\endcsname}\fi
+                    #7}\else
+        \def\@svsechd{#6\hskip #3\relax  %% \relax added 2 May 90
+                   \@svsec #8\csname #1mark\endcsname
+                      {#7}\addcontentsline
+                           {toc}{#1}{\ifnum #2>\c@secnumdepth \else
+                             \protect\numberline{\csname the#1\endcsname}\fi
+                       #7}}\fi
+     \@xsect{#5}}
+%
+\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
+   \ifdim \@tempskipa>\z@
+     \begingroup #4\noindent{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup
+   \else \def\@svsechd{#4\hskip #1\relax #5}\fi
+    \@xsect{#3}}
+
+\setlength\leftmargini{2em}
+\setlength\leftmarginii{2em}
+\setlength\leftmarginiii{1.8em}
+\setlength\leftmarginiv{1.6em}
+\setlength\leftmarginv{1em}
+\setlength\leftmarginvi{1em}
+\setlength\leftmargin{\leftmargini}
+\setlength\labelsep{0.5em}
+\setlength\labelwidth{\leftmargini}
+\addtolength\labelwidth{-\labelsep}
+\@beginparpenalty -\@lowpenalty
+\@endparpenalty   -\@lowpenalty
+\@itempenalty     -\@lowpenalty
+\renewcommand\theenumi{\roman{enumi}}
+\renewcommand\theenumii{\alph{enumii}}
+\renewcommand\theenumiii{\arabic{enumiii}}
+\renewcommand\theenumiv{\Alph{enumiv}}
+\newcommand\labelenumi{(\theenumi)}
+\newcommand\labelenumii{(\theenumii)}
+\newcommand\labelenumiii{\theenumiii.}
+\newcommand\labelenumiv{(\theenumiv)}
+\renewcommand\p@enumii{(\theenumi)}
+\renewcommand\p@enumiii{(\theenumi.\theenumii)}
+\renewcommand\p@enumiv{(\theenumi.\theenumii.\theenumiii)}
+\newcommand\labelitemi{$\m@th\bullet$}
+\newcommand\labelitemii{\normalfont\bfseries --}
+\newcommand\labelitemiii{$\m@th\ast$}
+\newcommand\labelitemiv{$\m@th\cdot$}
+\newenvironment{description}
+               {\list{}{\labelwidth\z@ \itemindent-\leftmargin
+                        \let\makelabel\descriptionlabel}}
+               {\endlist}
+\newcommand\descriptionlabel[1]{\hspace\labelsep
+                                \normalfont\bfseries #1}
+\newenvironment{abstract}{%
+      \vspace{16pt plus3pt minus3pt}
+      \begin{indented}
+      \item[]{\bfseries \abstractname.}\quad\rm\ignorespaces} 
+      {\end{indented}\if@titlepage\newpage\else\vspace{18\p@ plus18\p@}\fi}
+\newenvironment{verse}
+               {\let\\=\@centercr
+                \list{}{\itemsep      \z@
+                        \itemindent   -1.5em%
+                        \listparindent\itemindent
+                        \rightmargin  \leftmargin
+                        \advance\leftmargin 1.5em}%
+                \item[]}
+               {\endlist}
+\newenvironment{quotation}
+               {\list{}{\listparindent 1.5em%
+                        \itemindent    \listparindent
+                        \rightmargin   \leftmargin
+                        \parsep        \z@ \@plus\p@}%
+                \item[]}
+               {\endlist}
+\newenvironment{quote}
+               {\list{}{\rightmargin\leftmargin}%
+                \item[]}
+               {\endlist}
+\newenvironment{titlepage}
+    {%
+        \@restonecolfalse\newpage
+      \thispagestyle{empty}%
+      \if@compatibility
+        \setcounter{page}{0}
+      \else
+        \setcounter{page}{1}%
+      \fi}%
+    {\newpage\setcounter{page}{1}}
+\def\appendix{\@ifnextchar*{\@appendixstar}{\@appendix}}
+\def\@appendix{\eqnobysec\@appendixstar}
+\def\@appendixstar{\@@par
+ \ifnumbysec                         %  Added 30/4/94 to get Table A1,
+ \@addtoreset{table}{section}        %  Table B1 etc if numbering by
+ \@addtoreset{figure}{section}\fi    %  section
+ \setcounter{section}{0}
+ \setcounter{subsection}{0}
+ \setcounter{subsubsection}{0}
+ \setcounter{equation}{0}
+ \setcounter{figure}{0}
+ \setcounter{table}{0}
+ \def\thesection{Appendix \Alph{section}}   
+ \def\theequation{\ifnumbysec
+      \Alph{section}.\arabic{equation}\else
+      \Alph{section}\arabic{equation}\fi}  % Comment A\arabic{equation} maybe
+ \def\thetable{\ifnumbysec                 % better? 15/4/95
+      \Alph{section}\arabic{table}\else
+      A\arabic{table}\fi}
+ \def\thefigure{\ifnumbysec
+      \Alph{section}\arabic{figure}\else
+      A\arabic{figure}\fi}}
+\def\noappendix{\setcounter{figure}{0}
+     \setcounter{table}{0}
+     \def\thetable{\arabic{table}}
+     \def\thefigure{\arabic{figure}}}
+\setlength\arraycolsep{5\p@}
+\setlength\tabcolsep{6\p@}
+\setlength\arrayrulewidth{.4\p@}
+\setlength\doublerulesep{2\p@}
+\setlength\tabbingsep{\labelsep}
+\skip\@mpfootins = \skip\footins
+\setlength\fboxsep{3\p@}
+\setlength\fboxrule{.4\p@}
+\renewcommand\theequation{\arabic{equation}}
+\newcounter{figure}
+\renewcommand\thefigure{\@arabic\c@figure}
+\def\fps@figure{tbp}
+\def\ftype@figure{1}
+\def\ext@figure{lof}
+\def\fnum@figure{\figurename~\thefigure}
+\newenvironment{figure}{\footnotesize\rm\@float{figure}}%
+    {\end@float\normalsize\rm}
+\newenvironment{figure*}{\footnotesize\rm\@dblfloat{figure}}{\end@dblfloat}
+\newcounter{table}
+\renewcommand\thetable{\@arabic\c@table}
+\def\fps@table{tbp}
+\def\ftype@table{2}
+\def\ext@table{lot}
+\def\fnum@table{\tablename~\thetable}
+\newenvironment{table}{\footnotesize\rm\@float{table}}%
+   {\end@float\normalsize\rm}
+\newenvironment{table*}{\footnotesize\rm\@dblfloat{table}}%
+   {\end@dblfloat\normalsize\rm}
+\newlength\abovecaptionskip
+\newlength\belowcaptionskip
+\setlength\abovecaptionskip{10\p@}
+\setlength\belowcaptionskip{0\p@}
+%
+% Added redefinition of \@caption so captions are not written to 
+% aux file therefore less need to \protect fragile commands
+%
+\long\def\@caption#1[#2]#3{\par\begingroup
+    \@parboxrestore
+    \normalsize
+    \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
+  \endgroup}
+% 
+\long\def\@makecaption#1#2{\vskip \abovecaptionskip 
+ \begin{indented}
+ \item[]{\bf #1.} #2
+ \end{indented}\vskip\belowcaptionskip}
+\let\@portraitcaption=\@makecaption
+
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
+\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
+\ifiopams
+\renewcommand{\cal}{\protect\pcal}
+\else
+\newcommand{\cal}{\protect\pcal}
+\fi
+\newcommand{\pcal}{\@fontswitch{\relax}{\mathcal}}
+\ifiopams
+\renewcommand{\mit}{\protect\pmit}
+\else
+\newcommand{\mit}{\protect\pmit}
+\fi
+\newcommand{\pmit}{\@fontswitch{\relax}{\mathnormal}}
+\newcommand\@pnumwidth{1.55em}
+\newcommand\@tocrmarg {2.55em}
+\newcommand\@dotsep{4.5}
+\setcounter{tocdepth}{3}
+\newcommand\tableofcontents{%
+    \section*{\contentsname
+        \@mkboth{\uppercase{\contentsname}}{\uppercase{\contentsname}}}%
+    \@starttoc{toc}%
+    }
+\newcommand\l@part[2]{%
+  \ifnum \c@tocdepth >-2\relax
+    \addpenalty{\@secpenalty}%
+    \addvspace{2.25em \@plus\p@}%
+    \begingroup
+      \setlength\@tempdima{3em}%
+      \parindent \z@ \rightskip \@pnumwidth
+      \parfillskip -\@pnumwidth
+      {\leavevmode
+       \large \bfseries #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
+       \nobreak
+       \if@compatibility
+         \global\@nobreaktrue
+         \everypar{\global\@nobreakfalse\everypar{}}
+      \fi
+    \endgroup
+  \fi}
+\newcommand\l@section[2]{%
+  \ifnum \c@tocdepth >\z@
+    \addpenalty{\@secpenalty}%
+    \addvspace{1.0em \@plus\p@}%
+    \setlength\@tempdima{1.5em}%
+    \begingroup
+      \parindent \z@ \rightskip \@pnumwidth
+      \parfillskip -\@pnumwidth
+      \leavevmode \bfseries
+      \advance\leftskip\@tempdima
+      \hskip -\leftskip
+      #1\nobreak\hfil \nobreak\hbox to\@pnumwidth{\hss #2}\par
+    \endgroup
+  \fi}
+\newcommand\l@subsection   {\@dottedtocline{2}{1.5em}{2.3em}}
+\newcommand\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
+\newcommand\l@paragraph    {\@dottedtocline{4}{7.0em}{4.1em}}
+\newcommand\l@subparagraph {\@dottedtocline{5}{10em}{5em}}
+\newcommand\listoffigures{%
+    \section*{\listfigurename
+      \@mkboth{\uppercase{\listfigurename}}%
+              {\uppercase{\listfigurename}}}%
+    \@starttoc{lof}%
+    }
+\newcommand\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
+\newcommand\listoftables{%
+    \section*{\listtablename
+      \@mkboth{\uppercase{\listtablename}}{\uppercase{\listtablename}}}%
+    \@starttoc{lot}%
+    }
+\let\l@table\l@figure
+\newenvironment{theindex}
+               {\if@twocolumn
+                  \@restonecolfalse
+                \else
+                  \@restonecoltrue
+                \fi
+                \columnseprule \z@
+                \columnsep 35\p@
+                \twocolumn[\section*{\indexname}]%
+                \@mkboth{\uppercase{\indexname}}%
+                        {\uppercase{\indexname}}%
+                \thispagestyle{plain}\parindent\z@
+                \parskip\z@ \@plus .3\p@\relax
+                \let\item\@idxitem}
+               {\if@restonecol\onecolumn\else\clearpage\fi}
+\newcommand\@idxitem  {\par\hangindent 40\p@}
+\newcommand\subitem   {\par\hangindent 40\p@ \hspace*{20\p@}}
+\newcommand\subsubitem{\par\hangindent 40\p@ \hspace*{30\p@}}
+\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax}
+\newcommand\contentsname{Contents}
+\newcommand\listfigurename{List of Figures}
+\newcommand\listtablename{List of Tables}
+\newcommand\refname{References}
+\newcommand\indexname{Index}
+\newcommand\figurename{Figure}
+\newcommand\tablename{Table}
+\newcommand\partname{Part}
+\newcommand\appendixname{Appendix}
+\newcommand\abstractname{Abstract}
+\newcommand\today{\number\day\space\ifcase\month\or
+  January\or February\or March\or April\or May\or June\or
+  July\or August\or September\or October\or November\or December\fi
+  \space\number\year}
+\setlength\columnsep{10\p@}
+\setlength\columnseprule{0\p@}
+
+\newcommand{\Tables}{\clearpage\section*{Tables and table captions}
+    \def\fps@table{hp}\noappendix}
+\newcommand{\Figures}{\clearpage\section*{Figure captions}
+    \def\fps@figure{hp}\noappendix}
+%
+\newcommand{\Figure}[1]{\begin{figure}
+  \caption{#1}
+  \end{figure}}
+%
+\newcommand{\Table}[1]{\begin{table}
+  \caption{#1}
+  \begin{indented}
+  \lineup
+  \item[]\begin{tabular}{@{}l*{15}{l}}}
+
+\def\endTable{\end{tabular}\end{indented}\end{table}}
+\let\endtab=\endTable
+%
+\newcommand{\fulltable}[1]{\begin{table}
+  \caption{#1}
+  \lineup
+  \begin{tabular*}{\textwidth}{@{}l*{15}{@{\extracolsep{0pt plus 12pt}}l}}}
+\def\endfulltable{\end{tabular*}\end{table}}
+%
+%
+\newcommand{\Bibliography}[1]{\section*{References}\par\numrefs{#1}}
+\newcommand{\References}{\section*{References}\par\refs}
+
+\def\thebibliography#1{\list
+ {\hfil[\arabic{enumi}]}{\topsep=0\p@\parsep=0\p@
+ \partopsep=0\p@\itemsep=0\p@
+ \labelsep=5\p@\itemindent=-10\p@
+ \settowidth\labelwidth{\footnotesize[#1]}%
+ \leftmargin\labelwidth
+ \advance\leftmargin\labelsep
+ \advance\leftmargin -\itemindent
+ \usecounter{enumi}}\footnotesize
+ \def\newblock{\ }
+ \sloppy\clubpenalty4000\widowpenalty4000
+ \sfcode`\.=1000\relax}
+\let\endthebibliography=\endlist
+\def\numrefs#1{\begin{thebibliography}{#1}}
+\def\endnumrefs{\end{thebibliography}}
+\let\endbib=\endnumrefs
+%
+\def\thereferences{\list{}{\topsep=0\p@\parsep=0\p@
+ \partopsep=0\p@\itemsep=0\p@\labelsep=0\p@\itemindent=-18\p@
+\labelwidth=0\p@\leftmargin=18\p@
+}\footnotesize\rm
+\def\newblock{\ }
+\sloppy\clubpenalty4000\widowpenalty4000
+\sfcode`\.=1000\relax
+}
+%
+\let\endthereferences=\endlist
+\newlength{\indentedwidth}
+\newdimen\mathindent
+\indentedwidth=\mathindent
+%
+% Macro to used for references in the Harvard system
+%
+\newenvironment{harvard}{\list{}{\topsep=0\p@\parsep=0\p@
+\partopsep=0\p@\itemsep=0\p@\labelsep=0\p@\itemindent=-18\p@
+\labelwidth=0\p@\leftmargin=18\p@
+}\footnotesize\rm
+\def\newblock{\ }
+\sloppy\clubpenalty4000\widowpenalty4000
+\sfcode`\.=1000\relax}{\endlist}
+%
+\def\refs{\begin{harvard}}
+\def\endrefs{\end{harvard}}
+%
+\newenvironment{indented}{\begin{indented}}{\end{indented}}
+\newenvironment{varindent}[1]{\begin{varindent}{#1}}{\end{varindent}}
+%
+\def\indented{\list{}{\itemsep=0\p@\labelsep=0\p@\itemindent=0\p@
+   \labelwidth=0\p@\leftmargin=\mathindent\topsep=0\p@\partopsep=0\p@
+   \parsep=0\p@\listparindent=15\p@}\footnotesize\rm}
+
+\let\endindented=\endlist 
+
+\def\varindent#1{\setlength{\varind}{#1}%
+   \list{}{\itemsep=0\p@\labelsep=0\p@\itemindent=0\p@
+   \labelwidth=0\p@\leftmargin=\varind\topsep=0\p@\partopsep=0\p@
+   \parsep=0\p@\listparindent=15\p@}\footnotesize\rm}
+
+\let\endvarindent=\endlist 
+
+\def\[{\relax\ifmmode\@badmath\else
+ \begin{trivlist}
+ \@beginparpenalty\predisplaypenalty
+ \@endparpenalty\postdisplaypenalty
+ \item[]\leavevmode
+ \hbox to\linewidth\bgroup$ \displaystyle
+ \hskip\mathindent\bgroup\fi}
+\def\]{\relax\ifmmode \egroup $\hfil \egroup \end{trivlist}\else \@badmath \fi}
+\def\equation{\@beginparpenalty\predisplaypenalty
+ \@endparpenalty\postdisplaypenalty
+\refstepcounter{equation}\trivlist \item[]\leavevmode
+ \hbox to\linewidth\bgroup $ \displaystyle
+\hskip\mathindent}
+\def\endequation{$\hfil \displaywidth\linewidth\@eqnnum\egroup \endtrivlist}
+%
+\@namedef{equation*}{\[}
+\@namedef{endequation*}{\]}
+%
+\def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
+\global\@eqnswtrue
+\global\@eqcnt\z@\tabskip\mathindent\let\\=\@eqncr
+\abovedisplayskip\topsep\ifvmode\advance\abovedisplayskip\partopsep\fi
+\belowdisplayskip\abovedisplayskip
+\belowdisplayshortskip\abovedisplayskip
+\abovedisplayshortskip\abovedisplayskip
+$$\halign to
+\linewidth\bgroup\@eqnsel$\displaystyle\tabskip\z@
+ {##{}}$&\global\@eqcnt\@ne $\displaystyle{{}##{}}$\hfil
+ &\global\@eqcnt\tw@ $\displaystyle{{}##}$\hfil
+ \tabskip\@centering&\llap{##}\tabskip\z@\cr}
+\def\endeqnarray{\@@eqncr\egroup
+ \global\advance\c@equation\m@ne$$\global\@ignoretrue }
+\mathindent = 6pc
+%
+\def\eqalign#1{\null\vcenter{\def\\{\cr}\openup\jot\m@th
+  \ialign{\strut$\displaystyle{##}$\hfil&$\displaystyle{{}##}$\hfil
+      \crcr#1\crcr}}\,}
+%
+\def\eqalignno#1{\displ@y \tabskip\z@skip
+  \halign to\displaywidth{\hspace{5pc}$\@lign\displaystyle{##}$%
+    \tabskip\z@skip
+    &$\@lign\displaystyle{{}##}$\hfill\tabskip\@centering
+    &\llap{$\@lign\hbox{\rm##}$}\tabskip\z@skip\crcr
+    #1\crcr}}
+%
+\newif\ifnumbysec
+\def\theequation{\ifnumbysec
+      \arabic{section}.\arabic{equation}\else
+      \arabic{equation}\fi}
+\def\eqnobysec{\numbysectrue\@addtoreset{equation}{section}}
+
+\newcounter{eqnval}
+\def\numparts{\addtocounter{equation}{1}%
+     \setcounter{eqnval}{\value{equation}}%
+     \setcounter{equation}{0}%
+     \def\theequation{\ifnumbysec
+     \arabic{section}.\arabic{eqnval}{\it\alph{equation}}%
+     \else\arabic{eqnval}{\it\alph{equation}}\fi}}
+
+\def\endnumparts{\def\theequation{\ifnumbysec
+     \arabic{section}.\arabic{equation}\else
+     \arabic{equation}\fi}%
+     \setcounter{equation}{\value{eqnval}}}
+%
+\def\cases#1{%
+     \left\{\,\vcenter{\def\\{\cr}\normalbaselines\openup1\jot\m@th%
+     \ialign{\strut$\displaystyle{##}\hfil$&\tqs
+     \rm##\hfil\crcr#1\crcr}}\right.}%
+%
+\newcommand{\e}{\mathrm{e}}
+\newcommand{\rme}{\mathrm{e}}
+\newcommand{\rmi}{\mathrm{i}}
+\newcommand{\rmd}{\mathrm{d}}
+\renewcommand{\qquad}{\hspace*{25pt}}
+\newcommand{\tdot}[1]{\stackrel{\dots}{#1}}   % Added 1/9/94
+\newcommand{\tqs}{\hspace*{25pt}}
+\newcommand{\fl}{\hspace*{-\mathindent}}
+\newcommand{\Tr}{\mathop{\mathrm{Tr}}\nolimits}
+\newcommand{\tr}{\mathop{\mathrm{tr}}\nolimits}
+\newcommand{\Or}{\mathord{\mathrm{O}}} %changed from \mathop 20/1/95
+\newcommand{\lshad}{[\![}
+\newcommand{\rshad}{]\!]}
+\newcommand{\case}[2]{{\textstyle\frac{#1}{#2}}}
+\def\pt(#1){({\it #1\/})}
+\newcommand{\dsty}{\displaystyle}
+\newcommand{\tsty}{\textstyle}
+\newcommand{\ssty}{\scriptstyle}
+\newcommand{\sssty}{\scriptscriptstyle}
+\def\lo#1{\llap{${}#1{}$}}
+\def\eql{\llap{${}={}$}}
+\def\lsim{\llap{${}\sim{}$}}
+\def\lsimeq{\llap{${}\simeq{}$}}
+\def\lequiv{\llap{${}\equiv{}$}}
+%
+\newcommand{\eref}[1]{(\ref{#1})}
+\newcommand{\sref}[1]{section~\ref{#1}}
+\newcommand{\fref}[1]{figure~\ref{#1}}
+\newcommand{\tref}[1]{table~\ref{#1}}
+\newcommand{\Eref}[1]{Equation (\ref{#1})}
+\newcommand{\Sref}[1]{Section~\ref{#1}}
+\newcommand{\Fref}[1]{Figure~\ref{#1}}
+\newcommand{\Tref}[1]{Table~\ref{#1}}
+
+\newcommand{\opencircle}{\mbox{\Large$\circ\,$}}  % moved Large outside maths
+\newcommand{\opensquare}{\mbox{$\rlap{$\sqcap$}\sqcup$}}
+\newcommand{\opentriangle}{\mbox{$\triangle$}}
+\newcommand{\opentriangledown}{\mbox{$\bigtriangledown$}}
+\newcommand{\opendiamond}{\mbox{$\diamondsuit$}}
+\newcommand{\fullcircle}{\mbox{{\Large$\bullet\,$}}} % moved Large outside maths
+\newcommand{\fullsquare}{\,\vrule height5pt depth0pt width5pt}
+\newcommand{\dotted}{\protect\mbox{${\mathinner{\cdotp\cdotp\cdotp\cdotp\cdotp\cdotp}}$}}
+\newcommand{\dashed}{\protect\mbox{-\; -\; -\; -}}
+\newcommand{\broken}{\protect\mbox{-- -- --}}
+\newcommand{\longbroken}{\protect\mbox{--- --- ---}}
+\newcommand{\chain}{\protect\mbox{--- $\cdot$ ---}}
+\newcommand{\dashddot}{\protect\mbox{--- $\cdot$ $\cdot$ ---}}
+\newcommand{\full}{\protect\mbox{------}}
+
+\def\;{\protect\psemicolon}
+\def\psemicolon{\relax\ifmmode\mskip\thickmuskip\else\kern .3333em\fi}
+\def\lineup{\def\0{\hbox{\phantom{\footnotesize\rm 0}}}%
+    \def\m{\hbox{$\phantom{-}$}}%
+    \def\-{\llap{$-$}}}
+%
+%%%%%%%%%%%%%%%%%%%%%
+% Tables rules      %
+%%%%%%%%%%%%%%%%%%%%%
+
+\newcommand{\boldarrayrulewidth}{1\p@} 
+% Width of bold rule in tabular environment.
+
+\def\bhline{\noalign{\ifnum0=`}\fi\hrule \@height  
+\boldarrayrulewidth \futurelet \@tempa\@xhline}
+
+\def\@xhline{\ifx\@tempa\hline\vskip \doublerulesep\fi
+      \ifnum0=`{\fi}}
+
+%
+% Rules for tables with extra space around
+%
+\newcommand{\br}{\ms\bhline\ms}
+\newcommand{\mr}{\ms\hline\ms}
+%
+\newcommand{\centre}[2]{\multispan{#1}{\hfill #2\hfill}}
+\newcommand{\crule}[1]{\multispan{#1}{\hspace*{\tabcolsep}\hrulefill
+  \hspace*{\tabcolsep}}}
+\newcommand{\fcrule}[1]{\ifnum\thetabtype=1\multispan{#1}{\hrulefill
+  \hspace*{\tabcolsep}}\else\multispan{#1}{\hrulefill}\fi}
+%
+% Extra spaces for tables and displayed equations
+%
+\newcommand{\ms}{\noalign{\vspace{3\p@ plus2\p@ minus1\p@}}}
+\newcommand{\bs}{\noalign{\vspace{6\p@ plus2\p@ minus2\p@}}}
+\newcommand{\ns}{\noalign{\vspace{-3\p@ plus-1\p@ minus-1\p@}}}
+\newcommand{\es}{\noalign{\vspace{6\p@ plus2\p@ minus2\p@}}\displaystyle}%
+%
+\newcommand{\etal}{{\it et al\/}\ }
+\newcommand{\dash}{------}
+\newcommand{\nonum}{\par\item[]}                %\par added 1/9/93
+\newcommand{\mat}[1]{\underline{\underline{#1}}}
+%
+% abbreviations for IOPP journals
+%
+\newcommand{\CQG}{{\it Class. Quantum Grav.} }
+\newcommand{\CTM}{{\it Combust. Theory Modelling\/} }
+\newcommand{\DSE}{{\it Distrib. Syst. Engng\/} }
+\newcommand{\EJP}{{\it Eur. J. Phys.} } 
+\newcommand{\HPP}{{\it High Perform. Polym.} }              % added 4/5/93
+\newcommand{\IP}{{\it Inverse Problems\/} }
+\newcommand{\JHM}{{\it J. Hard Mater.} }                    % added 4/5/93
+\newcommand{\JO}{{\it J. Opt.} }
+\newcommand{\JOA}{{\it J. Opt. A: Pure Appl. Opt.} }
+\newcommand{\JOB}{{\it J. Opt. B: Quantum Semiclass. Opt.} }
+\newcommand{\JPA}{{\it J. Phys. A: Math. Gen.} }
+\newcommand{\JPB}{{\it J. Phys. B: At. Mol. Phys.} }      %1968-87
+\newcommand{\jpb}{{\it J. Phys. B: At. Mol. Opt. Phys.} } %1988 and onwards
+\newcommand{\JPC}{{\it J. Phys. C: Solid State Phys.} }   %1968--1988
+\newcommand{\JPCM}{{\it J. Phys.: Condens. Matter\/} }    %1989 and onwards
+\newcommand{\JPD}{{\it J. Phys. D: Appl. Phys.} }
+\newcommand{\JPE}{{\it J. Phys. E: Sci. Instrum.} }
+\newcommand{\JPF}{{\it J. Phys. F: Met. Phys.} }
+\newcommand{\JPG}{{\it J. Phys. G: Nucl. Phys.} }         %1975--1988
+\newcommand{\jpg}{{\it J. Phys. G: Nucl. Part. Phys.} }   %1989 and onwards
+\newcommand{\MSMSE}{{\it Modelling Simulation Mater. Sci. Eng.} }
+\newcommand{\MST}{{\it Meas. Sci. Technol.} }                 %1990 and onwards
+\newcommand{\NET}{{\it Network: Comput. Neural Syst.} }
+\newcommand{\NJP}{{\it New J. Phys.} }
+\newcommand{\NL}{{\it Nonlinearity\/} }
+\newcommand{\NT}{{\it Nanotechnology} }
+\newcommand{\PAO}{{\it Pure Appl. Optics\/} }
+\newcommand{\PM}{{\it Physiol. Meas.} }                        % added 4/5/93
+\newcommand{\PMB}{{\it Phys. Med. Biol.} }
+\newcommand{\PPCF}{{\it Plasma Phys. Control. Fusion\/} }      % added 4/5/93
+\newcommand{\PSST}{{\it Plasma Sources Sci. Technol.} }
+\newcommand{\PUS}{{\it Public Understand. Sci.} }
+\newcommand{\QO}{{\it Quantum Opt.} }
+\newcommand{\QSO}{{\em Quantum Semiclass. Opt.} }
+\newcommand{\RPP}{{\it Rep. Prog. Phys.} }
+\newcommand{\SLC}{{\it Sov. Lightwave Commun.} }               % added 4/5/93 
+\newcommand{\SST}{{\it Semicond. Sci. Technol.} }
+\newcommand{\SUST}{{\it Supercond. Sci. Technol.} }
+\newcommand{\WRM}{{\it Waves Random Media\/} }
+\newcommand{\JMM}{{\it J. Micromech. Microeng.\/} }
+%
+% Other commonly quoted journals
+%
+\newcommand{\AC}{{\it Acta Crystallogr.} }
+\newcommand{\AM}{{\it Acta Metall.} }
+\newcommand{\AP}{{\it Ann. Phys., Lpz.} }
+\newcommand{\APNY}{{\it Ann. Phys., NY\/} }
+\newcommand{\APP}{{\it Ann. Phys., Paris\/} }
+\newcommand{\CJP}{{\it Can. J. Phys.} }
+\newcommand{\JAP}{{\it J. Appl. Phys.} }
+\newcommand{\JCP}{{\it J. Chem. Phys.} }
+\newcommand{\JJAP}{{\it Japan. J. Appl. Phys.} }
+\newcommand{\JP}{{\it J. Physique\/} }
+\newcommand{\JPhCh}{{\it J. Phys. Chem.} }
+\newcommand{\JMMM}{{\it J. Magn. Magn. Mater.} }
+\newcommand{\JMP}{{\it J. Math. Phys.} }
+\newcommand{\JOSA}{{\it J. Opt. Soc. Am.} }
+\newcommand{\JPSJ}{{\it J. Phys. Soc. Japan\/} }
+\newcommand{\JQSRT}{{\it J. Quant. Spectrosc. Radiat. Transfer\/} }
+\newcommand{\NC}{{\it Nuovo Cimento\/} }
+\newcommand{\NIM}{{\it Nucl. Instrum. Methods\/} }
+\newcommand{\NP}{{\it Nucl. Phys.} }
+\newcommand{\PL}{{\it Phys. Lett.} }
+\newcommand{\PR}{{\it Phys. Rev.} }
+\newcommand{\PRL}{{\it Phys. Rev. Lett.} }
+\newcommand{\PRS}{{\it Proc. R. Soc.} }
+\newcommand{\PS}{{\it Phys. Scr.} }
+\newcommand{\PSS}{{\it Phys. Status Solidi\/} }
+\newcommand{\PTRS}{{\it Phil. Trans. R. Soc.} }
+\newcommand{\RMP}{{\it Rev. Mod. Phys.} }
+\newcommand{\RSI}{{\it Rev. Sci. Instrum.} }
+\newcommand{\SSC}{{\it Solid State Commun.} }
+\newcommand{\ZP}{{\it Z. Phys.} }
+%
+\pagestyle{headings}
+\pagenumbering{arabic}      % Arabic page numbers
+\raggedbottom
+\onecolumn
+\endinput
+%% 
+%% End of file `iopart.cls'.
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopart10.clo
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopart10.clo	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopart10.clo	(revision 392)
@@ -0,0 +1,124 @@
+%% 
+%% This is file `iopart10.clo'
+%% 
+%% This file is distributed in the hope that it will be useful, 
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
+%% 
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+\ProvidesFile{iopart10.clo}[1997/01/13 v1.0 IOP Book file (size option)]
+\renewcommand\normalsize{%
+   \@setfontsize\normalsize\@xpt\@xiipt
+   \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
+   \abovedisplayshortskip \z@ \@plus3\p@
+   \belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@
+   \belowdisplayskip \abovedisplayskip
+   \let\@listi\@listI}
+\normalsize
+\newcommand\small{%
+   \@setfontsize\small\@ixpt{11}%
+   \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@
+   \abovedisplayshortskip \z@ \@plus2\p@
+   \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@
+   \def\@listi{\leftmargin\leftmargini
+               \topsep 4\p@ \@plus2\p@ \@minus2\p@
+               \parsep 2\p@ \@plus\p@ \@minus\p@
+               \itemsep \parsep}%
+   \belowdisplayskip \abovedisplayskip
+}
+\newcommand\footnotesize{%
+   \@setfontsize\footnotesize\@viiipt{9.5}%
+   \abovedisplayskip 6\p@ \@plus2\p@ \@minus4\p@
+   \abovedisplayshortskip \z@ \@plus\p@
+   \belowdisplayshortskip 3\p@ \@plus\p@ \@minus2\p@
+   \def\@listi{\leftmargin\leftmargini
+               \topsep 3\p@ \@plus\p@ \@minus\p@
+               \parsep 2\p@ \@plus\p@ \@minus\p@
+               \itemsep \parsep}%
+   \belowdisplayskip \abovedisplayskip
+}
+\newcommand\scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt}
+\newcommand\tiny{\@setfontsize\tiny\@vpt\@vipt}
+\newcommand\large{\@setfontsize\large\@xiipt{14}}
+\newcommand\Large{\@setfontsize\Large\@xivpt{18}}
+\newcommand\LARGE{\@setfontsize\LARGE\@xviipt{22}}
+\newcommand\huge{\@setfontsize\huge\@xxpt{25}}
+\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}
+\if@twocolumn
+  \setlength\parindent{12\p@}
+\else
+  \setlength\parindent{15\p@}
+\fi
+\setlength\headheight{12\p@}
+\setlength\headsep   {12\p@}
+\setlength\topskip   {10\p@}
+\setlength\footskip{20\p@}
+\setlength\maxdepth{.5\topskip}
+\setlength\@maxdepth\maxdepth
+\setlength\textwidth{31pc}
+\setlength\textheight{49pc}
+\setlength\oddsidemargin  {24\p@}
+\setlength\evensidemargin {24\p@}
+\setlength\marginparwidth {72\p@}
+\setlength\marginparsep {10\p@}
+\setlength\marginparpush{5\p@}
+\setlength\topmargin{\z@}
+\setlength\footnotesep{6.65\p@}
+\setlength{\skip\footins}  {9\p@ \@plus 4\p@ \@minus 2\p@}
+\setlength\floatsep       {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\textfloatsep   {20\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\intextsep      {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\dblfloatsep    {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\@fptop{0\p@}
+\setlength\@fpsep{8\p@ \@plus 2fil}
+\setlength\@fpbot{0\p@}
+\setlength\@dblfptop{0\p@}
+\setlength\@dblfpsep{8\p@ \@plus 2fil}
+\setlength\@dblfpbot{0\p@}
+\setlength\partopsep{2\p@ \@plus 1\p@ \@minus 1\p@}
+\def\@listI{\leftmargin\leftmargini
+            \parsep=\z@ 
+            \topsep=5\p@ \@plus3\p@ \@minus3\p@
+            \itemsep=3\p@ \@plus2\p@ \@minus\p@}
+\let\@listi\@listI
+\@listi
+\def\@listii {\leftmargin\leftmarginii
+     \labelwidth\leftmarginii
+     \advance\labelwidth-\labelsep
+     \topsep=2\p@ \@plus2\p@ \@minus\p@
+     \parsep=\z@
+     \itemsep=\parsep}
+\def\@listiii{\leftmargin\leftmarginiii
+     \labelwidth\leftmarginiii
+     \advance\labelwidth-\labelsep
+     \topsep=\z@
+     \parsep=\z@
+     \partopsep=\z@
+     \itemsep=\z@}
+\def\@listiv {\leftmargin\leftmarginiv
+     \labelwidth\leftmarginiv
+     \advance\labelwidth-\labelsep}
+\def\@listv  {\leftmargin\leftmarginv
+     \labelwidth\leftmarginv
+     \advance\labelwidth-\labelsep}
+\def\@listvi {\leftmargin\leftmarginvi
+     \labelwidth\leftmarginvi
+     \advance\labelwidth-\labelsep}
+\endinput
+%% 
+%% End of file `iopart.clo'.
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopart12.clo
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopart12.clo	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/iopart12.clo	(revision 392)
@@ -0,0 +1,125 @@
+%% 
+%% This is file `iopart12.clo'
+%% 
+%% This file is distributed in the hope that it will be useful, 
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
+%% 
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+\ProvidesFile{iopart12.clo}[1997/01/15 v1.0 LaTeX2e file (size option)]
+\renewcommand\normalsize{%
+   \@setfontsize\normalsize\@xiipt{16}%
+   \abovedisplayskip 12\p@ \@plus3\p@ \@minus7\p@
+   \abovedisplayshortskip \z@ \@plus3\p@
+   \belowdisplayshortskip 6.5\p@ \@plus3.5\p@ \@minus3\p@
+   \belowdisplayskip \abovedisplayskip
+   \let\@listi\@listI}
+\normalsize
+\newcommand\small{%
+   \@setfontsize\small\@xipt{14}%
+   \abovedisplayskip 11\p@ \@plus3\p@ \@minus6\p@
+   \abovedisplayshortskip \z@ \@plus3\p@
+   \belowdisplayshortskip 6.5\p@ \@plus3.5\p@ \@minus3\p@
+   \def\@listi{\leftmargin\leftmargini
+               \topsep 9\p@ \@plus3\p@ \@minus5\p@
+               \parsep 4.5\p@ \@plus2\p@ \@minus\p@
+               \itemsep \parsep}%
+   \belowdisplayskip \abovedisplayskip
+}
+\newcommand\footnotesize{%
+%   \@setfontsize\footnotesize\@xpt\@xiipt
+   \@setfontsize\footnotesize\@xpt{13}%
+   \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
+   \abovedisplayshortskip \z@ \@plus3\p@
+   \belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@
+   \def\@listi{\leftmargin\leftmargini
+               \topsep 6\p@ \@plus2\p@ \@minus2\p@
+               \parsep 3\p@ \@plus2\p@ \@minus\p@
+               \itemsep \parsep}%
+   \belowdisplayskip \abovedisplayskip
+}
+\newcommand\scriptsize{\@setfontsize\scriptsize\@viiipt{9.5}}
+\newcommand\tiny{\@setfontsize\tiny\@vipt\@viipt}
+\newcommand\large{\@setfontsize\large\@xivpt{18}}
+\newcommand\Large{\@setfontsize\Large\@xviipt{22}}
+\newcommand\LARGE{\@setfontsize\LARGE\@xxpt{25}}
+\newcommand\huge{\@setfontsize\huge\@xxvpt{30}}
+\let\Huge=\huge
+\if@twocolumn
+  \setlength\parindent{14\p@}
+\else
+  \setlength\parindent{18\p@}
+\fi
+\setlength\headheight{14\p@}
+\setlength\headsep{14\p@}
+\setlength\topskip{12\p@}
+\setlength\footskip{24\p@}
+\setlength\maxdepth{.5\topskip}
+\setlength\@maxdepth\maxdepth
+\setlength\textwidth{37.2pc}
+\setlength\textheight{56pc}
+\setlength\oddsidemargin  {\z@}
+\setlength\evensidemargin {\z@}
+\setlength\marginparwidth {72\p@}
+\setlength\marginparsep{10\p@}
+\setlength\marginparpush{5\p@}
+\setlength\topmargin{-12pt}
+\setlength\footnotesep{8.4\p@}
+\setlength{\skip\footins} {10.8\p@ \@plus 4\p@ \@minus 2\p@}
+\setlength\floatsep       {14\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\textfloatsep   {24\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\intextsep      {16\p@ \@plus 4\p@ \@minus 4\p@}
+\setlength\dblfloatsep    {16\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\dbltextfloatsep{24\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\@fptop{0\p@}
+\setlength\@fpsep{10\p@ \@plus 1fil}
+\setlength\@fpbot{0\p@}
+\setlength\@dblfptop{0\p@}
+\setlength\@dblfpsep{10\p@ \@plus 1fil}
+\setlength\@dblfpbot{0\p@}
+\setlength\partopsep{3\p@ \@plus 2\p@ \@minus 2\p@}
+\def\@listI{\leftmargin\leftmargini
+     \parsep=\z@
+     \topsep=6\p@  \@plus3\p@ \@minus3\p@
+     \itemsep=3\p@ \@plus2\p@ \@minus1\p@}
+\let\@listi\@listI
+\@listi
+\def\@listii {\leftmargin\leftmarginii
+     \labelwidth\leftmarginii
+     \advance\labelwidth-\labelsep
+     \topsep=3\p@ \@plus2\p@ \@minus\p@
+     \parsep=\z@
+     \itemsep=\parsep}
+\def\@listiii{\leftmargin\leftmarginiii
+     \labelwidth\leftmarginiii
+     \advance\labelwidth-\labelsep
+     \topsep=\z@
+     \parsep=\z@
+     \partopsep=\z@
+     \itemsep=\z@}
+\def\@listiv {\leftmargin\leftmarginiv
+     \labelwidth\leftmarginiv
+     \advance\labelwidth-\labelsep}
+\def\@listv{\leftmargin\leftmarginv
+     \labelwidth\leftmarginv
+     \advance\labelwidth-\labelsep}
+\def\@listvi {\leftmargin\leftmarginvi
+     \labelwidth\leftmarginvi
+     \advance\labelwidth-\labelsep}
+\endinput
+%% 
+%% End of file `iopart12.clo'.
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/ioplau2e.tex
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/ioplau2e.tex	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/ioplau2e.tex	(revision 392)
@@ -0,0 +1,1933 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%    INSTITUTE OF PHYSICS PUBLISHING                                   %
+%                                                                      %
+%   `Preparing an article for publication in an Institute of Physics   %
+%    Publishing journal using LaTeX'                                   %
+%                                                                      %
+%    LaTeX source code `ioplau2e.tex' used to generate `author         %
+%    guidelines', the documentation explaining and demonstrating use   %
+%    of the Institute of Physics Publishing LaTeX preprint files       %
+%    `iopart.cls, iopart12.clo and iopart10.clo'.                      %
+%                                                                      %
+%    `ioplau2e.tex' itself uses LaTeX with `iopart.cls'                %
+%                                                                      %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%
+% First we have a character check
+%
+% ! exclamation mark    " double quote  
+% # hash                ` opening quote (grave)
+% & ampersand           ' closing quote (acute)
+% $ dollar              % percent       
+% ( open parenthesis    ) close paren.  
+% - hyphen              = equals sign
+% | vertical bar        ~ tilde         
+% @ at sign             _ underscore
+% { open curly brace    } close curly   
+% [ open square         ] close square bracket
+% + plus sign           ; semi-colon    
+% * asterisk            : colon
+% < open angle bracket  > close angle   
+% , comma               . full stop
+% ? question mark       / forward slash 
+% \ backslash           ^ circumflex
+%
+% ABCDEFGHIJKLMNOPQRSTUVWXYZ 
+% abcdefghijklmnopqrstuvwxyz 
+% 1234567890
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+\documentclass[12pt]{iopart}
+% Uncomment next line if AMS fonts required
+%\usepackage{iopams}  
+\begin{document}
+
+\title[Author guidelines for IOPP journals]{Preparing an article for 
+publication in an Institute of Physics Publishing journal using \LaTeXe}
+
+\author{Neil Scriven\dag\ and Romneya Robertson\ddag  
+\footnote[3]{To
+whom correspondence should be addressed (romneya.robertson@iop.org)}
+}
+
+\address{\dag\ Production Editor, Institute of Physics 
+Publishing, Dirac
+House, Temple Back, Bristol BS1 6BE, UK}
+
+\address{\ddag\ Electronic Services Specialist, Institute of Physics Publishing, 
+Dirac House, Temple Back, Bristol BS1 6BE, UK}
+
+
+\begin{abstract}
+This document describes the  preparation of an article using \LaTeXe\ and 
+\verb"iopart.cls" (the IOP \LaTeXe\ preprint class file).
+This class file is designed to help 
+authors produce preprints in a form suitable for submission to any of the
+journals published by Institute of Physics Publishing.
+
+Authors submitting to any IOP journal, i.e.\ 
+to double-column journals as well as the single-column  
+ones,
+should follow the guidelines set out here. 
+On acceptance, their source code will be converted to 
+the appropriate journal format at Institute of Physics Publishing. 
+For the printed version, Times fonts (and Helvetica in double-column 
+journals) will be used instead of the Computer Modern used in the preprint
+form. 
+
+\end{abstract}
+
+%Uncomment for PACS numbers title message
+%\pacs{00.00, 20.00, 42.10}
+
+% Uncomment for Submitted to journal title message
+%\submitto{\JPA}
+
+% Comment out if separate title page not required
+\maketitle
+
+\section{Introduction}
+Many authors use \LaTeX\ to 
+produce their typescripts
+and we can use the source code to produce the printed version;  this gives 
+more rapid publication with a smaller chance of typographical 
+error.
+
+We explain here the procedures and specific requirements for 
+the preparation and presentation of text and illustrations for 
+articles in \LaTeXe\ using the IOPP class file 
+\verb"iopart.cls". We also illustrate \verb"iopart.cls" through 
+its use in the creation of this document. The
+class file and accompanying documentation are available to all authors 
+and copies can be 
+obtained (free of charge)
+\begin{itemize}
+\item from the World Wide Web (\verb"http://www.iop.org/Journals/texstyle")
+by downloading zipped files for PCs or tar compressed format files for
+Unix
+\item from the World Wide Web by using our 
+Author Enquiry Service\\ (\verb"http://www.iop.org/Journals/AES")
+to request that the files be sent on disk
+\item by contacting the Electronic Services Specialist,
+Institute of Physics Publishing, Dirac House, Temple Back, 
+Bristol BS1~6BE, UK (\verb"esub@ioppublishing.co.uk") and requesting 
+the files be sent by e-mail or on 3$1\over2$ inch PC or Macintosh disk
+\end{itemize}
+
+There are 10 and 12 point versions of the style, but the 12pt
+version should be used for preprints and is selected by opening the file
+with the initial line:
+\begin{verbatim}
+\documentclass[12pt]{iopart}
+\end{verbatim}
+If the \verb"[12pt]" is omitted the article will be set in 10pt type (i.e.
+in the same size type as in the printed journal).
+The 12pt version 
+of the style gives a `preprint' form with a page width and type size 
+1.2 times larger than that for normal single-column journals
+with extra spacing between lines. The page depth is less than 1.2 times
+the normal page depth so that articles will fit on the page on both 
+A4 and Letter paper.
+This form is the one required for 
+the initial submission of a typescript for 
+refereeing and copy editing. Authors need not aim to optimize the line and
+page breaks as they will inevitably change when converted to the final
+format for printing.
+
+The 10 pt version has the same page dimensions and type sizes as a
+single-column journal and shows approximately 
+how the text would appear in print. It can also be used to produce 
+camera-ready copy for journal special issues.
+
+Other compatible
+\LaTeXe\ packages can be used if they are available in the normal
+distribution of \LaTeXe; if it is essential to use
+a non-standard package then the extra files needed to process the 
+article must also be sent in. Authors should be aware that the final 
+version will be printed on a different page size and using different fonts 
+to the preprint version so that any special effects used should not
+contain material that is not easily scalable.
+
+We recommend that authors use the IOPP \LaTeXe\ class file; 
+however articles prepared using almost any  version of \TeX\ or \LaTeX\ 
+can be 
+handled (${\cal AMS}$\TeX, L${\cal AMS}$TeX, PHYZZX, etc) 
+and authors not using the IOPP 
+style files
+can submit their source code in the way described 
+below. 
+Alterations to the source code will be made in-house by the 
+Production Department in order to conform to IOPP house style and 
+journal format.
+
+We aim to maintain our normal standards 
+for articles published from \TeX\ and \LaTeX\ files so we reserve 
+the right to make small alterations  to clarify and improve the 
+English where necessary and to put the article into IOPP house style.
+
+\subsection{Double-column journals}
+Authors writing for double-column journals should also use the IOPP preprint
+macros. Conversion from the single-column format to the double-column 
+output required for printing will be done by the Production Department 
+at Institute of Physics
+Publishing.
+
+
+\section{Submitting new articles}
+
+\subsection{Sending in files for submission to internally refereed journals}
+\label{int}
+Articles for consideration for publication in the journals listed in 
+table~\ref{e-mail} may be submitted electronically without the need to 
+supply hard copies of the manuscript. 
+Those journals are refereed internally. 
+Articles for consideration by all other IOPP journals must be submitted in hard copy form. Electronic files can then be sent in on acceptance or when requested by the editor.
+
+Authors are asked to prepare their articles using the 12pt 
+style and submit by World Wide Web upload, e-mail, FTP or on PC or Mac 
+floppy disk.
+Please send all files necessary to reproduce your article, 
+including the article itself and all figure files. 
+Combine all your files into a single archive using a compression or archiving 
+program. Utilities like WinZIP or StuffIt will both archive and compress your 
+files. Alternatively you could archive your files using a program like TAR 
+and compress the resulting file using gzip.
+
+
+\subsection{By World Wide Web upload}
+Users of Netscape (version 2 or higher) or Internet Explorer 
+(version 4 or higher) can submit using our World Wide Web upload form.
+This can be found at 
+\verb"http://www.iop.org/Journals/authorsubs"
+Complete the on-line form with information about your submission and then upload 
+your article in one of two ways.
+
+\begin{enumerate}
+\item Having created a single compressed file containing an archive of your text 
+and graphics files, use the `Browse...' button on the form to select that file.
+
+\item If your article has already been posted to the LANL e-print archive, select 
+the archive name and enter the e-print number. ({\it Note}: We cannot download 
+your paper from the LANL e-print server until it has been publicly released, 
+usually by 10 pm on the day you submitted it there.) Use the `Transfer File' 
+button at the bottom of the form to submit your file.
+\end{enumerate}
+
+
+\subsection{By E-mail} 
+\label{byemail}
+Files should be sent to the relevant journal mailbox (see table~\ref{e-mail}).
+Please send articles as attachments to e-mail messages. 
+Any additional files such as figure files should be combined into a single archive with the article file as described in section~\ref{int}. 
+All information about the submission should be included in the main body of the message.
+This must include:
+\begin{itemize}
+\item Your full name
+\item The name of the journal to which you are submitting
+\item The full title of the article
+\item The full list of authors
+\item The article type (e.g. Paper, Letter to the Editor etc.)
+\item The status of the article (i.e. new revised or accepted)
+\item Your postal address
+\item Your e-mail address
+\item Your telephone number
+\item Your fax number (if applicable)
+\item The article file format (i.e. \LaTeXe)
+\item The number of separate figure files
+\end{itemize}
+
+\begin{table}
+\caption{\label{e-mail}E-mail addresses for all the journals to which authors can 
+submit electronically.}
+\lineup
+\begin{tabular}{@{}ll}
+\br
+Journal&{\rm E-mail address}\\
+\mr
+Journal of Physics A: Mathematical and General&jphysa@ioppublishing.co.uk\\
+Journal of Physics B: Atomic, Molecular and Optical Physics
+&jphysb@ioppublishing.co.uk\\
+Journal of Physics: Condensed Matter&jpcm@ioppublishing.co.uk\\
+Journal of Physics D: Applied Physics&jphysd@ioppublishing.co.uk\\
+Journal of Physics G: Nuclear and Particle Physics&jphysg@ioppublishing.co.uk\\ 
+Classical and Quantum Gravity&cqg@ioppublishing.co.uk\\ 
+Combustion Theory and Modelling&ctm@ioppublishing.co.uk\\ 
+European Journal of Physics&ejp@ioppublishing.co.uk\\ 
+Inverse Problems&ip@ioppublishing.co.uk\\ 
+High Performance Polymers&hpp@ioppublishing.co.uk\\
+Journal of Micromechanics and Microengineering&jmm@ioppublishing.co.uk\\ 
+Journal of Optics A: Pure and Applied Optics&jopa@ioppublishing.co.uk\\ 
+Journal of Optics B: Quantum and Semiclassical Optics&jopb@ioppublishing.co.uk\\
+Measurement Science and Technology&mst@ioppublishing.co.uk\\ 
+Nanotechnology&nano@ioppublishing.co.uk\\ 
+Nonlinearity&non@ioppublishing.co.uk\\ 
+New Journal of Physics&njp@ioppublishing.co.uk\\
+Physics Education&ped@ioppublishing.co.uk\\ 
+Physics in Medicine and Biology&pmb@ioppublishing.co.uk\\
+Physiological Measurement&pmea@ioppublishing.co.uk\\ 
+Plasma Physics and Controlled Fusion&ppcf@ioppublishing.co.uk\\ 
+Reports on Progress in Physics&rop@ioppublishing.co.uk\\ 
+Semiconductor Science and Technology&sst@ioppublishing.co.uk\\ 
+Superconductor Science and Technology&sust@ioppublishing.co.uk\\ 
+Waves in Random Media&wrm@ioppublishing.co.uk\\  
+\br
+\end{tabular}
+\end{table}
+
+\subsection{By FTP}
+Create a file named \verb"readme.txt" containing all your submission information 
+(e.g. your name, the name of the journal you are submitting to etc. See section ~\ref{byemail} 
+for full list).
+Create a single compressed file containing an archive of your text and graphics 
+files along with the file \verb"readme.txt".
+Files should be sent by anonymous FTP to \verb"ftp.iop.org". 
+Please logon with the username {\it anonymous} and use your e-mail address as 
+the password.
+Change to the directory \verb"/incoming" and then change to the directory of the
+journal to which you wish to submit and
+upload your files. 
+Please do not create any new directories on our server.
+Your files will remain in the \verb"/incoming" directory for no more than 90 minutes 
+before they are moved to a secure location.
+
+\subsection{On Floppy Disk}
+Files may be sent in on 3.5 inch PC or Apple Macintosh formatted disk. 
+Please include a file named \verb"readme.txt" containing all your submission 
+information as described above.
+
+
+\section{Preparing your article}
+Using \LaTeX\ with the \verb"iopart" class file 
+provides a simple way of 
+producing an article in a form suitable for publication in one 
+of the IOPP journals. Authors may add their own macros 
+at the start of an article 
+provided they do not overwrite existing definitions and 
+that they send copies of their new macros with their text file.
+\verb"iopart" can be used with other package files such
+as those loading the AMS extension fonts 
+\verb"msam" and \verb"msbm" (these fonts provide the 
+blackboard bold alphabet 
+and various extra maths symbols as well as symbols useful in figure 
+captions); an extra style file \verb"iopams.sty" is provided to load these
+packages and provide extra definitions for bold Greek letters.
+
+In preparing your article you are 
+requested to follow these guidelines as closely as possible; this will 
+minimize the amount of file editing required and will hasten the 
+production process. This is particularly important with regard to the 
+reference list.
+
+The file name can be up to eight characters long with the suffix 
+\verb".tex". 
+Please use files names that are likely to be unique, and include 
+commented material to identify the journal, author and reference number if 
+known. The first non-commented line should be 
+\verb"\documentclass[12pt]{iopart}"  to load the preprint class 
+file. Other standard predeclared option files can be included in 
+square brackets;
+copies of any non-standard options must be sent in with the source code.
+Omitting \verb"[12pt]" produces an article with the normal journal
+page and type sizes. Macros for the individual paper not included 
+in a style file
+should be inserted in the preamble to the paper with comments to
+describe any complex or non-obvious ones.
+The start of the article text is signalled by 
+\verb"\begin{document}".
+Authors of very long articles may find it convenient to separate 
+their article 
+into a series of files each containing a section, each of which is called 
+in turn by the primary file. 
+
+\section{The title and abstract page} 
+The code for setting the title page information is slightly different from
+the normal default in \LaTeX. 
+
+\subsection{Titles and article types}
+The title is set in bold unjustified type using the command
+\verb"\title{#1}", where \verb"#1" is the title of the article. The
+first letter 
+of the title should be capitalized with the rest in lower case. 
+Mathematical expressions within the title may be left in light-face type 
+rather than bold because the Computer Modern bold maths and symbol
+fonts may not be available at the size required for the title.  
+The final 
+printed version will have bold mathematical expressions 
+in the title. If the title is unsuitable for use as a running head a short
+form can be provided as an optional argument (in square brackets)
+before the full title, i.e. \verb"\title[Short title]{Full title}".
+A short title is required 
+when the title itself is too long to 
+be used 
+as the short title or when the title contains a footnote. 
+
+For article types other than papers the IOPP class file, \verb"iopart.cls", 
+allows 
+a generic heading \verb"\article[Short title]{TYPE}{Full title}" 
+and the specific 
+definitions given in table~\ref{arttype}. In each case (apart from Letters
+to the Editor) an 
+optional argument can be used immediately after the control sequence name
+to specify the short title; where no short title is given the full title
+will be used as the running head at the top of each page apart from the
+first. 
+For Letters no short title is required as 
+the running head is automatically defined to be {\it Letter to the Editor}.
+The generic heading could be used for 
+articles such as those presented at a conference or workshop, e.g.
+\begin{verbatim}
+\article[Short title]{WORKSHOP ON HIGH-ENERGY PHYSICS}{Title}
+\end{verbatim}
+
+
+\begin{table}
+\caption{\label{arttype}Types of article defined in the {\tt iopart.cls} 
+class file.}
+\begin{tabular*}{\textwidth}{@{}l*{15}{@{\extracolsep{0pt plus12pt}}l}}
+\br
+Command&Type&Heading on first page\\
+\mr
+\verb"\title{#1}"&Paper&---\\
+\verb"\review{#1}"&Review&REVIEW\\
+\verb"\topical{#1}"&Topical review&TOPICAL REVIEW\\
+\verb"\comment{#1}"&Comment&COMMENT\\
+\verb"\note{#1}"&Note&NOTE\\
+\verb"\paper{#1}"&Paper&---\\
+\verb"\prelim{#1}"&Preliminary communication&PRELIMINARY COMMUNICATION\\
+\verb"\rapid{#1}"&Rapid communication&RAPID COMMUNICATION\\
+\verb"\letter{#1}"&Letter&LETTER TO THE EDITOR\\
+\verb"\article{#1}{#2}"&Other articles&Whatever is entered as {\tt 
+\#1}\\
+\br
+\end{tabular*}
+\end{table}
+
+\subsection{Authors' names and addresses}
+The next information required is the list of authors' names and 
+their affiliations. For the authors' names type \verb"\author{#1}", 
+where \verb"#1" is the 
+list of all authors' names. The style for the names is initials then
+surname, with a comma after all but the last 
+two names, which are separated by `and'. Initials should {\it not} have 
+full stops. First names may be used if 
+desired. If the authors are at different addresses one of the symbols 
+\dag, \ddag, \S, $\|$, \P, $^+$, *, $\sharp$ should be used after each 
+surname to reference an author to his/her address. 
+The symbols should be used in the order given.  If 
+an author has additional information to appear as a footnote, such as 
+a permanent address, and the
+footnote symbols are not being used to identify an address,
+the footnote should be entered after the surname
+as a normal \LaTeX\ footnote, without
+specifying a sign. Where footnote symbols are being used to indicate
+which address the author is at, the 
+symbol used for a footnote should be the next one from the list given 
+above and has to be selected individually using the command
+\verb"\footnote[<num>]{Text of footnote}", where \verb"<num>" is a
+number representing the position of the desired symbol in the list above,
+i.e.\ 1 for \dag, 2 for \ddag, etc.
+
+The addresses of the authors' affiliations follow the list of authors. 
+Each address is set by using
+\verb"\address{#1}" with the address as the single parameter in braces. 
+If there is more 
+than one address then the appropriate symbol should come at the start of
+the address.
+ 
+Please also add the corresponding author's e-mail address if applicable. This is done by inserting the 
+command \verb"\ead{#1}" before the command \verb"\maketitle" where \verb"#1" is the e-mail address.  
+See section~\ref{startsample} for sample coding. For more than one e-mail address, please use the command 
+\verb"\eads{\mailto{#1}, \mailto{#2}}" with \verb"\mailto" surrounding each e-mail address. These 
+macros allow us to convert e-mail addresses to `mailto' links when articles are published on our 
+website.
+
+\subsection{The abstract}
+The abstract follows the addresses and
+should give readers concise information about the content 
+of the article and indicate the main results obtained and conclusions 
+drawn. It should be complete in itself with no table numbers, figure 
+numbers or references included and should not normally exceed 200 
+words.
+To indicate the start 
+of the abstract type \verb"\begin{abstract}" followed by the text of the 
+abstract (not in braces).  The abstract should normally be restricted 
+to a single paragraph and is terminated by the command
+\verb"\end{abstract}"
+
+\subsection{Subject classification numbers}
+Following the abstract come any
+Physics and Astronomy Classification System (PACS) codes
+or American Mathematical Society 
+(AMS) classification scheme numbers.  
+The command 
+\verb"\pacs{#1}", with the subject classification numbers from the  
+Physics and Astronomy Classification Scheme as the parameter, defines 
+the subject area of the paper (or for a single number \verb"\pacno{#1}").  
+If PACS numbers are not readily 
+available, {\it Physics Abstracts\/} classification scheme numbers can be 
+given instead. If this command  is omitted the 
+classification numbers for indexing
+will be allocated by IOPP staff. It is 
+unnecessary to supply PACS numbers for {\it Inverse 
+Problems} and {\it Physics in Medicine and Biology}.
+AMS classification numbers may be given as well as, or instead of, PACS 
+numbers for mathematical articles, they are specified using the 
+command \verb"\ams{#1}".
+After any classification numbers the command
+\verb"\submitto{#1}" can be inserted, where \verb"#1" is the journal name written in full or the appropriate control sequence as
+given in 
+~\ref{jlab1}. This will print a line indicating that the article has been submitted to one of the Institute of Physics journals. The command is not essential to the running of the file.  
+
+
+\subsection{Making a separate title page}
+The command \verb"\maketitle" forces a page break after the point where it
+is inserted and so to keep the header material on a separate page from the
+body of the text insert \verb"\maketitle" or \verb"\newpage" after the
+classification codes 
+or the end of the abstract. 
+If \verb"\maketitle" is not included the text of the
+article will start immediately after the abstract.  
+
+
+\subsection{Sample coding for the start of an article}
+\label{startsample}
+The code for the start of a title page of a typical paper might read:
+\begin{verbatim}
+\documentclass[12pt]{iopart}
+\begin{document}
+\title[The anomalous magnetic moment of the 
+neutrino]{The anomalous magnetic moment of the 
+neutrino and its relation to the solar neutrino problem}
+
+\author{P J Smith\dag, T M Collins\ddag, 
+R J Jones\ddag\footnote[3]{Present address:
+Department of Physics, University of Bristol, Tyndalls Park Road, 
+Bristol BS8 1TS, UK.} and Janet Williams\P}
+
+\address{\dag\ Mathematics Faculty, Open University, 
+Milton Keynes MK7~6AA, UK}
+\address{\ddag\ Department of Mathematics, 
+Imperial College, Prince Consort Road, London SW7~2BZ, UK}
+\address{\P\ Department of Computer Science, 
+University College London, Gower Street, London WC1E~6BT, UK}
+
+\ead{williams@ucl.ac.uk}
+
+\begin{abstract}
+...
+\end{abstract}
+
+\submitto{\JPG}
+\pacs{1315, 9440T}
+
+\maketitle
+\end{verbatim}
+
+\subsection{AMS macros}
+Please do not use the style file \verb"amsmath.sty" (part of the AMSTeX package) in conjunction with \verb"iopart.cls". This will result in several errors. To make use of the macros defined in \verb"amsmath.sty", we have provided the file \verb"setstack.sty" which reproduces the following useful macros from \verb"amsmath.sty":
+\begin{verbatim}
+\overset
+\underset
+\sideset
+\substack
+\boxed
+\leftroot
+\uproot
+\dddot
+\ddddot
+\varrow
+\harrow
+\end{verbatim}
+\section{The text}
+\subsection{Sections, subsections and subsubsections}
+The text of papers and reviews, but not comments or letters, should be 
+divided into sections, subsections and, where necessary, 
+subsubsections. To start a new section, end the previous paragraph and 
+then include \verb"\section" followed by the section heading within braces. 
+Numbering of sections is done {\it automatically} in the headings: 
+sections will be numbered 1, 2, 3, etc, subsections will be numbered 
+2.1, 2.2,  3.1, etc, and subsubsections will be numbered 2.3.1, 2.3.2, 
+etc.  Cross references to other sections in the text should, where
+possible, be made using 
+labels (see section~\ref{xrefs}) but can also
+be made manually. See section~\ref{eqnum} for information on the numbering of displayed equations. Subsections and subsubsections are 
+similar to sections but 
+the commands are \verb"\subsection" and \verb"\subsubsection" respectively. 
+Sections have a bold heading, subsections an italic heading and 
+subsubsections an italic heading with the text following on directly.
+\begin{verbatim}
+\section{This is the section title}
+\subsection{This is the subsection title}
+\end{verbatim}
+
+
+The first section is normally an introduction,  which should state clearly 
+the object of the work, its scope and the main advances reported, with 
+brief references to relevant results by other workers. In long papers it is 
+helpful to indicate the way in which the paper is arranged and the results 
+presented.
+
+For articles not divided into sections, precede the 
+start of the text (without leaving a blank line)
+with the command \verb"\nosections", which provides the 
+appropriate space and causes the paragraph indentation to be cancelled 
+for the first paragraph.
+
+Footnotes should be avoided whenever possible. If required they should be 
+used only for brief notes that do not fit conveniently into the text. The 
+standard \LaTeX\ macro \verb"\footnote" should be used and will normally
+give an appropriate symbol; if a footnote sign needs to be specified
+directly \verb"\footnote[<num>]{Text}" can be used instead where
+\verb"<num>" is the number of the appropriate symbol as discussed in 
+relation to authors (1~=~\verb"\dag", 2~=~\verb"\ddag", 3~=~\verb"\S", 
+etc).  
+
+\subsection{Acknowledgments}
+Authors wishing to acknowledge assistance or encouragement from 
+colleagues, special work by technical staff or financial support from 
+organizations should do so in an unnumbered Acknowledgments section 
+immediately following the last numbered section of the paper. The 
+command \verb"\ack" sets the acknowledgments heading as an unnumbered
+section. For Letters 
+\verb"\ack" does not set a heading but leaves a line space and does not 
+indent the next paragraph.
+
+\subsection{Appendices}
+Technical detail that it is necessary to include, but that interrupts 
+the flow of the article, may be consigned to an appendix. 
+Any appendices should be included at the end of the main text of the paper, after the acknowledgments section (if any) but before the reference list.
+If there are 
+two or more appendices they will be called Appendix A, Appendix B, etc. 
+Numbered equations will be in the form (A.1), (A.2), etc,
+figures will appear as figure A1, figure B1, etc and tables as table A1,
+table B1, etc.
+
+The command \verb"\appendix" is used to signify the start of the
+appendixes. Thereafter \verb"\section", \verb"\subsection", etc, will 
+give headings appropriate for an appendix. To obtain a simple heading of 
+`Appendix' use the code \verb"\section*{Appendix}". If it contains
+numbered equations, figures or tables the command \verb"\appendix" should
+precede it and \verb"\setcounter{section}{1}" must follow it. 
+ 
+\subsection{Some matters of style}
+It will help your readers if your article is written in a clear,
+consistent and concise manner. The Production Department at Institute of Physics
+Publishing will try to make sure that your work is presented to its
+readers in the best possible way without sacrificing the individuality of
+your writing.
+
+The main elements of consistency and style we look for 
+are presented in the booklet 
+{\it Notes for Authors} (available upon request from Institute of Physics 
+Publishing, 
+Dirac House, Temple Back, Bristol, BS1 6BE, UK or from our World Wide
+Web site (\verb"http://www.iop.org/Journals/nfa/"). Some recommended 
+points to note, however, are the following.
+\begin{enumerate}
+\item Authors are often inconsistent in the use of `ize' and `ise' endings.
+We recommend using `-ize' spellings (diagonalize, 
+renormalization, minimization, etc) but there are some common 
+exceptions to this, for example: devise, 
+promise and advise.
+
+\item English spellings are preferred (colour, flavour, behaviour, 
+tunnelling, artefact, focused, focusing, fibre, etc). We write of a 
+computer program on disk; otherwise, we use `programme' and `disc'.
+
+\item The words table, figure, equation and reference should be written 
+in full and {\bf not} contracted to Tab., fig., eq. and ref.
+\end{enumerate}
+
+Please check your article carefully for accuracy, consistency and clarity before
+submission. Remember that your article will probably be read by many
+people whose native language is not English and who may not therefore 
+be aware of many of the subtle meanings of words or idiomatic phases
+present in the English language. It therefore helps if you try and keep
+sentences as short and simple as possible.
+
+\section{Mathematics}
+\subsection{Two-line constructions}
+The great advantage of \LaTeX\ 
+over other text processing systems is its 
+ability to handle mathematics to almost any degree of complexity. However, 
+in order to produce an article suitable for publication within a journal, 
+authors should exercise some restraint on the constructions used.
+For simple fractions in the text the solidus \verb"/", as in 
+$\lambda/2\pi$, should be used instead of \verb"\frac" or \verb"\over", 
+care being taken to use parentheses where necessary to avoid ambiguity, 
+for example to distinguish between $1/(n-1)$ and $1/n-1$. Exceptions to 
+this are the proper fractions $\frac12$, $\frac13$, $\frac34$, 
+etc, which are better left in this form. In displayed equations 
+horizontal lines are preferable to solidi provided the equation is 
+kept within a height of two lines. A two-line solidus should be 
+avoided where possible; the construction $(\ldots)^{-1}$ should be 
+used instead; for example use:
+\begin{equation*}
+\frac{1}{M_{\rm a}}\left(\int^\infty_0{\rm d}
+\omega\;\frac{|S_o|^2}{N}\right)^{-1}
+\end{equation*}
+instead of
+\begin{equation*}
+\frac{1}{M_{\rm a}}\biggl/\int^\infty_0{\rm d}
+\omega\;\frac{|S_o|^2}{N}.
+\end{equation*}
+
+
+\subsection{Roman and italic in mathematics}
+In mathematics mode \LaTeX\ automatically sets variables in an italic 
+font. In most cases authors should accept this italicization. However, 
+there are some cases where it is better to use a Roman font; for 
+instance, IOPP journals use a Roman d for a differential d, a Roman e 
+for an exponential e and a Roman i for the square root of $-1$. To 
+accommodate this and to simplify the  typing of equations we have 
+provided some extra definitions. \verb"\rmd", \verb"\rme" and \verb"\rmi" 
+now gives Roman d, e and i respectively for use in equations, 
+e.g.\ $\rmi x\rme^{2x}\rmd x/\rmd y$ 
+is obtained by typing \verb"$\rmi x\rme^{2x}\rmd x/\rmd y$". 
+ 
+
+Certain other common mathematical functions, such as cos, sin, det and 
+ker, should appear in Roman type. \LaTeX\ provides macros for 
+most of these functions 
+(in the cases above, \verb"\cos", \verb"\sin", \verb"\det" and \verb"\ker" 
+respectively); we have also provided 
+additional definitions for $\Tr$, $\tr$ and 
+$\Or$ (\verb"\Tr", \verb"\tr" and \verb"\Or", respectively). 
+
+Subscripts and superscripts should be in Roman type if they are labels 
+rather than variables or characters that take values. For example in the 
+equation
+\[
+\epsilon_m=-g\mu_{\rm n}Bm
+\]
+$m$, the $z$ component of the nuclear spin, is italic because it can have 
+different values whereas n is Roman because it 
+is a label meaning nuclear ($\mu_{\rm n}$ 
+is the nuclear magneton).
+
+\subsection{Alignment of mathematics}
+\subsubsection{Alignment on the secondary margin.}
+IOPP style for displayed mathematics in single-column journals
+is not to centre equations, 
+as \LaTeX\ normally does, but to have each equation indented to a 
+secondary margin a fixed 
+distance from the left-hand margin of the text, except for long 
+equations that will just fit on one line, or need to be continued on 
+subsequent lines, which start full left.  
+Any continuation lines are indented the fixed amount. 
+The macros in the IOPP preprint style automatically 
+line equations up on the 
+secondary margin unless they are set within double dollar signs.
+Thus the use of double dollar signs should be avoided and the alternative
+\verb"\[ ... \]" should be used instead for unnumbered equations.
+The equation environment should normally be used for numbered single-line
+equations and the eqnarray array environment for multiline equations.
+It is then only necessary to indicate which lines 
+should start full left and this is done by including \verb"\fl" (full
+left) at the start of the lines. 
+Thus the equations:
+\begin{eqnarray}
+\phi_{k}(\vec{r})=(2\pi)^{-3/2} \exp(\rmi\vec{k}\cdot\vec{r}) \\
+N^+=\exp(\case12\pi\nu)\Gamma(1-\rmi\nu).
+\end{eqnarray} 
+are set with the code
+\begin{verbatim}
+\begin{eqnarray}
+\phi_{k}(\vec{r})=(2\pi)^{-3/2} \exp(\rmi\vec{k}\bdot\vec{r}) \\
+N^+=\exp(\case12\pi\nu)\Gamma(1-\rmi\nu).
+\end{eqnarray} 
+\end{verbatim}
+Where an equation will not fit on a line if indented but would if it 
+were not, then the equation is started full left and this is achieved 
+simply by adding \verb"\fl" to the start of the line. For example
+the equation
+\begin{equation}
+\fl R_{\rho l m,\rho'l'm'}(E)=\frac{1}{r_0}\sum_{i,j}\;\langle\rho l m r_0
+\mid\Phi_i\rangle\; [(H_{\Omega}+B)-ES_{\Omega}]^{-1}_{i,j}\;\langle\Phi_j
+\mid\rho'l'm'r_0\rangle. 
+\end{equation}
+does not fit on the line if indented to the secondary margin but fits in 
+comfortably when full left.
+
+
+For equations which do not fit on one line, even if started full left,
+the first line should be set full left with the turnover lines at the 
+secondary margin. This is achieved by using the eqnarray
+environment
+and adding \verb"\fl" at the start 
+of the first line and \verb"\\" at the end of each line (apart from
+the final line of the equation). Equations should be split at 
+mathematically sound points, often at =, + or $-$ signs or between 
+terms multiplied together. The connecting signs are not repeated and 
+appear only at the beginning of the turned-over line. A multiplication 
+sign should be added to the start of turned-over lines where the break 
+is between two multiplied terms. Where an equation is broken at an 
+equals sign (or similar, i.e.\ $\equiv$, $\le$, $\sim$, etc) the sign 
+is made more prominent by aligning it to the left of the secondary 
+margin; where it is a +, $-$ or $\times$ the sign goes to the right. 
+Alignment to the left of the secondary margin is achieved by adding 
+\verb"\lo" in front of the sign (and enclosing the sign within braces if it 
+consists of more than one character or control sequence, e.g.\ 
+\verb"\lo{:=}"). An example demonstrating these features is: 
+\begin{eqnarray} 
+\fl\langle\cos(q\Omega_s)\rangle=\frac12\int^\infty_0 
+\frac{k_s(b)}{k^{\rm tot}_s}\{\cos[q\Omega^{\rm o}_S(b_f,R^s_{x})]+
+\cos[q\Omega^{\rm i}_S(b_f,R^s_{x})]\}
+2\pi b\, \rmd b\nonumber\\ 
+\lo=\sum_c{(\mu^s_c)^2/\vert\Delta V'_s(R^s_{\rm c})\vert \over \sum_n 
+(R^s_n\mu^s_n)^2(1-V^s_n/E)^{1/2}/\vert\Delta'_s(R^s_n)\vert}\nonumber\\ 
+\times \frac12\int^{b_{\rm max}}_0 
+\{\cos[q\Omega^{\rm o}_S(b_f,R^s_{\rm c})]
++\cos[q\Omega^{\rm i}_S(b_f,R^s_{\rm c})]\} 
+b\, \rmd b/v_s(b,R^s_{\rm c}). 
+\end{eqnarray} 
+where a simplified version of the 
+code used is: 
+\begin{verbatim} 
+\begin{eqnarray} 
+\fl    <first line>  \nonumber\\ 
+\lo=   <second line> \nonumber\\
+\times <third line>  
+\end{eqnarray} 
+\end{verbatim} 
+
+Note that alignment at the secondary margin normally takes 
+precedence over aligning equals signs so there is usually no need 
+to include any ampersands within the 
+\verb"eqnarray" environment.
+
+
+\subsubsection{Secondary alignment.}
+While the primary alignment either on the secondary 
+margin or full left is adequate in most cases 
+there are examples where additional 
+alignment is desirable. Firstly, for repeated series of short 
+equations, secondly for
+equations with attached conditions and thirdly for connected 
+series of equations with a short left-hand side which together
+occupy more than a full line but where each individual 
+part is short. In these cases the \verb"eqnarray" environment 
+should be used; there will still be alignment at the 
+secondary margin but ampersands should be positioned to 
+provide the secondary alignment. For equations with conditions the
+space separating the longest part from its condition is provided by 
+\verb"\qquad". Examples of equations requiring secondary alignment are:
+\begin{eqnarray}
+A^{(3/2)}=A^{(+)}-A^{(-)}&(I=\case32)\\
+A^{(1/2)}=A^{(+)}+2A^{(-)}\qquad&(I=\case12)\\            
+A^{(0)}&({\rm otherwise}).
+\end{eqnarray}
+which is obtained with the code
+\begin{verbatim}
+\begin{eqnarray}
+A^{(3/2)}=A^{(+)}-A^{(-)}&(I=\case32)\\
+A^{(1/2)}=A^{(+)}+2A^{(-)}\qquad&(I=\case12)\\            
+A^{(0)}&({\rm otherwise}).
+\end{eqnarray}
+\end{verbatim}
+and
+\begin{eqnarray}
+C(12)&=[\vec\pi(x)\cdot\vec\phi(x+r)]\nonumber\\
+&\simeq 1-{\rm const}{r^2\over L^2}\int^L_r{x\, \rmd x\over 
+x^2}+\cdots\\
+&\simeq 1-{\rm const}{r^2\over L^2}\ln\left({L\over r}\right)+\cdots.
+\end{eqnarray}
+for which the code is
+\begin{verbatim}
+\begin{eqnarray}
+C(12)&=[\vec\pi(x)\cdot\vec\phi(x+r)]\nonumber\\
+&\simeq 1-{\rm const}{r^2\over L^2}\int^L_r{x\, \rmd x\over 
+x^2}+\cdots\\
+&\simeq 1-{\rm const}{r^2\over L^2}\ln\left({L\over r}\right)+\cdots.
+\end{eqnarray}
+\end{verbatim}
+
+\subsection{Displayed equations in double-column journals}
+The way equations are displayed in the Institute of Physics Publishing
+double-column journals differs from that in single-column journals. 
+However
+authors submitting to double-column journals can produce their equations
+as described above for single-column journals
+and conversion to the proper double-column format will
+take place here as proofs are being prepared. 
+
+\subsection{Special characters for mathematics}
+Bold italic characters are used in our journals to signify vectors (rather
+than using an upright bold or an over arrow). To obtain this effect
+use \verb"\bi{#1}" within maths mode, e.g. $\bi{ABCdef}$. If upright 
+bold characters are required in maths use \verb"\mathbf{#1}" within maths
+mode, e.g. $\mathbf{XYZabc}$. The calligraphic (script) uppercase alphabet
+is obtained with \verb"\mathcal{AB}" or \verb"\cal{CD}" 
+($\mathcal{AB}\cal{CD}$).
+
+The American Mathematical Society provides a series of extra symbol fonts
+to use with \LaTeX\ and packages containing the character definitions to
+use these fonts. Authors wishing to use Fraktur 
+\ifiopams$\mathfrak{ABC}$ \fi
+or Blackboard Bold \ifiopams$\mathbb{XYZ}$ \fi can include the appropriate
+AMS package (e.g. amsgen, amsfonts, amsbsy, amssymb) with a 
+\verb"\usepackage" command or add the command \verb"\usepackage{iopams}"
+which loads the four AMS packages mentioned above and also provides
+definitions for extra bold characters (all Greek letters and some
+additional other symbols). 
+
+The package iopams uses the definition \verb"\boldsymbol" in amsbsy
+which allows individual non-alphabetical symbols and Greek letters to be 
+made bold within equations.
+The bold Greek lowercase letters \ifiopams$\balpha \ldots\bomega$,\fi 
+are obtained with the commands 
+\verb"\balpha" \dots\ \verb"\bomega" (but note that
+bold eta\ifiopams, $\bfeta$,\fi\ is \verb"\bfeta" rather than \verb"\beta")
+and the capitals\ifiopams, $\bGamma\ldots\bOmega$,\fi\ with commands 
+\verb"\bGamma" \dots\
+\verb"\bOmega". Bold versions of the following symbols are
+predefined in iopams: 
+bold partial\ifiopams, $\bpartial$,\fi\ \verb"\bpartial",
+bold `ell'\ifiopams, $\bell$,\fi\  \verb"\bell", 
+bold imath\ifiopams, $\bimath$,\fi\  \verb"\bimath", 
+bold jmath\ifiopams, $\bjmath$,\fi\  \verb"\bjmath", 
+bold infinity\ifiopams, $\binfty$,\fi\ \verb"\binfty", 
+bold nabla\ifiopams, $\bnabla$,\fi\ \verb"\bnabla", 
+bold centred dot\ifiopams, $\bdot$,\fi\  \verb"\bdot", other 
+characters are made bold using 
+\verb"\boldsymbol{\symbolname}".
+
+Table~\ref{math-tab2} lists some other macros for use in 
+mathematics with a brief description of their purpose.
+Both \verb"\ms" (medium space) and \verb"\bs" (big space) can be used to
+provide extra spacing between lines of a displayed equation or table.
+This space may be necessary when several separate equations are within the
+same equation environment. 
+
+\begin{table}
+\caption{\label{math-tab2}Other macros defined in IOPP macros for use in maths.}
+\begin{tabular*}{\textwidth}{@{}l*{15}{@{\extracolsep{0pt plus
+12pt}}l}}
+\br
+Macro&Result&Description\\
+\mr
+Spaces\\
+\verb"\fl"&&Start line of equation full left\\
+\verb"\ms"&&Spread out lines in displayed equations slightly ($\sim$3pt)\\
+\verb"\bs"&&Bigger space ($\sim$6pt) to separate lines in displays\\
+\verb"\ns"&&Small negative space between lines in displays\\
+\bs
+\multispan{3}{For symbols to left of 5 pica indent\hfill}&\\
+\verb"\lo{#1}"&$\#1$&Any symbol overhanging to left\\
+\verb"\eql"&$=$&Left overhanging equals sign\\
+\verb"\lsim"&$\sim$&Left overhanging tilde\\ 
+\verb"\lsime"q&$\simeq$&Left overhanging approximately equals\\
+\verb"\lequiv"&$\equiv$&Left overhanging equivalent sign\\
+\bs
+Miscellaneous\\
+\verb"\case{#1}{#2}"&$\case{\#1}{\#2}$&Text style fraction in display\\
+\verb"\Tr"&$\Tr$&Roman Tr (Trace)\\
+\verb"\tr"&$\tr$&Roman tr (trace)\\
+\verb"\Or"&$\Or$&Roman O (of order of)\\
+\verb"\tdot{#1}"&$\tdot{x}$&Triple dot over character\\
+\verb"\lshad"&$\lshad$&Text size left shadow bracket\\
+\verb"\rshad"&$\rshad$&Text size right shadow bracket\\
+\br
+\end{tabular*}
+\end{table}
+
+\subsection{Miscellaneous points}
+Exponential expressions, especially those containing subscripts or 
+superscripts, are clearer if the notation $\exp(\ldots)$ is used except for 
+simple examples. For instance $\exp[\rmi(kx-\omega t)]$ and $\exp(z^2)$ are 
+preferred to $\e^{\rmi(kx-\omega t)}$ and $\e^{z^2}$, but 
+$\e^2$ 
+is acceptable. Similarly the square root sign $\sqrt{\phantom{b}}$ should 
+only be used with relatively
+simple expressions, e.g.\ $\sqrt2$ and $\sqrt{a^2+b^2}$;
+in other cases the 
+power $1/2$ should be used.
+
+It is important to distinguish between $\ln = \log_\e$ and $\lg 
+=\log_{10}$. Braces, brackets and parentheses should be used in the 
+following order: $\{[(\;)]\}$. The same ordering of brackets should be 
+used within each size. However, this ordering can be ignored if the
+brackets have a 
+special meaning (e.g.\ if they denote an average or a function).  Decimal 
+fractions should 
+always be preceded by a zero: for example 0.123 {\bf not} .123. For long 
+numbers commas are not inserted but instead a thin space is added after 
+every third character away from the position of the decimal point unless 
+this leaves a single separated character: e.g.\ $60\,000$, $0.123\,456\,78$ 
+but 4321 and 0.7325.
+
+Equations that are referred to in the text should be numbered with 
+the number on the right-hand side. 
+
+
+\subsection{Equation numbering}
+\label{eqnum}
+\LaTeX\ provides facilities for automatically numbering equations 
+and these should be used where possible. Sequential numbering (1), (2), 
+etc, is the default numbering system although, if the command
+\verb"\eqnobysec" is included in the preamble, equation numbering
+by section is obtained, e.g.\ 
+(2.1), (2.2), etc. In articles with several appendixes equation numbering
+by section is useful in the appendixes even when sequential numbering has
+been used throughout the main body of the text and is switched on by the 
+\verb"\appendix" command. Equation numbering by section {\it must} 
+be used for {\it Reports on Progress in 
+Physics}. When referring to an equation in the text, either put 
+the equation number, in brackets, e.g.\ `as in (2)', or spell out the 
+word equation in full, e.g.\ `if equation (2) is factorized'; do not 
+use abbreviations such as eqn or eq.
+When cross-referencing is used, \verb"\ref{<label>}"
+ will produce `(\verb"<eqnum>")',
+\verb"\eref{<label>}" produces `equation (\verb"<eqnum>")' and
+\verb"\Eref{<label>}" produces `Equation (\verb"<eqnum>")', 
+where \verb"<label>" 
+is the
+label to produce equation number \verb"<eqnum>".
+
+
+If an equation number is centred between lines then the 
+command \verb"\eqalign{...}" 
+can be used within the `equation' environment.
+After \verb"\begin{equation}" enclose the lines over 
+which the number is
+to be centred 
+within \verb"\eqalign{...}"  with 
+\verb"\\" or \verb"\cr"
+at the end of each line. Ampersands are unnecessary within the
+\verb"\eqalign" but can be used for secondary alignment if necessary.
+The code 
+\begin{verbatim}
+\begin{equation}
+\eqalign{T_{11}&=(1+P_\e)I_{\uparrow\uparrow}-(1-P_\e)
+I_{\uparrow\downarrow}\\
+T_{-1-1}&=(1+P_\e)I_{\downarrow\downarrow}-(1-P_\e)
+I_{\uparrow\downarrow}\\
+S_{11}&=(3+P_\e)I_{\downarrow\uparrow}-(3-P_e)I_{\uparrow\uparrow}\\
+S_{-1-1}&=(3+P_\e)I_{\uparrow\downarrow}-(3-P_\e)
+I_{\downarrow\downarrow}}
+\end{equation}
+\end{verbatim}
+gives four equations with a centred 
+number:
+\begin{equation}
+\eqalign{T_{11}&=(1+P_\e)I_{\uparrow\uparrow}-(1-P_\e)
+I_{\uparrow\downarrow}\\
+T_{-1-1}&=(1+P_\e)I_{\downarrow\downarrow}-(1-P_\e)I_{\uparrow\downarrow}\\
+S_{11}&=(3+P_\e)I_{\downarrow\uparrow}-(3-P_e)I_{\uparrow\uparrow}\\
+S_{-1-1}&=(3+P_\e)I_{\uparrow\downarrow}-(3-P_\e)
+I_{\downarrow\downarrow}}
+\end{equation}
+Note that the secondary alignment at the equals signs would not normally
+be necessary but is included here for demonstration purposes.
+
+
+Sometimes it is useful to number equations as parts of the same
+basic equation. This can be accomplished by inserting the 
+commands \verb"\numparts" before the equations concerned and 
+\verb"\endnumparts" when reverting to the normal sequential numbering.
+The equations below show the previous equations numbered as separate parts
+using \verb"\numparts ... \endnumparts" and the \verb"eqnarray"
+environment
+\numparts
+\begin{eqnarray}
+T_{11}&=(1+P_\e)I_{\uparrow\uparrow}-(1-P_\e)
+I_{\uparrow\downarrow}\\
+T_{-1-1}&=(1+P_\e)I_{\downarrow\downarrow}-(1-P_\e)I_{\uparrow\downarrow}\\
+S_{11}&=(3+P_\e)I_{\downarrow\uparrow}-(3-P_e)I_{\uparrow\uparrow}\\
+S_{-1-1}&=(3+P_\e)I_{\uparrow\downarrow}-(3-P_\e)
+I_{\downarrow\downarrow}
+\end{eqnarray}
+\endnumparts
+
+
+\subsection{Miscellaneous extra commands for displayed equations}
+The \verb"\cases" command of Plain \TeX\ is available
+for use with \LaTeX\ but has been amended slightly to 
+increase the space between the equation and the condition. 
+\Eref{cases} 
+demonstrates simply the output from the \verb"\cases" command
+\begin{equation}
+\label{cases}
+X=\cases{1&for $x \ge 0$\\
+-1&for $x<0$\\}
+\end{equation}
+The code used was:
+\begin{verbatim}
+\begin{equation}
+\label{cases}
+X=\cases{1&for $x \ge 0$\\
+-1&for $x<0$\\}
+\end{equation}
+\end{verbatim}
+
+To obtain text style fractions within displayed maths the command 
+\verb"\case{#1}{#2}" can be used (see equations (2) and (5)) instead
+of the usual \verb"\frac{#1}{#2}" command or \verb"{#1 \over #2}".
+
+When two or more short equations are on the same line they should be 
+separated by a `qquad space' (\verb"\qquad"), rather than
+\verb"\quad" or any combination of \verb"\,", \verb"\>", \verb"\;" 
+and \verb"\ ".
+ 
+
+
+\section{Referencing}
+Two different styles of referencing are in common use: the Harvard 
+alphabetical system and the Vancouver
+numerical system. All the IOPP journals allow 
+the use of the Harvard system but the numerical system should {\bf not} be 
+used in {\it Physics in Medicine and Biology}.
+Brief descriptions of the use of the two 
+referencing systems are given below.
+
+\subsection{Harvard system}
+In the Harvard system the name of the author appears in the text together 
+with the year of publication. As appropriate, either the date or the name 
+and date are included within parentheses. Where there are only two authors 
+both names should be given in the text; if there are more than two 
+authors only the first name should appear followed by `{\it et al}' 
+(which can be obtained by 
+typing \verb"\etal"). When two or 
+more references to work by one author or group of authors occur for the 
+same year they should be identified by including a, b, etc after the date 
+(e.g.\ 1986a). If several references to different pages of the same article 
+occur the appropriate page number may be given in the text, e.g.\ Kitchen 
+(1982, p 39).
+
+The reference list at the end of an article consists of an 
+unnumbered section containing an
+alphabetical listing by authors' names and in date order for each 
+author or group of identical authors. The reference list in the 
+preprint style is started by including the command
+\verb"\section*{References}" and then
+\verb"\begin{harvard}".
+There will be two basic types of 
+entries within the reference list: (i) those to journal articles and 
+(ii) those to books, conference proceedings and reports. For both of 
+these types of references \verb"\item[]"
+is required before the start of an individual reference.
+The reference list is completed with \verb"\end{harvard}".
+There is also a shortened form of the coding; \verb"\section*{References}"
+and \verb"\begin{harvard}" can be replaced by the single command
+\verb"\References" and \verb"\end{harvard}" can be shortened to
+\verb"\endrefs".
+
+
+\subsubsection{References to journal articles.}
+A normal reference to a journal article contains three changes of 
+font:
+the authors and date appear in Roman type, the journal title in 
+italic, the volume number in bold and the page numbers in Roman again. 
+A typical journal entry would be:
+
+\smallskip
+\begin{harvard}
+\item[] Cisneros A 1971 {\it Astrophys.\ Space Sci.} {\bf 10} 87
+\end{harvard}
+\smallskip
+
+\noindent which would be obtained by typing, within the references
+environment 
+\begin{verbatim}
+\item[] Cisneros A 1971 {\it Astrophys. Space Sci.} {\bf 10} 87
+\end{verbatim}
+
+Features to note are the following.
+
+(i) The authors should be in the form surname (with only the first 
+letter capitalized) {\bf followed} by the initials with {\bf no} 
+periods after the initials. Authors should be separated by a comma 
+except for the last two which should be separated by `and' with no 
+comma preceding it. For journals that accept titles of articles in the 
+reference list,  the title should be in Roman (upright)
+lower case letters, except for an initial 
+capital, and should follow the date.
+
+(ii) The journal is in italic and is abbreviated. \ref{jlabs} 
+gives a list of 
+macros that will give the correct abbreviation for 
+many of the common journals. If a journal has several parts denoted by 
+different letters the part letter
+should be inserted after the journal in Roman type, e.g.\ 
+{\it Phys.\ Rev.\ \rm A}. 
+
+(iii) The volume number is bold; the page number is Roman.
+ Both the initial and final page 
+numbers should be given where possible. The final page number should be in 
+the shortest possible form and separated from the initial page number by an 
+en rule (\verb"--"), e.g.\ 1203--14.
+
+(iv) Where there are two or more references with identical authors, 
+the authors' names should not be repeated but should be replaced by 
+\verb"\dash" on the second and following occasions. Thus
+\begin{verbatim}
+\item[]Davis R, Mann A K and Wolfenstein L 1989  {\it Ann. Rev. Nucl.
+Part. Sci.} {\bf 39} 467
+\item[]\dash 1990 Private communication 
+\end{verbatim}
+
+\subsection{Electronic journal references}
+These do not always follow the conventional {\it year-journal-volume-page numbers} pattern.
+The journals may be electronic {\it and} print (e.g. {\it Phys. Rev.} D) or electronic only (e.g. {\it Living Reviews in Relativity}).
+Electronic journals with unique referencing systems are given below.
+
+\begin{itemize}
+\item {\it Phys. Rev. (parts A, C and D).} Each article has a six-digit unique reference number which is cited after the volume number. So, for example, 
+\smallskip
+\numrefs{1}
+\item Carlip S and Vera R 1998 {\it Phys. Rev.} D {\bf 58} 011345 
+\endnumrefs
+\smallskip
+Note that page numbers are no longer used.
+
+\item {\it Journal of High Energy Physics.}
+This journal is primarily electronic, with a print version for archive purposes.
+Papers are cited as per the following example.
+\smallskip
+\numrefs{1}
+\item Davies K and Brown G 1997 {\it J. High Energy Phys.}
+JHEP12(1997)002
+\endnumrefs
+\smallskip
+with no spaces, where JHEP is obvious, 12 is the month (December in this case), 1997 is the year and 002 is the paper number.
+
+\item {\it Living Reviews in Relativity.}
+This journal is electronic only. The short form for this journal is {\it Liv. Rev. Rel.} and papers are cited simply by a number consisting of year and article number. So, for example,
+\smallskip
+\numrefs{1}
+\item Gundlach C 1999 {\it Liv. Rev. Rel.} 1994-4
+\endnumrefs
+\smallskip
+\end{itemize}
+
+\subsection{Preprint references}
+Since the introduction of the LANL preprint server this class of references has grown in importance. 
+To reflect this and to maximize  the number of hyperlinks available through IOPP's Hypercite service in our electronic journals, each preprint reference should be given in as much detail as possible. Such references should include authors, year of work and preprint number (preceded by the word {\it Preprint}). 
+An example would be
+\smallskip
+\numrefs{1}
+\item Harrison M 1999 Dipheomorphism-invariant manifolds {\it Preprint} hep-th/9909196
+\endnumrefs
+\smallskip
+If the preprint has been published then the full published reference is given first and the preprint details can be added in brackets after, on a separate line. So, for example,
+\smallskip
+\numrefs{1}
+\item Neilson D and Choptuik M 2000 {\it Class. Quantum Grav.} {\bf 17} 761
+\item[](Neilson D and Choptuik M 1998 {\it Preprint} gr-qc/9812053)
+\endnumrefs
+\smallskip
+
+\subsubsection{References to books, conference proceedings and reports.}
+
+References to books, proceedings and reports are similar, but have only two
+changes of font. The authors and date of publication are in Roman, the 
+title of the book is in italic, and the editors, publisher, 
+town of publication 
+and page number are in Roman. A typical reference to a book and a
+conference paper might be
+
+\smallskip
+\begin{harvard}
+\item[] Dorman L I 1975 {\it Variations of Galactic Cosmic Rays} 
+(Moscow: Moscow State University Press) p~103
+\item[] Caplar R and Kulisic P 1973 {\it Proc.\
+Int.\ Conf.\ on Nuclear Physics (Munich)} vol~1 (Amsterdam:  
+North-Holland/American Elsevier) p~517
+\end{harvard}
+\smallskip
+
+\noindent which would be obtained by typing
+\begin{verbatim}
+\item[] Dorman L I 1975 {\it Variations of Galactic Cosmic Rays} 
+(Moscow: Moscow State University Press) p~103
+\item[] Caplar R and Kulisic P 1973 {\it Proc. Int. Conf. on Nuclear 
+Physics (Munich)} vol~1 (Amsterdam: North-Holland/American 
+Elsevier) p~517
+\end{verbatim}
+\noindent respectively.
+
+
+Features to note are the following.
+
+(i) Book titles are in italic and should be spelt out in full with 
+initial capital letters for all except minor words. Words such as 
+Proceedings, Symposium, International, Conference, Second, etc should 
+be abbreviated to Proc., Symp., Int., Conf., 2nd, 
+respectively, but the rest of the title should be given in full, 
+followed by the date of the conference and the 
+town or city where the conference was held. For 
+Laboratory Reports the Laboratory should be spelt out wherever 
+possible, e.g.\ {\it Argonne National Laboratory Report}.
+
+(ii) The volume number as, for example, vol~2, should be followed by 
+the editors, if any, in a form such as ed~A~J~Smith and P~R~Jones. Use 
+\etal if there are more than two editors. Next comes the town of 
+publication and publisher, within brackets and separated by a colon, 
+and finally the page numbers preceded by p if only one number is given 
+or pp if both the initial and final numbers are given.
+
+Cross referencing between the text and the 
+reference list is not necessary for alphabetic referencing 
+in the Harvard system as adding or deleting a reference 
+does not normally change any of the other references.
+
+\subsection{Numerical system}
+In the numerical system references are numbered sequentially 
+throughout the text. The numbers occur within square brackets and one 
+number can be used to designate several references. A numerical 
+reference list in the preprint style is started by including the 
+command \verb"\section*{References}" and then
+\verb"\begin{thebibliography}{<num>}", where \verb"<num>" is the largest
+number in the reference list (or any other number with the same number
+of digits).  The 
+reference list gives the references in 
+numerical, not alphabetical, order and is completed by
+\verb"\end{thebibliography}". Short forms of the commands are again
+available: \verb"\Bibliography{<num>}" can be used at the start of the
+references section and \verb"\endbib" at the end.
+(Note that footnotes should not be 
+part of a numerical reference system, but should be included in the 
+text using the symbols \dag, \ddag, etc.)
+
+References to journals and books are similar to those in the Harvard 
+system, except that two or more references with identical authors are 
+spelt out in full, i.e.\ they are {\bf not} replaced with \verb"\dash". 
+When one number covers two or more separate references \verb"\nonum"
+or \verb"\par\item[]" should be included at
+the start of each reference in a group after the first.
+A typical numerical reference list might begin
+
+\smallskip
+
+\numrefs{1}
+\item Dorman L I 1975 {\it Variations of Galactic Cosmic Rays} (Moscow: 
+Moscow State University Press) p~103
+\item Caplar R and Kulisic P 1973 {\it Proc.\ Int.\ Conf.\ 
+on Nuclear Physics (Munich)} vol~1 (Amsterdam:  
+North-Holland/American Elsevier) p~517
+\item Cisneros A 1971 {\it Astrophys. Space Sci.} {\bf 10} 87
+\endnumrefs
+\smallskip
+
+\noindent which would be obtained by typing
+
+\begin{verbatim}
+\item Dorman L I 1975 {\it Variations of Galactic Cosmic Rays} 
+(Moscow: Moscow State University Press) p~103
+\item Caplar R and Kulisic P 1973 {\it Proc. Int. Conf. 
+on Nuclear Physics (Munich)} vol~1 (Amsterdam:  
+North-Holland/American Elsevier) p~517
+\item Cisneros A 1971 {\it Astrophys. Space Sci.} {\bf 10} 87
+\end{verbatim}
+
+The point to note is that this is identical to the entries in the 
+Harvard system except that square brackets following
+\verb"\item" are no longer required.
+If you are using \LaTeX's cross-referencing system then \verb"\item" would be replaced by \verb"\bibitem{label}" corresponding to \verb"\cite{label}" in the text (see section \ref{refs}).
+ 
+\subsection{Reference lists}
+A complete reference should provide the reader with enough information to 
+locate the article concerned and should consist of: name(s) and initials, 
+date published, title of journal or book, volume number, editors, if any, 
+and town of publication and publisher in parentheses for books, 
+and finally the 
+page numbers. Titles of journal articles may also be included.
+Up to twenty authors may be given in a particular reference; where 
+there are more than twenty only the first should be given followed by 
+`{\it et al}'. Abbreviations of the names of periodicals used by Institute
+of Physics Publishing are usually the same as those 
+given in British Standard 
+BS 4148: 1985. If an author is unsure of an abbreviation and the 
+journal is not given in~\ref{jlabs}, 
+it is best to leave the title in 
+full. The terms {\it loc.\ cit.\ }and {\it ibid.\ }should not be used. 
+Unpublished conferences and reports should generally not be included 
+in the reference list and articles in the course of publication should 
+be entered only if the journal of publication is known. 
+A thesis submitted for a higher degree may be included 
+in the reference list if it has not been superseded by a published 
+paper and is available through a library; sufficient information 
+should be given for it to be traced readily.
+
+\section{Cross referencing\label{xrefs}}
+The facility to cross reference items in the text is very useful when 
+composing articles the precise form of which is uncertain at the start 
+and where revisions and amendments may subsequently be made. When using 
+cross referencing, labels are given to elements in the text, for 
+instance sections, figures, tables or equations and the elements may 
+be referred to elsewhere
+in the text by using the label. When the article is 
+first processed the labels are read in and assigned, e.g.\ 2.1 for a 
+subsection or (4) for an equation number. When the article is 
+processed a second or subsequent time the label assignments are read 
+in at the start of the file and the correct values given in the text. 
+\LaTeX\ provides excellent facilities for doing cross-referencing
+and these can be very useful in preparing articles.
+
+\subsection{References}
+\label{refs}
+Cross referencing is useful for numeric reference lists because, if it 
+is used, adding 
+another reference to the list does not then involve renumbering all 
+subsequent references. It is not necessary for referencing 
+in the Harvard system where the final reference list is alphabetical 
+and normally no other changes are necessary when a reference is added or
+deleted.
+Two passes are necessary initially to get the cross references right 
+but once they are correct a single run is usually sufficient provided an 
+\verb".aux" file is available and the file 
+is run to the end each time.
+\verb"\cite" and \verb"\bibitem" are used to link citations in the text
+with their entry in the reference list;
+if the 
+reference list contains an entry \verb"\bibitem{label}", 
+then \verb"\bibitem{label}" 
+will produce the correct number in the reference list and 
+\verb"\cite{label}" will produce the number within square brackets in the 
+text. \verb"label" may contain alphabetic letters, 
+or punctuation characters but must not contain spaces or commas. It is also
+recommended that the underscore character \_{} is not used in cross
+referencing. 
+Thus labels for the form 
+\verb"eq:partial", \verb"fig:run1", \verb"eq:dy'", 
+etc, may be used. When several 
+references occur together in the text \verb"\cite" may be used with 
+multiple labels with commas but no spaces separating them; 
+the output will be the 
+numbers within a single pair of square brackets with a comma and a 
+thin space separating the numbers. Thus \verb"\cite{label1,label2,label4}"
+would give [1,\,2,\,4]. Note that no attempt is made to sort the 
+labels and no shortening of groups of consecutive numbers is done.
+Authors should therefore try to use multiple labels in the correct 
+order.
+
+The numbers for the cross referencing are generated in the order the 
+references appear in the reference list, so that if the entries in the 
+list are not in the order in which the references appear in the text 
+then the 
+numbering within the text will not be sequential. To correct this 
+change the ordering of the entries in the reference list and then 
+rerun {\it twice}.
+
+\subsection{Equation numbers, sections, subsections, figures and 
+tables}
+Cross references can be made to equation numbers, sections, 
+subsections, figures and tables or
+any numbered environment
+and this is a very useful feature when 
+writing a document as its final structure is often not fully defined 
+at the start. Thus a later section can be referred to by a label 
+before its precise number is known and when it is defined there is no 
+need to search back through the document to insert the correct value 
+manually. For this reason the use of cross referencing 
+can save considerable time. 
+
+Labels for equation numbers, sections, subsections, figures and tables 
+are all defined with the \verb"\label{label}" command and cross references 
+to them are made with the \verb"\ref{label}" command. The \verb"\label" 
+macro 
+identifies the type of environment it is used in and converts \verb"label" 
+into the correct form for that type of environment, thus \verb"\ref{label}" 
+might give (2.3) for an equation number but 3.1 for a subsection and 2 
+for a figure or table number. 
+
+Any section, subsection, subsubsection, appendix or subappendix 
+command defines a section type label, e.g. 1, 2.2, A2, A1.2 depending 
+on context. A typical article might have in the code of its introduction 
+`The results are discussed in section\verb"~\ref{disc}".' and
+the heading for the discussion section would be:
+\begin{verbatim}
+\section{Results}
+\label{disc}
+\end{verbatim}
+Labels to sections, etc, may occur anywhere within that section except
+within another numbered environment. 
+Within a maths environment labels can be used to tag equations which are 
+referred to within the text. 
+An example of an equation with a label and a reference to it 
+is:
+\begin{verbatim}
+\begin{equation}
+X=a\cos\theta+ b\sin\phi. \label{cossin}
+\end{equation}
+Equation (\ref{cossin}) ...
+\end{verbatim}
+which produces
+\begin{equation}
+X=a\cos\theta+ b\sin\phi. \label{cossin}
+\end{equation}
+Equation (\ref{cossin}) ...
+
+In addition to the standard \verb"\ref{<label>}" the abbreviated
+forms given in the \tref{abrefs}
+are available for reference to standard parts of the text
+
+\Table{\label{abrefs}Alternatives to the normal references $\backslash${\tt ref} 
+and the text generated by
+them. Note it is not normally necessary to include the word equation
+before an equation number except where the number starts a sentence. The
+versions producing an initial capital should only be used at the start of
+sentences.} 
+\br
+Reference&Text produced\\
+\mr
+\verb"\eref{<label>}"&equation (\verb"<num>")\\
+\verb"\Eref{<label>}"&Equation (\verb"<num>")\\
+\verb"\fref{<label>}"&figure \verb"<num>"\\
+\verb"\Fref{<label>}"&Figure \verb"<num>"\\
+\verb"\sref{<label>}"&section \verb"<num>"\\
+\verb"\Sref{<label>}"&Section \verb"<num>"\\
+\verb"\tref{<label>}"&table \verb"<num>"\\
+\verb"\Tref{<label>}"&Table \verb"<num>"\\
+\br
+\endTable
+
+\section{Tables and table captions}
+Tables are numbered serially and referred to in the text 
+by number (table 1, etc, {\bf not} tab. 1). Each table should have an 
+explanatory caption which should be as concise as possible. If a table 
+is divided into parts these should be labelled \pt(a), \pt(b), 
+\pt(c), etc but there should be only one caption for the whole 
+table, not separate ones for each part.
+
+In the preprint style the tables may be included in the text 
+or listed separately after the reference list 
+starting on a new page. 
+
+\subsection{The basic table format}
+The standard form for a table is:
+\begin{verbatim}
+\begin{table}
+\caption{\label{label}Table caption.}
+\begin{indented}
+\item[]\begin{tabular}{@{}llll}
+\br
+Head 1&Head 2&Head 3&Head 4\\
+\mr
+1.1&1.2&1.3&1.4\\
+2.1&2.2&2.3&2.4\\
+\br
+\end{tabular}
+\end{indented}
+\end{table}
+\end{verbatim}
+
+Points to note are:
+\begin{enumerate}
+\item The caption comes before the table. It should have a full stop at
+the end.
+
+\item Tables are normally set in a smaller type than the text.
+The normal style is for tables to be indented in the same way as
+equations. This is accomplished
+by using \verb"\begin{indented}" \dots\ \verb"\end{indented}"
+and putting \verb"\item[]" before the start of the tabular environment.
+Omit these
+commands for any tables which will not fit on the page when indented.
+
+\item The default alignment of columns should be aligned left and 
+adding \verb"@{}" omits the extra space before the first column.
+
+\item Tables have only horizontal rules and no vertical ones. The rules at
+the top and bottom are thicker than internal rules and are set with
+\verb"\br" (bold rule). 
+The rule separating the headings from the entries is set with
+\verb"\mr" (medium rule).
+
+\item Numbers in columns should be aligned on the decimal point;
+to help do this a control sequence \verb"\lineup" has been defined 
+which sets \verb"\0" equal to a space the size of a digit, \verb"\m"
+to be a space the width of a minus sign, and \verb"\-" to be a left
+overlapping minus sign. \verb"\-" is for use in text mode while the other
+two commands may be used in maths or text.
+(\verb"\lineup" should only be used within a table
+environment after the caption so that \verb"\-" has its normal meaning
+elsewhere.) See table~\ref{tabone} for an example of a table where
+\verb"\lineup" has been used.
+\end{enumerate}
+
+\begin{table}
+\caption{\label{tabone}A simple example produced using the standard table commands 
+and $\backslash${\tt lineup} to assist in aligning columns on the 
+decimal point. The width of the 
+table and rules is set automatically by the 
+preamble.} 
+
+\begin{indented}
+\lineup
+\item[]\begin{tabular}{@{}*{7}{l}}
+\br                              
+$\0\0A$&$B$&$C$&\m$D$&\m$E$&$F$&$\0G$\cr 
+\mr
+\0\023.5&60  &0.53&$-20.2$&$-0.22$ &\01.7&\014.5\cr
+\0\039.7&\-60&0.74&$-51.9$&$-0.208$&47.2 &146\cr 
+\0123.7 &\00 &0.75&$-57.2$&\m---   &---  &---\cr 
+3241.56 &60  &0.60&$-48.1$&$-0.29$ &41   &\015\cr 
+\br
+\end{tabular}
+\end{indented}
+\end{table}
+
+\subsection{Simplified coding and extra features for tables}
+The basic coding format can be simplified using extra commands provided in
+the \verb"iopart" class file. The commands up to and including 
+the start of the tabular environment
+can be replaced by
+\begin{verbatim}
+\Table{\label{label}Table caption}
+\end{verbatim}
+this also activates the definitions within \verb"\lineup".
+The final three lines can also be reduced to \verb"\endTable" or
+\verb"\endtab". Similarly for a table which does not fit in when indented
+\verb"\fulltable{\label{label}caption}" \dots\ \verb"\endfulltable" or \verb"\endtab"
+can be used. \LaTeX\ optional positional parameters can, if desired, be added after 
+\verb"\Table{\label{label}caption}" and \verb"\fulltable{\label{label}caption}".
+
+
+\verb"\centre{#1}{#2}" can be used to centre a heading 
+\verb"#2" over \verb"#1" 
+columns and \verb"\crule{#1}" puts a rule across 
+\verb"#1" columns. A negative 
+space \verb"\ns" is usually useful to reduce the space between a centred 
+heading and a centred rule. \verb"\ns" should occur immediately after the 
+\verb"\\" of the row containing the centred heading (see code for
+\tref{tabl3}). A small space can be 
+inserted between rows of the table 
+with \verb"\ms" and a half line space with \verb"\bs" 
+(both must follow a \verb"\\" but should not have a 
+\verb"\\" following them).
+   
+\Table{\label{tabl3}A table with headings spanning two columns and containing notes. 
+To improve the 
+visual effect a negative skip ($\backslash${\tt ns})
+has been put in between the lines of the 
+headings. Commands set-up by $\backslash${\tt lineup} are used to aid 
+alignment in columns. $\backslash${\tt lineup} is defined within
+the $\backslash${\tt Table} definition.}
+\br
+&&&\centre{2}{Separation energies}\\
+\ns
+&Thickness&&\crule{2}\\
+Nucleus&(mg\,cm$^{-2}$)&Composition&$\gamma$, n (MeV)&$\gamma$, 2n (MeV)\\
+\mr
+$^{181}$Ta&$19.3\0\pm 0.1^{\rm a}$&Natural&7.6&14.2\\
+$^{208}$Pb&$\03.8\0\pm 0.8^{\rm b}$&99\%\ enriched&7.4&14.1\\
+$^{209}$Bi&$\02.86\pm 0.01^{\rm b}$&Natural&7.5&14.4\\
+\br
+\end{tabular}
+\item[] $^{\rm a}$ Self-supporting.
+\item[] $^{\rm b}$ Deposited over Al backing.
+\end{indented}
+\end{table}
+
+Units should not normally be given within the body of a table but 
+given in brackets following the column heading; however, they can be 
+included in the caption for long column headings or complicated units. 
+Where possible tables should not be broken over pages. 
+If a table has related notes these should appear directly below the table
+rather than at the bottom of the page. Notes can be designated with
+footnote symbols (preferable when there are only a few notes) or
+superscripted small roman letters. The notes are set to the same width as
+the table and in normal tables follow after \verb"\end{tabular}", each
+note preceded by \verb"\item[]". For a full width table \verb"\noindent"
+should precede the note rather than \verb"\item[]". To simplify the coding 
+\verb"\tabnotes" can, if desired, replace \verb"\end{tabular}" and 
+\verb"\endtabnotes" replaces
+\verb"\end{indented}\end{table}".
+
+If all the tables are grouped at the end of a document
+the command \verb"\Tables" is used to start a new page and 
+set a heading `Tables and table captions'.
+  
+\section{Figures and figure captions}
+Figures may be included in an article as encapsulated PostScript files or
+using the \LaTeX\ picture environment. Alternatively authors may send in 
+high quality printed versions of their figures (fair copies) and 
+attach copies of the fair copies to each 
+typescript. The fair copies should be in black 
+Indian ink or printing on tracing paper, plastic or white card or 
+paper, or glossy photographs.
+
+Each figure should have a brief caption describing it and, if 
+necessary, interpreting the various lines and symbols on the figure. 
+As much lettering as possible should be removed from the figure itself and 
+included in the caption. If a figure has parts, these should be 
+labelled ($a$), ($b$), ($c$), etc. 
+\Tref{blobs} gives the definitions for describing symbols and lines often
+used within figure captions (more symbols are available
+when using the optional packages loading the AMS extension fonts).
+
+\begin{table}
+\caption{\label{blobs}Control sequences to describe lines and symbols in figure 
+captions.}
+\begin{indented}
+\item[]\begin{tabular}{@{}lllll}
+\br
+Control sequence&Output&&Control sequence&Output\\
+\mr
+\verb"\dotted"&\dotted        &&\verb"\opencircle"&\opencircle\\
+\verb"\dashed"&\dashed        &&\verb"\opentriangle"&\opentriangle\\
+\verb"\broken"&\broken&&\verb"\opentriangledown"&\opentriangledown\\
+\verb"\longbroken"&\longbroken&&\verb"\fullsquare"&\fullsquare\\
+\verb"\chain"&\chain          &&\verb"\opensquare"&\opensquare\\
+\verb"\dashddot"&\dashddot    &&\verb"\fullcircle"&\fullcircle\\
+\verb"\full"&\full            &&\verb"\opendiamond"&\opendiamond\\
+\br
+\end{tabular}
+\end{indented}
+\end{table}
+
+Unless the figures files are incorporated into the text 
+the captions should be listed at the end of the article.
+
+\subsection{Figure captions where figure files are not available}
+The command \verb"\Figures" starts a new page and an unnumbered section
+with the heading `Figure captions'. 
+The captions should then be set with the commands:
+\begin{verbatim}
+\begin{figure}
+\caption{\label{label}Figure caption.}
+\end{figure}
+\end{verbatim}
+or more simply
+\begin{verbatim}
+\Figure{\label{label}Figure caption.}                                         
+\end{verbatim}
+The caption should finish with a full stop and the printed version will be 
+indented as in Institute of Physics Publishing single-column journals.
+
+\subsection{Inclusion of graphics files}
+If graphics files are available as encapsulated PostScript (EPS) files 
+(or are created within the \LaTeX\ picture environment) they may
+be included within the body of the text at an appropriate point using a
+standard graphics inclusion package. Authors should ensure EPS files meet
+the following criteria.
+\begin{itemize}
+\item The Bounding Box should indicate the area of the figure 
+with a minimum of white space around it and not the dimensions of the
+page.
+\item Any fonts used should be from the standard PostScript set (Times,
+Helvetica, Courier and Symbol).
+\item Scanned images should be of 600 dpi resolution for line art (black
+and white) and 150 dpi resolution for grayscale or colour.
+\item Captions and labels (e.g.\ Figure 1) should not be included in the
+EPS file although part letters (e.g.\ ($a$)) are acceptable provided they
+are placed close or within the boundary of the figure. 
+\end{itemize}
+
+The precise coding required will depend on the graphics package being used
+and the printer driver. We use a printer driver compatible with DVIPS but
+authors should avoid using special effects generated by including verbatim
+PostScript code within the \LaTeX\ file with specials other than the
+standard figure inclusion ones.
+
+Using the epsf package figures can be included using code such as:
+\begin{verbatim}
+\begin{figure}
+\begin{center}
+\epsfbox{file.eps}
+\end{center}
+\caption{\label{label}Figure caption}
+\end{figure}
+\end{verbatim}
+
+
+\clearpage
+
+\appendix
+\section{List of macros for formatting text, figures and tables}
+
+
+\begin{table}[hb]
+\caption{Macros available for use in text. Parameters in square brackets 
+are optional.}
+\footnotesize\rm
+\begin{tabular}{@{}*{7}{l}}
+\br
+Macro name&Purpose\\
+\mr
+\verb"\title[#1]{#2}"&Title of article and short title (optional)\\
+\verb"\paper[#1]{#2}"&Title of paper and short title (optional)\\
+\verb"\letter{#1}"&Title of Letter to the Editor\\
+\verb"\comment[#1]{#2}"&Title of Comment and short title (optional)\\
+\verb"\topical[#1]{#2}"&Title of Topical Review and short title 
+(optional)\\
+\verb"\review[#1]{#2}"&Title of review article and short title (optional)\\
+\verb"\note[#1]{#2}"&Title of Note and short title (optional)\\
+\verb"\prelim[#1]{#2}"&Title of Preliminary Communication \& short title\\
+\verb"\author{#1}"&List of all authors\\
+\verb"\article[#1]{#2}{#3}"&Type and title of other articles and 
+short title (optional)\\
+\verb"\address{#1}"&Address of author\\
+\verb"\pacs{#1}"&PACS classification codes\\
+\verb"\pacno{#1}"&Single PACS classification code\\
+\verb"\ams{#1}"&American Mathematical Society classification code\\
+\verb"\submitto{#1}"&`Submitted to' message\\
+\verb"\maketitle"&Creates title page\\
+\verb"\begin{abstract}"&Start of abstract\\
+\verb"\end{abstract}"&End of abstract\\
+\verb"\nosections"&Inserts space before text when no sections\\
+\verb"\section{#1}"&Section heading\\
+\verb"\subsection{#1}"&Subsection heading\\
+\verb"\subsubsection{#1}"&Subsubsection heading\\
+\verb"\appendix"&Start of appendixes\\
+\verb"\ack"&Acknowledgments heading\\
+\verb"\References"&Heading for reference list\\
+\verb"\begin{harvard}"&Start of alphabetic reference list\\
+\verb"\end{harvard}"&End of alphabetic reference list\\
+\verb"\begin{thebibliography}{#1}"&Start of numeric reference list\\
+\verb"\end{thebibliography}"&End of numeric reference list\\
+\verb"\etal"&\etal for text and reference lists\\
+\verb"\dash"&Rule for repeated authors in alphabetical reference list\\
+\verb"\nonum"&Unnumbered entry in numerical reference list\\
+\br
+\end{tabular}
+\end{table}
+
+
+\begin{table}
+\caption{Macros defined within {\tt iopart.cls}
+for use with figures and tables.}
+\begin{indented}
+\item[]\begin{tabular}{@{}l*{15}{l}}
+\br
+Macro name&Purpose\\
+\mr
+\verb"\Figures"&Heading for list of figure captions\\
+\verb"\Figure{#1}"&Figure caption\\
+\verb"\Tables"&Heading for tables and table captions\\
+\verb"\Table{#1}"&Table caption\\
+\verb"\fulltable{#1}"&Table caption for full width table\\
+\verb"\endTable"&End of table created with \verb"\Table"\\
+\verb"\endfulltab"&End of table created with \verb"\fulltable"\\
+\verb"\endtab"&End of table\\
+\verb"\br"&Bold rule for tables\\
+\verb"\mr"&Medium rule for tables\\
+\verb"\ns"&Small negative space for use in table\\
+\verb"\centre{#1}{#2}"&Centre heading over columns\\
+\verb"\crule{#1}"&Centre rule over columns\\
+\verb"\lineup"&Set macros for alignment in columns\\
+\verb"\m"&Space equal to width of minus sign\\
+\verb"\-"&Left overhanging minus sign\\
+\verb"\0"&Space equal to width of a digit\\
+\br
+\end{tabular}
+\end{indented}
+\end{table}
+
+
+\clearpage
+\section{Control sequences for journal
+abbreviations}
+\label{jlabs}
+\begin{table}[hb]
+\caption{\label{jlab1}Abbreviations for the IOPP journals.}
+\begin{indented}
+\item[]
+\begin{tabular}{@{}lll}
+\br
+Macro name&{\rm Short form of journal title}&Years relevant\\
+\mr
+{\it Current journals}\\
+\mr
+\verb"\CQG"&Class. Quantum Grav.\\
+\verb"\CTM"&Combust. Theory Modelling\\
+\verb"\EJP"&Eur. J. Phys.\\
+\verb"\HPP"&High Performance Polymers\\
+\verb"\IP"&Inverse Problems\\
+\verb"\JHEP"&J. High Energy Phys.&1999 and onwards\\
+\verb"\JMM"&J. of Michromech. and Microeng.\\
+\verb"\JOA"&J. Opt. A: Pure and Applied Opt.&1998 and onwards\\
+\verb"\JOB"&J. Opt. B: Quantum and Semiclass. Opt.&1999 and onwards\\
+\verb"\JPA"&J. Phys. A: Math. Gen.\\
+\verb"\jpb"&J. Phys. B: At. Mol. Opt. Phys.&1988 and onwards\\
+\verb"\JPCM"&J. Phys: Condens. Matter&1989 and onwards\\
+\verb"\JPD"&J. Phys. D: Appl. Phys.\\
+\verb"\JPF"&J. Phys. F: Met. Phys.\\
+\verb"\jpg"&J. Phys. G: Nucl. Part. Phys.&1989 and onwards\\
+\verb"\MSMSE"&Modelling Simul. Mater. Sci. Eng.\\
+\verb"\MST"&Meas. Sci. Technol.&1990 and onwards\\
+\verb"\NET"&Network:Comput. Neural Syst.\\
+\verb"\NJP"&New J. Phys.&1999 and onwards\\
+\verb"\NL"&Nonlinearity\\
+\verb"\NT"&Nanotechnology\\
+\verb"\PM"&Physiol. Meas.\\
+\verb"\PMB"&Phys. Med. Biol.\\
+\verb"\PPCF"&Plasma Physics and Controlled Fusion\\
+\verb"\PSST"&Plasma Sources Sci. Technol.\\
+\verb"\PUS"&Public Understand. Sci.\\
+\verb"\RPP"&Rep. Prog. Phys.\\
+\verb"\SST"&Semicond. Sci. Technol.\\
+\verb"\SUST"&Supercond. Sci. Technol.\\
+\verb"\WRM"&Waves in Random Media\\
+\mr
+{\it No Longer Published}\\
+\mr
+\verb"\BIO"&Bioimaging&1998\\
+\verb"\DSE"&Distributed Systems Eng.&1993--1999\\
+\verb"\JO"&J. Opt.&1970--1998\\
+\verb"\JPB"&J. Phys. B: At. Mol. Phys.&1968--1987\\
+\verb"\JPC"&J. Phys. C: Solid State Phys.&1968--1988\\
+\verb"\JPE"&J. Phys. E: Sci. Instrum.&1968--1989\\
+\verb"\JPG"&J. Phys. G: Nucl. Phys.&1975--1988\\
+\verb"\PAO"&Pure and Applied Opt.&1992--1998\\
+\verb"\QO"&Quantum Opt.&1989--1994\\
+\verb"\QSO"&Quantum and Semiclass. Opt.&1995--1998\\
+\br
+\end{tabular}
+\end{indented}
+\end{table}
+
+
+
+\begin{table}
+
+\caption{\label{jlab2}Abbreviations for some more 
+common non-IOPP journals.}
+\begin{indented}
+\item[]\begin{tabular}{@{}ll}
+\br
+Macro name&{\rm Short form of journal}\\
+\mr
+\verb"\AC"&Acta Crystallogr.\\
+\verb"\AM"&Acta Metall.\\
+\verb"\AP"&Ann. Phys., Lpz\\
+\verb"\APNY"&Ann. Phys., NY\\
+\verb"\APP"&Ann. Phys., Paris\\
+\verb"\CJP"&Can. J. Phys.\\
+\verb"\GRG"&Gen. Rel. Grav.\\
+\verb"\JAP"&J. Appl. Phys.\\
+\verb"\JCP"&J. Chem. Phys.\\
+\verb"\JJAP"&Japan. J. Appl. Phys.\\
+\verb"\JMMM"&J. Magn. Magn. Mater.\\
+\verb"\JMP"&J. Math. Phys.\\
+\verb"\JOSA"&J. Opt. Soc. Am.\\
+\verb"\JP"&J. Physique\\
+\verb"\JPhCh"&J. Phys. Chem.\\
+\verb"\JPSJ"&J. Phys. Soc. Japan\\
+\verb"\JQSRT"&J. Quant. Spectrosc. Radiat. Transfer\\
+\verb"\NC"&Nuovo Cimento\\
+\verb"\NIM"&Nucl. Instrum. Methods\\
+\verb"\NP"&Nucl. Phys.\\
+\verb"\PF"&Phys. Fluids\\
+\verb"\PL"&Phys. Lett.\\
+\verb"\PR"&Phys. Rev.\\
+\verb"\PRL"&Phys. Rev. Lett.\\
+\verb"\PRS"&Proc. R. Soc.\\
+\verb"\PS"&Phys. Scr.\\
+\verb"\PSS"&Phys. Status Solidi\\
+\verb"\PTRS"&Phil. Trans. R. Soc.\\
+\verb"\RMP"&Rev. Mod. Phys.\\
+\verb"\RSI"&Rev. Sci. Instrum.\\
+\verb"\SSC"&Solid State Commun.\\
+\verb"\SPJ"&Sov. Phys.--JETP\\
+\verb"\ZP"&Z. Phys.\\
+\br
+\end{tabular}
+\end{indented}
+\end{table}
+
+\end{document}
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejus/setstack.sty
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@@ -0,0 +1,139 @@
+%%
+%% This is file `setstack.sty', created by VIK 15 Dec 1998
+%% Reproduces useful macros from amsmath.sty, thus avoiding the need to load the entire
+%% amsmath.sty and run into conflicts
+%% Adds definitions for \overset, \underset, \sideset, \substack, \boxed, \leftroot,
+%% \uproot, \dddot, \ddddot, \varrow, \harrow (see The LateX Companion, pp 225-227)
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1998/12/15]% LaTeX date must December 1998 or later
+\ProvidesPackage{setstack}
+\DeclareRobustCommand{\text}{%
+  \ifmmode\expandafter\text@\else\expandafter\mbox\fi}
+  \let\nfss@text\text
+  \def\text@#1{\mathchoice
+    {\textdef@\displaystyle\f@size{#1}}%
+      {\textdef@\textstyle\tf@size{\firstchoice@false #1}}%
+        {\textdef@\textstyle\sf@size{\firstchoice@false #1}}%
+          {\textdef@\textstyle \ssf@size{\firstchoice@false #1}}%
+            \check@mathfonts
+}
+\def\textdef@#1#2#3{\hbox{{%
+             \everymath{#1}%
+             \let\f@size#2\selectfont #3}}}
+
+% adds underset, overset, sideset and 
+% substack features from amsmath.sty (Companion p. 226)
+
+\def\invalid@tag#1{\@amsmath@err{#1}{\the\tag@help}\gobble@tag}
+\def\dft@tag{\invalid@tag{\string\tag\space not allowed here}}
+\def\default@tag{\let\tag\dft@tag}
+
+\def\Let@{\let\\\math@cr}
+\def\restore@math@cr{\def\math@cr@@@{\cr}}
+
+\def\overset#1#2{\binrel@{#2}%
+\binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
+\def\underset#1#2{\binrel@{#2}%
+\binrel@@{\mathop{\kern\z@#2}\limits_{#1}}}
+\def\sideset#1#2#3{%
+\@mathmeasure\z@\displaystyle{#3}%
+\global\setbox\@ne\vbox to\ht\z@{}\dp\@ne\dp\z@
+ \setbox\tw@\box\@ne
+\@mathmeasure4\displaystyle{\copy\tw@#1}%
+\@mathmeasure6\displaystyle{#3\nolimits#2}%
+\dimen@-\wd6 \advance\dimen@\wd4 \advance\dimen@\wd\z@
+\hbox to\dimen@{}\mathop{\kern-\dimen@\box4\box6}%
+}
+
+\newenvironment{subarray}[1]{%
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+$\m@th\scriptstyle##$\hfil\crcr
+}{%
+\crcr\egroup\egroup
+}
+\newcommand{\substack}[1]{\subarray{c}#1\endsubarray}
+
+% definitions of dddot and ddddot(p. 225)
+
+\def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+ \hbox{\normalfont ...}\vss}}}}
+\def\ddddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+ \hbox{\normalfont....}\vss}}}}
+
+% definitions of leftroot, uproot (p.225)
+
+\begingroup \catcode`\"=12
+\gdef\@@sqrt#1{\radical"270370 {#1}}
+\endgroup
+
+\def\leftroot{\@amsmath@err{\Invalid@@\leftroot}\@eha}
+\def\uproot{\@amsmath@err{\Invalid@@\uproot}\@eha}
+\newcount\uproot@
+\newcount\leftroot@
+\def\root{\relaxnext@
+  \DN@{\ifx\@let@token\uproot\let\next@\nextii@\else
+   \ifx\@let@token\leftroot\let\next@\nextiii@\else
+   \let\next@\plainroot@\fi\fi\next@}%
+  \def\nextii@\uproot##1{\uproot@##1\relax\FN@\nextiv@}%
+  \def\nextiv@{\ifx\@let@token\@sptoken\DN@. {\FN@\nextv@}\else
+   \DN@.{\FN@\nextv@}\fi\next@.}%
+  \def\nextv@{\ifx\@let@token\leftroot\let\next@\nextvi@\else
+   \let\next@\plainroot@\fi\next@}%
+  \def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
+   \def\nextiii@\leftroot##1{\leftroot@##1\relax\FN@\nextvii@}%
+  \def\nextvii@{\ifx\@let@token\@sptoken
+   \DN@. {\FN@\nextviii@}\else
+   \DN@.{\FN@\nextviii@}\fi\next@.}%
+  \def\nextviii@{\ifx\@let@token\uproot\let\next@\nextix@\else
+   \let\next@\plainroot@\fi\next@}%
+  \def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
+  \bgroup\uproot@\z@\leftroot@\z@\FN@\next@}
+\def\plainroot@#1\of#2{\setbox\rootbox\hbox{%
+ $\m@th\scriptscriptstyle{#1}$}%
+ \mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
+ {\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
+\def\r@@t#1#2{\setboxz@h{$\m@th#1\@@sqrt{#2}$}%
+ \dimen@\ht\z@\advance\dimen@-\dp\z@
+ \setbox\@ne\hbox{$\m@th#1\mskip\uproot@ mu$}%
+ \advance\dimen@ by1.667\wd\@ne
+ \mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
+ \mkern-10mu\mkern\leftroot@ mu\boxz@}
+ 
+%   definition of \boxed (math in frame, no dollars) p 225
+
+\def\boxed#1{\fbox{\m@th$\displaystyle#1$}}
+
+% definition of \smash for top and bottom parts of expression in braces (p.227)
+\renewcommand{\smash}[2][tb]{%
+  \def\smash@{#1}%
+  \ifmmode\@xp\mathpalette\@xp\mathsm@sh\else
+        \@xp\makesm@sh\fi{#2}}
+
+% additional difinitions for arrows 
+% zero mm wide #2 mm long vertical arrow shifted 1 mm to left, 1 mm up
+\newcommand{\varrow}[2]{%
+\unitlength=1mm
+  \begin{picture}(0,6) % (0,0)
+  % - for #1 to point arrow down,+ to point arrow up
+  \end{picture}%
+  \put(0,6){\vector(0,#1 3){#2}}    % 6,- for down, 0, + for up
+}
+% 1 mm high #2 mm long horizontal arrow shifted 1 mm up (0,-1)
+\newcommand{\harrow}[2]{%
+\unitlength=1mm
+  \begin{picture}(8,1)(0,-1) %
+  % 1 mm distance between arrow and stackreled object over it (8,1)
+  \put(0,0){\vector(#1 2,0){#2}}     % - to point arrow left, + right
+  \end{picture}%
+}
+
+\endinput
+%% end of setstack.sty
+%% Corrections history:
+%% 
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/.cache
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--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/.cache+	(revision 392)
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@@ -0,0 +1,48 @@
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--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus-old.tex	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus-old.tex	(revision 392)
@@ -0,0 +1,1023 @@
+%\documentclass[epj,nopacs,referee]{svjour}
+\documentclass[epj,nopacs]{svjour}
+%%
+%----------------------------------------------------------------------------
+%
+%\usepackage{slashbox}
+\usepackage[T1]{fontenc}
+\usepackage[latin1]{inputenc}
+\usepackage{graphicx}
+\usepackage{epsfig}
+%\usepackage{vmargin}
+%\usepackage{multicol}
+%\usepackage[footnotesize,normal,up]{caption}
+%\usepackage{subeqnarray}
+%\usepackage[francais,american]{babel}
+\usepackage{amssymb}
+%\usepackage{amsmath}
+%\usepackage{setstack}
+\usepackage{latexsym}
+
+
+%\newcommand{\beq}[1]{\begin{equation}\label{eq:#1}}
+%\newcommand{\enq}{\end{equation}}
+%\newcommand{\refeq}[1]{\ref{eq:#1}}
+%\newcommand{\biz}{\begin{itemize}}
+%\newcommand{\eiz}{\end{itemize}}
+%\newcommand{\beqa}{\begin{eqnarray}}
+%\newcommand{\enqa}{\end{eqnarray}}
+%\newcommand{\ol}{\overline}
+%\newcommand{\virg}{\mbox{,}}
+%\newcommand{\pt}{\mbox{.}}
+
+%
+\newcommand{\centre}[2]{\multispan{#1}{\hfill #2\hfill}}
+\newcommand{\dotted}{\protect\mbox{${\mathinner{\cdotp\cdotp\cdotp\cdotp\cdotp\cdotp}}$}}
+\newcommand{\dashed}{\protect\mbox{- - - -}}
+\newcommand{\broken}{\protect\mbox{-- -- --}}
+\newcommand{\longbroken}{\protect\mbox{--- --- ---}}
+\newcommand{\chain}{\protect\mbox{--- $\cdot$ ---}}
+\newcommand{\dashddot}{\protect\mbox{--- $\cdot$ $\cdot$ ---}}
+\newcommand{\full}{\protect\mbox{------}}
+%
+% abbreviations for IOPP journals
+%
+\newcommand{\CQG}{{\it Class. Quantum Grav.} }
+\newcommand{\CTM}{{\it Combust. Theory Modelling\/} }
+\newcommand{\DSE}{{\it Distrib. Syst. Engng\/} }
+\newcommand{\EJP}{{\it Eur. J. Phys.} } 
+\newcommand{\HPP}{{\it High Perform. Polym.} }              % added 4/5/93
+\newcommand{\IP}{{\it Inverse Problems\/} }
+\newcommand{\JHM}{{\it J. Hard Mater.} }                    % added 4/5/93
+\newcommand{\JO}{{\it J. Opt.} }
+\newcommand{\JOA}{{\it J. Opt. A: Pure Appl. Opt.} }
+\newcommand{\JOB}{{\it J. Opt. B: Quantum Semiclass. Opt.} }
+\newcommand{\JPA}{{\it J. Phys. A: Math. Gen.} }
+\newcommand{\JPB}{{\it J. Phys. B: At. Mol. Phys.} }      %1968-87
+\newcommand{\jpb}{{\it J. Phys. B: At. Mol. Opt. Phys.} } %1988 and onwards
+\newcommand{\JPC}{{\it J. Phys. C: Solid State Phys.} }   %1968--1988
+\newcommand{\JPCM}{{\it J. Phys.: Condens. Matter\/} }    %1989 and onwards
+\newcommand{\JPD}{{\it J. Phys. D: Appl. Phys.} }
+\newcommand{\JPE}{{\it J. Phys. E: Sci. Instrum.} }
+\newcommand{\JPF}{{\it J. Phys. F: Met. Phys.} }
+\newcommand{\JPG}{{\it J. Phys. G: Nucl. Phys.} }         %1975--1988
+\newcommand{\jpg}{{\it J. Phys. G: Nucl. Part. Phys.} }   %1989 and onwards
+\newcommand{\MSMSE}{{\it Modelling Simulation Mater. Sci. Eng.} }
+\newcommand{\MST}{{\it Meas. Sci. Technol.} }                 %1990 and onwards
+\newcommand{\NET}{{\it Network: Comput. Neural Syst.} }
+\newcommand{\NJP}{{\it New J. Phys.} }
+\newcommand{\NL}{{\it Nonlinearity\/} }
+\newcommand{\NT}{{\it Nanotechnology} }
+\newcommand{\PAO}{{\it Pure Appl. Optics\/} }
+\newcommand{\PM}{{\it Physiol. Meas.} }                        % added 4/5/93
+\newcommand{\PMB}{{\it Phys. Med. Biol.} }
+\newcommand{\PPCF}{{\it Plasma Phys. Control. Fusion\/} }      % added 4/5/93
+\newcommand{\PSST}{{\it Plasma Sources Sci. Technol.} }
+\newcommand{\PUS}{{\it Public Understand. Sci.} }
+\newcommand{\QO}{{\it Quantum Opt.} }
+\newcommand{\QSO}{{\em Quantum Semiclass. Opt.} }
+\newcommand{\RPP}{{\it Rep. Prog. Phys.} }
+\newcommand{\SLC}{{\it Sov. Lightwave Commun.} }               % added 4/5/93 
+\newcommand{\SST}{{\it Semicond. Sci. Technol.} }
+\newcommand{\SUST}{{\it Supercond. Sci. Technol.} }
+\newcommand{\WRM}{{\it Waves Random Media\/} }
+\newcommand{\JMM}{{\it J. Micromech. Microeng.\/} }
+%
+% Other commonly quoted journals
+%
+\newcommand{\AC}{{\it Acta Crystallogr.} }
+\newcommand{\AM}{{\it Acta Metall.} }
+\newcommand{\AP}{{\it Ann. Phys., Lpz.} }
+\newcommand{\APNY}{{\it Ann. Phys., NY\/} }
+\newcommand{\APP}{{\it Ann. Phys., Paris\/} }
+\newcommand{\CJP}{{\it Can. J. Phys.} }
+\newcommand{\JAP}{{\it J. Appl. Phys.} }
+\newcommand{\JCP}{{\it J. Chem. Phys.} }
+\newcommand{\JJAP}{{\it Japan. J. Appl. Phys.} }
+\newcommand{\JP}{{\it J. Physique\/} }
+\newcommand{\JPhCh}{{\it J. Phys. Chem.} }
+\newcommand{\JMMM}{{\it J. Magn. Magn. Mater.} }
+\newcommand{\JMP}{{\it J. Math. Phys.} }
+\newcommand{\JOSA}{{\it J. Opt. Soc. Am.} }
+\newcommand{\JPSJ}{{\it J. Phys. Soc. Japan\/} }
+\newcommand{\JQSRT}{{\it J. Quant. Spectrosc. Radiat. Transfer\/} }
+\newcommand{\NC}{{\it Nuovo Cimento\/} }
+\newcommand{\NIM}{{\it Nucl. Instrum. Methods\/} }
+\newcommand{\NP}{{\it Nucl. Phys.} }
+\newcommand{\PL}{{\it Phys. Lett.} }
+\newcommand{\PR}{{\it Phys. Rev.} }
+\newcommand{\PRL}{{\it Phys. Rev. Lett.} }
+\newcommand{\PRS}{{\it Proc. R. Soc.} }
+\newcommand{\PS}{{\it Phys. Scr.} }
+\newcommand{\PSS}{{\it Phys. Status Solidi\/} }
+\newcommand{\PTRS}{{\it Phil. Trans. R. Soc.} }
+\newcommand{\RMP}{{\it Rev. Mod. Phys.} }
+\newcommand{\RSI}{{\it Rev. Sci. Instrum.} }
+\newcommand{\SSC}{{\it Solid State Commun.} }
+\newcommand{\ZP}{{\it Z. Phys.} }
+
+\newcommand{\etal}{{et al.\/}\ }
+
+%
+%
+%----------------------------------------------------------------------------
+%----------------------------------------------------------------------------
+%
+
+\begin{document}
+%
+\title{The $\theta_{13}$ and $\delta_{CP}$ sensitivities of the SPL-Fréjus project revisited}
+\author{Jean Eric Campagne, Antoine Cazes}
+\institute{ Laboratoire de l'Accélérateur Linéaire -
+Université Paris-Sud - B\^at. 200 - BP 34 -
+91898 Orsay Cedex, France}
+\mail{campagne@lal.in2p3.fr}, \mail{cazes@lal.in2p3.fr}
+\date{\today}
+%
+%
+%
+%\selectlanguage{francais}
+%
+\abstract{
+An optimization of the CERN SPL beam line has been performed guided by the sensitivity to the $\theta_{13}$ mixing angle and to the $\delta_{CP}$ Dirac CP violating phase performances. A UNO-like 440 ktons water \v{C}erenkov detector located at 130~km from the target in a new foreseen Fréjus laboratory has been used as a generic detector. Concerning $\theta_{13}$ sensitivity, a gain of about $24\%$ may be reached using a $4.5$~GeV proton beam compared to the up to now considered $2.2$~GeV beam energy. This may motivate new machine developments to upgrade the nominal SPL proton beam energy.
+}
+%\pacs{14.60.Pq, 14.60.Lm}
+
+\maketitle
+
+
+\section{Introduction}
+The very near future of the neutrino long baseline experiments is devoted to the study of the oscillation mechanism in the range of $\Delta m^2 = \Delta m^2_{atm} \approx 2.7\,10^{-3}\mathrm{eV}^2$ \cite{SKNU04,K2KNU04} using conventional $\nu_\mu$ beams. The current K2K experiment in Japan \cite{K2KNU04}, and the forthcoming MINOS in the USA \cite{MINOS} take benefit of low energy beam to measure the $\Delta m^2$ parameter using the disappearance mode $\nu_\mu\rightarrow\nu_\mu$, while OPERA/ICARUS experiments \cite{OPERA,ICARUS} using the high energy CNGS beam \cite{CNGS} will be able to detect $\nu_\tau$ appearance. If we do not consider the LSND anomaly \cite{LSND} that will be further studied soon by MiniBooNE experiment \cite{MINIBOONE}, the three flavor family scenario will be confirmed and accommodated by a $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix \cite{PMNS} with three angles ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase $\delta_{CP}$.  
+
+Beyond this medium term plan, two of the next future tasks of neutrino physics are to improve the sensitivity of the last unknown mixing angle parameter, the so-called $\theta_{13}$, and to explore the CP violation mechanism in the leptonic sector. The present upper bound on $\theta_{13}$ is $\sin^22\theta_{13}<0.1$ for large $\Delta m^2$ at $90\%$~CL \cite{CHOOZ}. This sensitivity can be improved using reactor and accelerator experiments. In reactor experiments, one uses $\bar{\nu}_e$ in disappearance mode and may reach $\sin^22\theta_{13}<0.03$ \cite{Wpaper}. In accelerator experiments, one can use $\nu_e$ and $\bar{\nu}_e$ from $\beta$ beams \cite{BETABEAM} in both  disappearance and appearance modes (\textsl{i.e} $\stackrel{\scriptscriptstyle (-)}{\nu}_e\rightarrow \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$), and also $\nu_\mu$ in appearance mode (\textsl{i.e} $\nu_\mu\rightarrow\nu_e$) with conventional beams either with sub-mega watt proton drivers \cite{NOVA,T2K} or with multi-mega watt proton drivers \cite{T2K,BNLHS,CERN}. The later neutrino beam type, called Superbeam, is foreseen to be extended to produce $\nu_\mu$ beam and $\bar{\nu}_\mu$ beam from muon decays, the so-called Neutrino Factory, in order to study the eventual leptonic CP violation. Such Neutrino Complex is under study in Japan, in USA and also in Europe at CERN and details may be found in reference \cite{CERN}. A comparison of the performances of $\beta$ beam and Superbeam may be found for instance in reference \cite{DONINI}.  The reactor experiment result on $\theta_{13}$ is straight forward as compared to Superbeam and Neutrino Factory results that are on one hand reacher but in an other hand more complex to analyse due to the interplay between the different physics factors $\theta_{13}$, $\delta_{CP}$, sign$(\Delta m^2_{23})$, sign$(\tan(2\theta_{23}))$ \cite{DONINI,DOUBLE-CHOOZ}. 
+
+This paper presents results of a new simulation of the SPL (Super Proton Linac) Superbeam that could take place at CERN \cite{SPL}, using for definitiveness a UNO-like 440kT fiducial water \v{C}erenkov detector \cite{UNO} located in a new enlarged underground laboratory under study in the Fréjus tunnel, $130$~km away from CERN \cite{mosca}. The SPL neutrino beam is created by  decays of pions, muons and kaons produced by the interactions of a $4$~MW proton beam impinging a liquid mercury jet \cite{CERN}. Pions, muons and kaons are collected using two concentric electromagnetic lenses (horns), the inner one and the outer one are hereafter called "Horn" and "Reflector" respectively \cite{Meer}. Horns are followed by a decay tunnel where most of the neutrinos are produced. A sketch of the beam line is shown on figure~\ref{fig:Sbeam}.  
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.2]{../picts/cernmeg3_6-02.eps}
+\caption{\label{fig:Sbeam}Sketch of the SPL neutrino Superbeam from CERN to the Fréjus tunnel.}	
+\end{figure}
+
+The analysis chain consists of different stages: the simulation of the interactions between the proton beam and the mercury target, the propagation of the resulting secondary particles through the magnetic field and the materials of the horns, the tracking of $\pi^\pm$, $K^{\pm,0}$ and $\mu^\pm$ until they decay, the computation of the neutrino flux at the detector site, and finally the statistical analysis. A part of the simulation chain has already been described in reference \cite{nuFact134,MMWPSCazes}. 
+
+
+Compared to recent papers on the same subject \cite{DONINI,JJG,Mezzetto}, we have reoptimized the Horn and Reflector shapes \cite{nuFact138}, and introduced the kaon background simulation which allows us to update the SPL beam energy. The organization of this document follows the simulation chain: the interaction between the proton beam and the mercury target is presented in the second section. The kaon production is detailed in the third section. The simulation of the horns is described in the forth section, while the algorithms used to compute the neutrino fluxes are explained in the fifth section. Then, the sensitivities to $\theta_{13}$ and $\delta_{CP}$ are revisited with new studies about the optimization of the proton beam energy, the pion collection and the decay tunnel geometry.
+
+\section{Target simulation}
+\label{sec:target}
+Since hadronic processes are crucial to describe the interactions of the proton beam on the target, the FLUKA simulator \cite{fluka} has been chosen for this first step of the simulation. 
+%
+\begin{table}
+\caption{\label{tab:targ}Liquid mercury jet parameters.}
+\begin{tabular}{ll}
+\hline\noalign{\smallskip}
+    \centre{2}{Hg target}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+      Hg jet speed & $20$~m/s \\
+      density & $13.546$ \\
+      Length, radius & $30$~cm, $7.5$~mm \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%\Table{\label{tab:targ}Liquid mercury jet parameters.}
+%    \br
+%     \centre{2}{Hg target}\\
+%     \mr
+%      Hg jet speed & $20$~m/s \\
+%      density & $13.546$ \\
+%      Length, radius & $30$~cm, $7.5$~mm \\
+%      \br
+%\endTable
+The target used in the present study is a mercury liquid jet \cite{CERN} simulated by a cylinder $30$~cm long (representing two hadronic lengths) and $1.5$~cm diameter (see table~\ref{tab:targ}). The pencil like simulated proton beam is composed with  $10^6$ mono-energetic protons. The beam axis is also the symmetry axis of the target and the horns and the decay tunnel. Simulations have been performed for $2.2$~GeV proton kinetic energy, the up to now nominal design \cite{SPL}, as well as for $3.5$~GeV, $4.5$~GeV, $6.5$~GeV and $8$~GeV according to possible new designs \cite{MMWPSGaroby}.
+
+
+Particle production yields are summarized in table~\ref{tab:nbPart}. The secondary proton and neutron rates induce important radiation damages and power dissipation in the horns which have been addressed in reference \cite{nuFact134}, and which will require specific R\&D effort. At $2.2$~GeV, kaon yields are very low, but it has a dramatic energy dependence as further studied in section~\ref{sec:kaon}. It is worth to mention that the numbers in table~\ref{tab:nbPart} are not to be taken as face values, because the cross sections of pion and kaon productions using proton beam are still under studies as for instance by the HARP experiment \cite{harp} and in the future by the MINERVA experiment \cite{minerva}.
+
+
+%
+\begin{table*}
+\caption{\label{tab:nbPart}Average number of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA). The $\mu^+/\mu^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+$E_k$ (GeV) & p & n & $\gamma$ & $e^-$ & $e^+$ & $\pi^+$ & $\pi^-$ & $\mu^+$ & $\mu^-$ & $K^+$ & $K^0$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+2.2 & $1.4$     &  $17$   & $5.0$  &  $0.17$   &  $0.08$    &  $0.24$   &  $0.18$ & $4$ & $1$ & $7$ & $6$ \\
+
+3.5 &$1.8$    &  $17$  & 7.0  &  0.28   &  0.15    &  0.41   &  0.37 & $10$ & $3$ & $35$ & $30$ \\
+
+$4.5$ &  $2.3$  &  $17$ & $7.7$ &  $0.35$  & $0.21$   &  $0.57$ & $0.39$&  $11$ & $3.3$  &  $93$ &  $68$       \\
+
+$8$   &  $3.1$  &  $17$ & $11.0$ & $0.63$  & $0.41$   &  $1.00$  &  $0.85$ &  $30$ &  $9.5$ &  $413$ &    $340$  \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+
+%\fulltable{\label{tab:nbPart}Average number of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA). The $\mu^+/\mu^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}
+%\br
+%$E_k$ (GeV) & p & n & $\gamma$ & $e^-$ & $e^+$ & $\pi^+$ & $\pi^-$ & $\mu^+$ & $\mu^-$ & $K^+$ & $K^0$ \\
+%\mr
+%2.2 & $1.4$     &  $17$   & $5.0$  &  $0.17$   &  $0.08$    &  $0.24$   &  $0.18$ & $4$ & $1$ & $7$ & $6$ \\
+%
+%3.5 &$1.8$    &  $17$  & 7.0  &  0.28   &  0.15    &  0.41   &  0.37 & $10$ & $3$ & $35$ & $30$ \\
+%
+%$4.5$ &  $2.3$  &  $17$ & $7.7$ &  $0.35$  & $0.21$   &  $0.57$ & $0.39$&  $11$ & $3.3$  &  $93$ &  $68$       \\
+%
+%$8$   &  $3.1$  &  $17$ & $11.0$ & $0.63$  & $0.41$   &  $1.00$  &  $0.85$ &  $30$ &  $9.5$ &  $413$ &    $340$         \\
+%
+%\br
+%\endfulltable
+
+The cross section uncertainties are the main source of discrepancy between simulator programs. Some comparisons between FLUKA and MARS \cite{MARS} have already been presented in the same context \cite{nuFact134}. The energy distribution of the pions exiting the target, computed with the two simulator programs FLUKA and MARS, is shown on figure~\ref{fig:compFlukaMars}a. Pions come from $\Delta$ decays which in turn are originated from two different sources. At low energy ($P<200$~MeV/c), $\Delta$ are produced by protons of the target excited by the beam interactions, while the highest energy part of the spectrum is due to transformation of protons of the beam into $\Delta$. The discrepancy is quite large for the low energy part. However, the horns are designed to focus the high energy part of the spectrum (see section~\ref{sec:horn}), and therefore, MARS and FLUKA are in better agreement for the energy spectrum computed at the entrance of the decay tunnel (figure~\ref{fig:compFlukaMars}b). So,  the discrepancy  at low energy between MARS and FLUKA does not matter too much for the present application.
+
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/compMarsFluka.eps}
+\caption{\label{fig:compFlukaMars}Pion momentum distribution at the exit the target (a) and at the exit of the horns (b), simulated by FLUKA (\dashed) and by MARS (\full).}
+%\caption{\label{fig:compFlukaMars}Pion momentum distribution at the exit the target (a) and at the exit of the horns (b), simulated by FLUKA and by MARS.}
+
+\end{figure}
+%
+\section{Kaon production}
+\label{sec:kaon}
+The possibility to increase the SPL energy in order to study the optimization of the physics program has been recently pointed out \cite{MMWPSGaroby}. Then, the kaon production should be clearly addressed because it is a source of $\nu_e$ and $\bar{\nu}_e$ background events. The kaon decay channels and branching ratios are presented in table~\ref{tab:BRKP0SL} in \ref{sec:kaons}.
+
+The target simulation described in section~\ref{sec:target} has been used with $500,000$ p.o.t with kinetic energy uniformly distributed between $2.2$~GeV and $5$~GeV. The momentum of outgoing pions and kaons are recorded when they exit the target. The number of produced $K^{o,\pm}$ at different proton beam energies are presented on figure~\ref{fig:KaonsPions}a. In one hand the $K^o$ production rate is similar to the $K^+$ production rate, but in an other hand the $K^-$ production rate is almost forty times smaller. For comparison, the numbers of $\pi^+$ and $\pi^-$  produced in the same conditions are presented on figure~\ref{fig:KaonsPions}b. Pion production rate is about two orders of magnitude greater than the kaon production rate.
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/KaonProd.eps}
+\caption{\label{fig:KaonsPions}Kaon production (a) as a function of the incident proton beam energy ($E_p$) for $500~000$ incident protons with (\full) curve for $K^+$, (\dashed) curve for $K^-$ and (\dotted) curve for $K^o$. Pion production (b) in the same conditions with (\full) curve for $\pi^+$ and (\dashed) curve for $\pi^-$.}
+\end{figure}
+
+The behavior of the two pion and kaon production rates are quite different. The pion yield grows smoothly with the proton energy while the production of kaons seams to have two origins, which has been confirmed by FLUKA's authors \cite{FLUKAprivate}. For beam energy below approximatively $4$~GeV, the resonance production model is used, and one notices a low production rate with a maximum at about $3.4$~GeV. For beam energy above  $4$~GeV, the dual parton model is used, and the production rate experiences a threshold effect with a rapid rise. The ratio between positive kaon and pion production rates is about $0.5\%$ between $2.2$~GeV and $4$~GeV and grow up to $2.5\%$ at $5$~GeV. One notices that the maching between the two kaon production models may not be optimal.
+%
+\section{Horn simulation}
+\label{sec:horn}
+The simulation code of the electromagnetic horns is written using GEANT 3.2.1 \cite{geant} for convenience and since electromagnetic processes are dominant, FLUKA has not been considered as mandatory, but this may be revised in a future work. The geometry of the horns has been inspired by an existing CERN prototype and a Reflector design proposed in reference \cite{SIMONE1}. Depending of the current injection, only positive secondary particles or negative secondary particles are focused. The relevant parameters are detailed in table~\ref{tab:specif}.
+
+The mercury target is localized inside the Horn because of the low energy and the large emittance of the secondary pions produced: $<P_{\pi T}>/<P_\pi> \approx 240$~MeV$/400$~MeV ($2.2$~GeV proton beam energy). This explains the Horn design (figure~\ref{fig:plan}), with a cylindrical part around the target, called the neck, which is larger than the transversal size of the target to simulate the room for target handling, and a conic part designed such that the relevant pions are focused as much as possible to exit the magnetic field parallel to the beam axis.
+
+%\Table{\label{tab:specif}Relevant parameters of horns. The shapes of the conductors are not changed by proton beam energy changes, as the focusing has been optimized for a defined pion momentum.}
+%\br
+%\centre{2}{inner horn} & \centre{2}{reflector} \\
+%\mr
+%  neck inner radius & $3.7$~cm              & neck inner radius & $20.3$~cm \\
+%  neck length & $40$~cm                     & end cone inner radius & $35.7$~cm \\
+%  end cone inner radius & $15.7$~cm         & outer radius & $40$~cm \\
+%  outer radius & $20.3$~cm                  & total length & $200$~cm \\
+%  total length & $180$~cm                   & Peak current & $600$~kA \\
+%  Alu thickness  & $3$~mm                   & Frequency & $50$~Hz \\
+%  Peak current & $300$~kA                   & & \\
+%  Frequency & $50$~Hz                       & & \\
+%\br
+%\endTable
+%
+\begin{table}
+\caption{\label{tab:specif}Relevant parameters of horns. The shapes of the conductors are not changed by proton beam energy changes, as the focusing has been optimized for a defined pion momentum.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+\centre{2}{inner horn} & \centre{2}{reflector} \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+  neck inner radius & $3.7$~cm              & neck inner radius & $20.3$~cm \\
+  neck length & $40$~cm                     & end cone inner radius & $35.7$~cm \\
+  end cone inner radius & $15.7$~cm         & outer radius & $40$~cm \\
+  outer radius & $20.3$~cm                  & total length & $200$~cm \\
+  total length & $180$~cm                   & Peak current & $600$~kA \\
+  Alu thickness  & $3$~mm                   & Frequency & $50$~Hz \\
+  Peak current & $300$~kA                   & & \\
+  Frequency & $50$~Hz                       & & \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+
+The shape of the horns conductors is a crucial point since it determines the energy spectrum of the neutrino at the detector site. The details of the conductor shape optimization for the present context may be found in reference \cite{nuFact138}. We just recall here some ingredients. For a $\theta_{13}$ driven $\nu_\mu \rightarrow \nu_e$ oscillation, a $\Delta m^2_{23}$ parameter value of $2.5\ 10^{-3}\mathrm{eV}^2$, and a baseline distance of $130$~km, the first oscillation maximum occurs for a neutrino energy of $260$~MeV\footnote{If one includes an energy spectral shape of the neutrino beam with a typical $\sigma_E/E \approx 1/3$, then a 10\% increase of the average neutrino energy is expected. But, the induced change on the $\theta_{13}$ sensitivity is negligeable.}. The   optimization of the physics potential depends at first approximation on the pion neutrino characteristics, which energy is fully determined by the pion 2-body decay and boost. To reach an energy of $260$~MeV, the pion needs a $\beta=0.97$, which in turn induces a pion momentum of $600$~MeV/c. Then, the shape of the conic part of the horns is determined such that these $600$~MeV/c pions exit parallel to the beam axis.
+
+\begin{figure}
+\centering
+\includegraphics[width=0.75\textwidth]{../picts/corneSchema.eps}
+\caption{\label{fig:plan}Design of the Horn and the Reflector conductor shapes implemented in the GEANT simulation. The Hg target is located inside the cylindrical part of the Horn.}
+\end{figure}
+
+Before closing this section, it is worth to quote that the Horn/Reflector conductor shapes optimized in the present study to focus a given pion momentum value, is not affected by a proton beam energy change. What is affected is the production rate of the relevant pions. This Horn/Reflector design consideration would be different if one wishes to focus as much as possible all the pions produced for which the mean energy is of course affected by a proton beam energy change.    
+%
+\section{Particle decay treatment and flux calculation}
+%
+The decay tunnel representation is a simple cylinder with variable length ($L_T$) and radius ($R_T$) filled with "vacuum". The base line design is a $20$~m long and $1$~m radius cylinder, but simulations have also been conducted with lengths of $10$~m and $40$~m, and radius of $1.5$~m in the spirit of reference \cite{donega}. In the GEANT simulation, to gain in CPU time, only pions, muons and kaons are tracked in the volume of the tunnel, and all particles exiting this volume are discarded. 
+
+
+Beyond the $1/L^2$ solid angle factor due to the source-detector distance ($L$) which decreases dramatically the fluxes, the neutrino beam focusing is very limited due to the small pion boost factor ($\approx 4$). Therefore, computational algorithms have been used to avoid a too prohibitive CPU time resulting from the simulation of each secondary particle decay. Otherwise, about $10^{15}$ p.o.t would have been necessary to obtain reliable statistics for the estimation of the $\bar{\nu}_e$ flux for instance.
+
+It is worth to mention that the particle decays occurring before the entrance of the decay tunnel are also taken into account and treated in the same manner, which is not the case in reference \cite{donega}. 
+
+\subsection{Algorithm description}
+\label{sec:algo}
+
+The decay code has been included in the GEANT code. The basic idea of this algorithm is to compute the neutrino fluxes using the probability of reaching the detector for each neutrino produced by a $\pi$ or a $K$ or a $\mu$ particle (on-axis neutrino beam). This method has already been used in reference \cite{donega} and has been modified and extended to the kaon decay chain for the present study. 
+
+Muon neutrino comes mostly from pion decay. In a first stage, each pion is tracked by GEANT until it decays. Then, the probability for the produced muon neutrino to reach the detector is computed. The flux is obtained applying the probability as a weight for each neutrino. All the pions produced in the simulation are therefore useful to compute the flux, and this allows to reduce the number of events in the simulation to $10^6$ p.o.t. In this computation, the decay region (horns and tunnel) is considered as point like compared to the source-detector distance. 
+
+The same method is applied for neutrino coming from muons and kaons with some modifications  because most of the muons do not decay, and there are very few kaons produced (see table~\ref{tab:nbPart}).
+The probability computation is presented in \ref{sec:decayprobcomp}. 
+
+%\Table{\label{tab:proton}Number of protons on target for different beam energy at 4~MW constant power.}
+%\br
+%			Beam energy  & number of proton \\
+%			  (GeV)      & per year ($10^{23}$ p.o.t/y) \\
+%\mr
+%			2.2 & 1.10 \\
+%			3.5 & 0.70 \\
+%			4.5 & 0.56 \\
+%			6.5 & 0.40 \\
+%			8.0 & 0.30 \\
+%\br
+%\endTable
+\begin{table}
+\caption{\label{tab:proton}Number of protons on target for different beam energy at 4~MW constant power.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			Beam energy  & number of proton \\
+			  (GeV)      & per year ($10^{23}$ p.o.t/y) \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			2.2 & 1.10 \\
+			3.5 & 0.70 \\
+			4.5 & 0.56 \\
+			6.5 & 0.40 \\
+			8.0 & 0.30 \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+\subsection{Validation of the algorithm}
+The validity of the method presented in the previous section have been tested against a straight forward  algorithm consisting of decaying each pion $N$ times ($N \approx 10^6$) in a full GEANT simulation of the event (decays included). Such method presents the advantage to keep all the information of the neutrino available for further studies. It can be a good approach to compute the muon neutrino flux coming from pion decays. It can also provide the beam profile, but it shows its limits for the muon induced fluxes, especially the $\bar{\nu}_e$ flux. Indeed, this means that each muon is duplicated $N$ times and when a muon decays, it must decay $N$ times again. For $N\approx 10^6$, this is a prohibitive CPU time consuming.
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/compGeantDonega.eps}
+\caption{\label{fig:compGeantDonega}Comparison between the probability method, (\full) curve, and the full GEANT simulation method, (\dashed) curve, for the $\nu_\mu$ from $\pi^+$ flux (left) and the $\bar{\nu}_\mu$ from $\pi^-$ flux  (right). The horns are set to focus positive particles.}
+\end{figure}
+
+The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are displayed on figure~\ref{fig:compGeantDonega} for both methods. The two spectra shows a clear agreement, and this makes confidence on the probability method.
+%
+\subsection{Simulated fluxes}
+The fluxes are computed at a distance of $100$~km from the source by convention and can be rescaled at any desired distance. They provide the number of the four neutrino species ($\nu_\mu$, $\bar{\nu}_\mu$, $\nu_e$, $\bar{\nu}_e$) passing through a $100$~m$^2$ fiducial area during $1$~year.
+
+In practice, the fluxes are given as a function of the neutrino energy via histograms composed of $20$~MeV bin width.  These histograms are filled with the energy of each neutrino weighted by the probability to reach the detector (section~\ref{sec:algo}). To obtain the fluxes, the histograms are rescaled to the number of p.o.t per year depending on the beam energy. Table~\ref{tab:proton} reports on the number of p.o.t per year for the different energies studied using the definition of one year being $10^7$~s and keeping the beam power constant (\textsl{i.e} $4$~MW).
+
+Three origins are identified in the composition of each neutrino flux:
+\begin{itemize}
+	\item neutrinos from pions, which includes neutrinos created by primary pion decays and neutrinos coming from the muons produced by pion decays or muons directly exiting the target. This is the component studied in reference \cite{donega} but with different settings and event generator;
+	\item neutrinos emitted during the decay chain of the charged kaons, either by direct production, or produced by the daughter pions and muons;
+	\item neutrinos coming from the decay chain of the neutral kaons.
+\end{itemize}
+
+The three components of the fluxes for the four neutrino species are presented on figure~\ref{fig:flux22p} for positive particle focusing and a proton beam kinetic energy of $2.2$~GeV. The $\nu_\mu$ flux is dominated by the neutrinos of pion decays, but a tail above $500$~MeV (zoom on the top left part) is created by the $K^+\rightarrow \mu^+\nu_\mu$ channel, which is anyway at least three order of magnitude below the flux maximum. The $\bar{\nu}_\mu$ flux is mostly due to the decays of $\pi^-$ that are not unfocused by the horns, but the higher energy part comes from $\mu^+$ decays. It is noticable that the $\nu_e$ and $\bar{\nu}_e$ fluxes are respectively more than $200$ and more than $7000$ times smaller than the $\nu_\mu$ flux. The $\bar{\nu}_e$ are produced in a large part by the $K^0_L\rightarrow\pi^+e^-\bar{\nu}_e$ decay channel and by $\mu^-$ decays, while the  $\nu_e$ flux is dominated by the $\mu^+$ decays.
+
+On figure~\ref{fig:flux22m}, the horns are set to focus negative particles keeping other parameters identical. By comparison with positive focusing, one can at first approximation translate the results by exchanging particles and anti-particles, except that the $K^+/K^-$ ratio is about 100  in the beam-target interactions (see table~\ref{tab:nbPart}).
+
+On figures~\ref{fig:flux45p} and \ref{fig:flux8p}, one observes the evolution of figure~\ref{fig:flux22p} when the proton beam kinetic energy increases to $4.5$~GeV and $8$~GeV, respectively. Correspondingly, the results for negative particle focusing are presented on figures~\ref{fig:flux45m} and \ref{fig:flux8m}. One clearly notices the increase of the kaon induced neutrino contents as the beam energy grows.
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux22p.eps}
+\caption{	\label{fig:flux22p}Neutrino fluxes $100$~km from the decay region and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$~GeV (4~MW), a decay tunnel with a length of $20$~m and a radius of $1$~m. The (\full) curve is the contribution from primary pions and the daughter muons, the (\dashed) curve is the contribution from the charged kaon decay chain, and the (\dotted) curve is the contribution from the $K^0$ decay chain.}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux22m.eps}
+\caption{\label{fig:flux22m}Same legend as for figure~\ref{fig:flux22p} but the horns are focusing negative particles.}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux45p.eps}
+\caption{\label{fig:flux45p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $4.5$~GeV (4~MW).}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux45m.eps}
+\caption{\label{fig:flux45m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $4.5$~GeV (4~MW).}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux8p.eps}
+\caption{\label{fig:flux8p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.6]{../picts/flux8m.eps}
+\caption{\label{fig:flux8m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure}
+
+\begin{table*}
+\caption{\label{tab:speciesfluxes}Integral of the different species fluxes with different settings. The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are expressed in $10^{13}/100\mathrm{m}^2/y$ unit while the $\nu_e$ and $\bar{\nu}_e$ fluxes are expressed in $10^{11}/100\mathrm{m}^2/y$ unit. The positive focusing  and negative focusing  are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. Setting (1) is the baseline option and means $L_T = 20$~m and $R_T = 1$~m, while setting (2) means $L_T = 10$~m and $R_T = 1$~m and setting (3) means $L_T = 40$~m and $R_T = 1$~m, and finally the setting (4) means $L_T = 20$~m and $R_T = 1.5$~m.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			Settings  & \centre{2}{$\nu_\mu$} & \centre{2}{$\nu_e$} 
+								&	\centre{2}{$\bar{\nu}_\mu$} & \centre{2}{$\bar{\nu}_e$} \\
+								\cline{2-9}
+								& $+$ & $-$ & $+$ & $-$ & $+$ & $-$ 
+								& $+$ & $-$ \\ 
+\noalign{\smallskip}\hline\noalign{\smallskip}
+
+(1): $2.2$~GeV  
+	& $7.6$         & $0.4$ 
+	& $3.2$ 				& $0.2$
+	& $0.3$ 				& $5.8$  
+	& $0.1$ 				& $1.6$ \\		  
+
+(1): $3.5$~GeV  
+	& $10.0$          & $0.9$ 
+	& $4.4$           & $0.6$
+	& $0.7$ 					& $8.5$  
+	& $0.3$ 					& $2.2$ \\		  
+
+(1): $4.5$~GeV  
+	& $10.9$          & $1.1$ 
+	& $5.1$           & $1.0$
+	& $0.7$ 					& $6.7$  
+	& $0.4$ 					& $1.8$ \\		  
+
+(1): $6.5$~GeV  
+	& $10.4$          & $1.4$ 
+	& $6.4$           & $2.0$
+	& $1.0$           & $7.1$  
+	& $0.9$ 					& $2.5$ \\	
+
+(1): $8.0$~GeV  
+	& $9.7$          & $1.5$ 
+	& $6.7$           & $2.3$
+	& $1.2$           & $7.1$  
+	& $1.1$ 					& $2.8$ \\
+
+
+(2): $4.5$~GeV  
+	& $7.1$          & $1.0$ 
+	& $2.8$          & $0.9$
+	& $0.5$          & $5.2$  
+	& $0.3$ 				  & $1.1$ \\		  
+
+(3): $4.5$~GeV  
+	& $12.3$          & $1.2$ 
+	& $7.2$           & $1.0$
+	& $0.8$           & $7.5$  
+	& $0.4$ 					& $2.6$ \\	
+
+(4): $4.5$~GeV  
+	& $13.2$          & $1.5$ 
+	& $6.9$           & $1.4$
+	& $0.9$           & $8.1$  
+	& $0.6$  					& $2.7$ \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%\fulltable{\label{tab:speciesfluxes}Integral of the different species fluxes with different settings. The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are expressed in $10^{13}/100\mathrm{m}^2/y$ unit while the $\nu_e$ and $\bar{\nu}_e$ fluxes are expressed in $10^{11}/100\mathrm{m}^2/y$ unit. The positive focusing  and negative focusing  are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. Setting (1) is the baseline option and means $L_T = 20$~m and $R_T = 1$~m, while setting (2) means $L_T = 10$~m and $R_T = 1$~m and setting (3) means $L_T = 40$~m and $R_T = 1$~m, and finally the setting (4) means $L_T = 20$~m and $R_T = 1.5$~m.}
+%
+%\br
+%
+%			Settings  & \centre{2}{$\nu_\mu$} & \centre{2}{$\nu_e$} 
+%								&	\centre{2}{$\bar{\nu}_\mu$} & \centre{2}{$\bar{\nu}_e$} \\
+%								\cline{2-9}
+%								& $+$ & $-$ & $+$ & $-$ & $+$ & $-$ 
+%								& $+$ & $-$ \\ 
+%\mr
+%
+%(1): $2.2$~GeV  
+%	& $7.6$         & $0.4$ 
+%	& $3.2$ 				& $0.2$
+%	& $0.3$ 				& $5.8$  
+%	& $0.1$ 				& $1.6$ \\		  
+%
+%(1): $3.5$~GeV  
+%	& $10.0$          & $0.9$ 
+%	& $4.4$           & $0.6$
+%	& $0.7$ 					& $8.5$  
+%	& $0.3$ 					& $2.2$ \\		  
+%
+%(1): $4.5$~GeV  
+%	& $10.9$          & $1.1$ 
+%	& $5.1$           & $1.0$
+%	& $0.7$ 					& $6.7$  
+%	& $0.4$ 					& $1.8$ \\		  
+%
+%(1): $6.5$~GeV  
+%	& $10.4$          & $1.4$ 
+%	& $6.4$           & $2.0$
+%	& $1.0$           & $7.1$  
+%	& $0.9$ 					& $2.5$ \\	
+%
+%(1): $8.0$~GeV  
+%	& $9.7$          & $1.5$ 
+%	& $6.7$           & $2.3$
+%	& $1.2$           & $7.1$  
+%	& $1.1$ 					& $2.8$ \\
+%
+%
+%(2): $4.5$~GeV  
+%	& $7.1$          & $1.0$ 
+%	& $2.8$          & $0.9$
+%	& $0.5$          & $5.2$  
+%	& $0.3$ 				  & $1.1$ \\		  
+%
+%(3): $4.5$~GeV  
+%	& $12.3$          & $1.2$ 
+%	& $7.2$           & $1.0$
+%	& $0.8$           & $7.5$  
+%	& $0.4$ 					& $2.6$ \\	
+%
+%(4): $4.5$~GeV  
+%	& $13.2$          & $1.5$ 
+%	& $6.9$           & $1.4$
+%	& $0.9$           & $8.1$  
+%	& $0.6$  					& $2.7$ \\
+%	
+%\br
+%\endfulltable
+
+On table~\ref{tab:speciesfluxes} are reported the integral of the fluxes when one modifies the decay tunnel length and radius, as well as the beam kinetic energy.  Switching the radius from $1$~m to $1.5$~m has increased the $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes by $20\%$ but also in paralell the $\nu_e$ and $\bar{\nu}_e$ fluxes by $38\%$. Increasing the decay tunnel length from $10$~m up to $40$~m yields an increase of the signal like flux by $75\%$ and also in paralell an increase of the background like flux by a factor $1.7$. Notice that the $\nu_\mu/\bar{\nu}_\mu$ flux ratio is rather insensitive to the decay tunnel length. The feeling that $L_T = 20$~m and $R_T = 1$~m is a good signal over background compromise is confirmed by sensitivity quantitative studies reported in section~\ref{sec:results}.  
+
+Looking at the evolution of $\nu_\mu$ flux with respect to the beam energy, one notices that a maximum is reached around $4.5$~GeV. This is due to the competition between the cross section rise with respect to the energy and the decrease of the number of p.o.t due to the constant SPL power ($4$~MW).
+%
+\section{Sensitivity computation ingredients}
+%
+The sensitivity to $\theta_{13}$ and $\delta_{CP}$ is computed for an $\nu_\mu\rightarrow\nu_e$ appearance experiment. An analysis program described in reference \cite{MEZZETTONUFACT060} has been used for such sensitivity computation. See table~\ref{tab:param} for the default user parameter values used in this paper. We just remind here some key points of the program. 
+
+It is included a full 3-flavors oscillation probability computation with matter effects, but no ambiguities are taken into account. This latest point may be revisited in a future work using reference \cite{DONINI-2}. Concerning the background events, the $\nu_e/\bar{\nu}_e$ from the beam, the $\nu_\mu e^-$ elastic scattering process, the $\pi^o$ production as well as the $\mu/e$ misidentification are taken into account. The cross-sections from the NUANCE program are used \cite{NUANCE}. The systematics error is a user parameter and we have used the $2\%$ value considered as a final goal, but also $5\%$ and $10\%$ \cite{MEZZETTONUFACT060}. The detector considered for definitiveness is similar to the UNO detector, i.e. a $440$~kt fiducial water \v{C}erenkov detector \cite{UNO}. It is located at $L = 130$~km from CERN, in the foreseen new Fréjus laboratory \cite{mosca}. It is worth to mention that if one wants to evaluate the influence of $L$ on the sensitivity, it would mean a re-optimization of the horns for each $L$ envisaged (see section~\ref{sec:horn}).  
+
+\begin{table}
+\caption{\label{tab:param}Default user parameters used to compute the sensitivity curves \cite{MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masses and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite{KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite{JJG}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			$\Delta m^2_{12} = 8.2 (0.5)\times 10^{-5}~\mathrm{eV}^2$ & $\sin^22\theta_{12} = 0.82 (9\%)$ \\
+			$\Delta m^2_{23} = 2.5 (0.1)\times 10^{-3}~\mathrm{eV}^2$ & $\sin^22\theta_{23} = 1.0 (1\%)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		  $L_T = 20$~m & $R_T = 1$~m \\ 
+		  $M=440$~kT   & $\epsilon_{syst}=2\%$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%\Table{\label{tab:param}Default user parameters used to compute the sensitivity curves \cite{MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masses and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite{KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite{JJG}.}
+%\br
+%			$\Delta m^2_{12} = 8.2 (0.5)\times 10^{-5}~\mathrm{eV}^2$ & $\sin^22\theta_{12} = 0.82 (9\%)$ \\
+%			$\Delta m^2_{23} = 2.5 (0.1)\times 10^{-3}~\mathrm{eV}^2$ & $\sin^22\theta_{23} = 1.0 (1\%)$ \\
+%\mr
+%		  $L_T = 20$~m & $R_T = 1$~m \\ 
+%		  $M=440$~kT   & $\epsilon_{syst}=2\%$ \\
+%\br
+%\endTable
+
+The running time scenario has been fixed to 5 years focusing positive particles for the $\theta_{13}$ sensitivity studies. This scenario gives comparable $\theta_{13}$ sensitivity than a mixed focusing scenario defined as 2 years focusing positive particles and 8 years focusing negative particles which is more appropriate for $\delta_{CP}$ sensitivity studies.
+%
+\section{Results}
+\label{sec:results}
+The $\theta_{13}$ and $\delta_{CP}$ sensitivities are computed with $\theta_{13} = 0^\circ$ and $\delta_{CP} = 0^\circ$ if not explicitly mentioned. 
+
+Table~\ref{tab:nbvsE} presents the number of signal and background events for a $5$ years positive focusing experiment, but with different beam energy settings. The significance parameter is defined in reference \cite{MEZZETTONUFACT060} as:
+\begin{equation}
+\mathcal{S} = \frac{N^{osc}_{\nu_e}}{\sqrt{N^{osc}_{\nu_e} + N^{beam}_{\nu_e} + N^{oth. bkg} + \left(\left(N^{osc}_{\nu_e}+N^{beam}_{\nu_e}\right)\times\epsilon_{syst}\right)^2}}
+\label{eq:significance}
+\end{equation}
+with $N^{osc}_{\nu_e}$ the number of $\nu_e/\bar{\nu}_e$ events due to $\nu_\mu/\bar{\nu}_\mu$ oscillations, $N^{beam}_{\nu_e}$ the number of background events coming from the $\nu_e/\bar{\nu}_e$ contamination of the beam, $N^{oth. bkg}$ the other kinds of background events and $\epsilon_{syst}$ the systematical factor. One can appreciate that $4.5$~GeV beam energy presents better results and may become the new base line energy.
+%
+
+%\Table{\label{tab:nbvsE}Number of events for 5 years positive focusing scenario with default parameters of table~\ref{tab:param}. : $\pi^0$, $\nu_\mu$-elast., $\mu/e$-missId. The significance parameter is defined by equation~\ref{eq:significance}.}
+%\br
+%
+%			 & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+%\mr
+%			non oscillated $\nu_\mu$       & $36917$  & $60969$  & $73202$  & $78024$ & $76068$ \\ 
+%			oscillated $\nu_e$             & $31$  & $44$  & $47$  & $44$ & $41$ \\
+%			beam $\nu_e$                   & $165$ & $222$ & $241$ & $287$ & $299$ \\
+%			other background & $70$  & $104$ & $126$ & $147$ & $152$ \\
+%\mr
+%			Significance                  &  $1.87$ & $2.18$  & $2.20$  & $1.92$ & $1.74$ \\
+%\br
+%\endTable
+\begin{table}
+\caption{\label{tab:nbvsE}Number of events for 5 years positive focusing scenario with default parameters of table~\ref{tab:param}. : $\pi^0$, $\nu_\mu$-elast., $\mu/e$-missId. The significance parameter is defined by equation~\ref{eq:significance}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			 & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			non oscillated $\nu_\mu$       & $36917$  & $60969$  & $73202$  & $78024$ & $76068$ \\ 
+			oscillated $\nu_e$             & $31$  & $44$  & $47$  & $44$ & $41$ \\
+			beam $\nu_e$                   & $165$ & $222$ & $241$ & $287$ & $299$ \\
+			other background & $70$  & $104$ & $126$ & $147$ & $152$ \\
+			Significance                  &  $1.87$ & $2.18$  & $2.20$  & $1.92$ & $1.74$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+The contours at $90\%$, $95\%$ and $99\%$~CL of the $\theta_{13}$ sensitivity are presented in the $(\sin^22\theta_{13}, \Delta m^2_{23})$ plane on figure~\ref{fig:sensi45} for $4.5$~GeV proton beam kinetic energy. The comparison between the contours at $90\%$~CL with $2.2$~GeV, $3.5$~GeV, $4.5$~GeV and $8$~GeV beam energies is shown on figure~\ref{fig:compSensi}. One notices a better perfomence reached with a $4.5$~GeV energy beam as a confirmation of significance parameter value. But, in fact there is not much visual difference between a sensitivity obtained with $3.5$~GeV and $4.5$~GeV, even if one should keep in mind that kaon production models are different at these two energies (see section~\ref{sec:kaon}). Quantitative studies of the minimum $\sin^22\theta_{13}$ with respect to the kinetic beam energy $E_k(proton)$, and the decay length $L_T$, and the systematics $\epsilon_{syst}$ are presented in tables~\ref{tab:thvsE} and \ref{tab:thvseps}. The influance of the systematical level is presented on figure~\ref{fig:compEpsSyst}.
+%
+\begin{figure}
+\centering
+\includegraphics[scale=0.4]{../picts/sensi45.eps}
+\caption{\label{fig:sensi45}Sensitivity contours obtained with a SPL energy of $4.5$~GeV and default parameters of table~\ref{tab:param}.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[scale=0.4]{../picts/compSensi.eps}
+\caption{\label{fig:compSensi}Comparison of 90\% sensitivity contours obtained with SPL energies of ($2.2$, $3.5$, $4.5$, $8$)~GeV and default parameters of table~\ref{tab:param}.}
+\end{figure}
+
+%\Table{\label{tab:thvsE}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for diferent decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$). Other parameters are fixed to default values (table~\ref{tab:param}).}
+%\br
+%		        & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV  \\
+%\mr
+%			$10$~m & $1.10$ & $0.96$ & $1.05$ & $1.10$ & $1.20$ \\
+%			$20$~m & $1.20$ & $0.96$ & $0.91$ & $1.05$ & $1.15$ \\
+%			$40$~m & $1.26$ & $1.00$ & $1.00$ & $1.10$ & $1.20$ \\
+%\br
+%\endTable
+\begin{table}
+\caption{\label{tab:thvsE}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for diferent decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$). Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		        & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV  \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$10$~m & $1.10$ & $0.96$ & $1.05$ & $1.10$ & $1.20$ \\
+			$20$~m & $1.20$ & $0.96$ & $0.91$ & $1.05$ & $1.15$ \\
+			$40$~m & $1.26$ & $1.00$ & $1.00$ & $1.10$ & $1.20$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+%\Table{\label{tab:thvseps}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for different level of systematics ($\epsilon_{syst}$) and kinetic beam energy ($E_k(proton)$). Other parameters are fixed to default values (table~\ref{tab:param}).}
+%\br			
+%			      & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+%\mr			
+%			$2\%$ & $1.20$ & $0.96$ & $0.91$ & $1.10$ & $1.20$ \\
+%			$5\%$ & $1.51$ & $1.26$ & $1.26$ & $1.51$ & $1.66$ \\
+%			$10\%$ & $2.40$ & $2.19$ & $2.29$ & $2.75$ & $3.16$ \\
+%\br			
+%\endTable
+\begin{table}
+\caption{\label{tab:thvseps}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for different level of systematics ($\epsilon_{syst}$) and kinetic beam energy ($E_k(proton)$). Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			      & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$2\%$ & $1.20$ & $0.96$ & $0.91$ & $1.10$ & $1.20$ \\
+			$5\%$ & $1.51$ & $1.26$ & $1.26$ & $1.51$ & $1.66$ \\
+			$10\%$ & $2.40$ & $2.19$ & $2.29$ & $2.75$ & $3.16$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+\begin{figure}
+\centering
+\includegraphics[scale=0.4]{../picts/compEpsSyst.eps}
+\caption{\label{fig:compEpsSyst}$90\%$ CL sensitivity contours obtained with a SPL energy of $4.5$~GeV and default parameters of table~\ref{tab:param} but for different $\epsilon_{syst}$ values.}
+\end{figure}
+
+There are also variations on the minimum $\sin^22\theta_{13}$ value that may be reached in a $\nu_\mu \rightarrow \nu_e$ experiment which are due to the $\mathrm{sign}(\Delta m^2_{23})$ ambiguity and the $\delta_{CP}$ value. On table~\ref{tab:sign} are presented these kind of variations. Other ambiguities coming from the sign$(\tan(2\theta_{23}))$ ignorance also take place as studied in reference \cite{DONINI}. From figure~9 of this reference, we estimate a 30\% effect on $\sin^2(2\theta_{13})$ sensivity due to these ambiguities.
+
+%\begin{figure}[htb]
+%	\centering
+%		\includegraphics{../picts/compDelta_thVSdm.eps}
+%	\caption{$\theta_{13}$-sensitivity dependence up on the $\delta_CP$ phase obtained for a $4.5$~GeV SPL beam and 5 years running with a positive focusing scenario.}
+%	\label{fig:compDelta_thVSdm}
+%\end{figure}
+ 
+%\Table{\label{tab:sign}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for different values of sign$(\Delta m^2_{23})$ and $\delta_{CP}$. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%\br
+%			    & $-180^\circ$ & $-90^\circ$ & $0^\circ$ & $90^\circ$ & $180^\circ$\\
+%\mr
+%			$+$ & $1.45$ & $0.43$ & $1.20$ & $11.48$ & $1.45$\\
+%			$-$ & $1.45$ & $12.02$& $1.15$ & $0.44$  & $1.45$ \\
+%\br
+%\endTable
+\begin{table}
+\caption{\label{tab:sign}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for different values of sign$(\Delta m^2_{23})$ and $\delta_{CP}$. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			    & $-180^\circ$ & $-90^\circ$ & $0^\circ$ & $90^\circ$ & $180^\circ$\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$+$ & $1.45$ & $0.43$ & $1.20$ & $11.48$ & $1.45$\\
+			$-$ & $1.45$ & $12.02$& $1.15$ & $0.44$  & $1.45$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+The combined $\sin^22\theta_{13}$ and $\delta_{CP}$ sensitivity is presented on figure~\ref{fig:compDeltaTheta}a for the 5 years positive focusing scenario to appreciate in an other way the above mentioned $\delta_{CP}$ ambiguity. 
+%
+\begin{figure}
+\centering
+\includegraphics[scale=0.4]{../picts/compDeltaTheta.eps}
+\caption{\label{fig:compDeltaTheta}Sensitivity contours obtained with SPL beam energy of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) at $90\%$ CL. Default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}
+\end{figure}
+%
+To improve the $\delta_{CP}$-independent limit on $\sin^22\theta_{13}$, one may envisaged a combination of 2 years with positive focusing and 8 years negative focusing as in references \cite{DONINI,JJG,Mezzetto}. The corresponding combined sensitivity contours are presented in figure~\ref{fig:compDeltaTheta}b. With this kind of mixed focusing scenario, one gets a limit $\sin^22\theta_{13} < 2.4 \times 10^{-3}$ ($90\%$ CL) independently of $\delta_{CP}$ with a $3.5$~GeV kinetic energy beam. Note that with a $2.2$~GeV beam or a $4.5$~GeV beam, one gets $\sin^22\theta_{13} < 2.7 \times 10^{-3}$ which is just a bit worse, but it is better than the limit of $\sin^22\theta_{13} < 3.2 \times 10^{-3}$ that may be reached with a $8$~GeV beam.
+%
+\section{Summary and outlook}
+A complete chain of simulation has been set up for the SPL-Fréjus project. The neutrino production has been extended to the kaon decay contribution, which is important to test SPL energy scenario above $2.2$~GeV.
+
+The beam line optimization has been performed using the sensitivity to $\sin^22\theta_{13}$. The shape of the focusing system has been updated and we have confirmed that the decay tunnel parameters $20$~m long and $1$~m radius may still be conserved as baseline values. 
+
+With a $4.5$~GeV SPL energy beam, in 5 years of focusing positive particles, one can reach a minimum value of $\sin^22\theta_{13} = 9.1\times 10^{-4}$ ($90\%$ CL, $\delta_{CP} = 0$) and realizes a $24\%$ gain compared to the up to now nominal $2.2$~GeV SPL energy beam. This may be the sign that a $4.5$~GeV SPL beam energy design is to be investigated from the machine development implication point of view. If one includes  a mixed focusing scenario to explore the ($\sin^22\theta_{13}$,$\delta_{CP}$) sensitivity, then their is no much difference between the $\delta_{CP}$-independant $\sin^22\theta_{13}$ minimum value that may be reached with a $2.2$~GeV energy beam and a $4.5$~GeV energy beam.
+
+The authors think that the present study may be extended in two directions. The beam line simulation part may be performed with a single simulator as FLUKA (or GEANT4 \cite{GEANT4} for comparison). The sensitivity analysis may be deeper investigated using the complete set of possible ambiguities as in reference \cite{DONINI}, and the $\theta_{13}$ or $\delta_{CP}$ measurement accuracy with new beam energy scenario may be investigated too.    
+%
+\begin{acknowledgement}
+The authors would like to thank M.~Mezzetto to have expressed his interest at early stage of this work and to have provided us his sensitivity computation program. Also the authors thank S.~Gilardoni for fruitful discussions.
+\end{acknowledgement}
+%
+\appendix
+\setcounter{section}{1}
+\section{Decay probability computations}
+\label{sec:decayprobcomp}
+This appendix contains the probability formulas and the algorithms used in the flux computation (see section~\ref{sec:algo}).
+
+\subsection{Pion neutrino probability computation}
+\label{sec:Ppi}
+Pions decay only as $\pi^+\rightarrow \mu^+ + \nu_\mu$ or $\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$ and the neutrinos are emitted isotropically in the pion rest frame, with an energy of about $30$~MeV given by the 2-body decay kinematics. Applying a Lorentz boost knowing the pion momentum and direction, it is possible to compute the probability to reach the detector for the neutrinos. Only neutrino parallel to the beam axis are supposed to pass through the detector fiducial area, and therefore, the neutrino must be emitted by the pion with an angle opposite to the angle between the pion and the beam axis (see figure~\ref{fig:pionDecay}). This gives:
+\begin{equation}
+\mathcal{P}_\pi = \frac{1}{4\pi}\frac{A}{L^2}\frac{1-\beta^2}{(\beta\cos\alpha-1)^2}
+\label{probaPi}
+\end{equation}
+where $\beta$ is the velocity of the pion in the tunnel frame, $A$ is the fiducial detector surface, $L$ the distance between the neutrino source and the detector, and $\alpha$ the angle between the pion direction and the beam axis in the laboratory frame.
+
+\begin{figure}
+\centering
+\includegraphics{../picts/pionDecay.eps}
+\caption{\label{fig:pionDecay}Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha$ is needed.}
+\end{figure}
+
+\subsection{Muon neutrino probability computation}
+\label{sec:Pmu}
+Muons decay only as $\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_\mu$ or $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$, and will produce background events. The mean decay length of the muons is $2$~km, therefore, most of them do not decay in the tunnel. This induces a lake of statistics to estimate the corresponding level of background. This problem has been solved using each muon appearing in the simulation in the following steps:
+\begin{enumerate}
+	\item the probability for the muon to decay into the tunnel has been computed using a straight line propagation;
+	\item the available energy for the neutrino in the tunnel frame has been divided in $20$~MeV energy bins; 
+	% (the number of bin depending of the muon energy).
+	\item one $\nu_e$ and one $\nu_\mu$ have been simulated in each of the energy bins (step 2). Then, the probability to reach the detector has been computed, and multiplied by the probability computed at step 1.%the neutrino energy is stored in an histogram, weighted with this probability and 
+\end{enumerate}
+After the probability computation, the non useful muon is discarded by GEANT to gain in CPU time. 
+
+The probability for the muon neutrino and the electron neutrino to be emitted parallel to the beam axis is \cite{donega}:
+\begin{equation}
+\frac{d\mathcal{P}_\mu}{dE_\nu} = \frac{1}{4\pi}\frac{A}{L^2}\frac{2}{m_\mu}\frac{1}{\gamma_\mu(1+\beta_\mu\cos\theta^*)}\frac{1-\beta_\mu^2}{(\beta_\mu\cos\rho-1)^2}\left[f_0(x)\mp \Pi_\mu^T f_1(x)\cos\theta^*\right]
+\label{probaMu}
+\end{equation}
+where $\beta_\mu$ and $\gamma_\mu$ are the velocity and the Lorentz boost of the muon in the tunnel frame, $\theta^*$ is the angle with respect to the beam axis of the muon in the muon rest frame, $\rho$ is the corresponding angle in the tunnel frame. Like in the pion case, this angle appears because the neutrino must be parallel to the beam axis. $\Pi_\mu^T$ is the muon transverse polarization, the parameter $x$ is defined as $x=2E_\nu^*/m_\mu$ where $E_\nu^*$ is the neutrino energy in the muon rest frame, and the function $f_0(x)$ and $f_1(x)$ coming from the matrix element of the muon decay are given in table~\ref{tab:Function}. The sign in front of $\Pi_\mu^T$ in equation~\ref{probaMu} is $(-)$ for the $\nu_\mu$ and $(+)$ for the $\bar{\nu}_\mu$, respectively.
+
+%\Table{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%\br
+%		      &  $f_0(x)$ & $f_1(x)$ \\
+%\mr
+%		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+%		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+%\br
+%\endTable
+\begin{table}
+\caption{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		      &  $f_0(x)$ & $f_1(x)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+Muon polarization is computed using the conservation of the transverse component of the velocity four-vector $\gamma(1,\beta)$ between the muon rest frame (where the polarization is computed) and the pion rest frame, where the muon helicity is $-1$, due to the parity non conservation. It yields \cite{picasso}:
+\begin{equation}
+\Pi_\mu^T = \frac{\gamma_\pi\beta_\pi}{\gamma_\mu\beta_\mu}\sin\theta^*
+%\mbox{ and }\Pi_\mu^L = \sqrt{1-\Pi_\mu^{T2}}\virg 
+\label{pola}
+\end{equation}
+where $\gamma_\pi$, $\beta_\pi$, $\gamma_\mu$, and $\beta_\mu$ are the Lorentz boost and velocity of the pion and of the muon in the tunnel frame, and $\theta^*$ the angle with respect to the beam axis of the muon in the pion rest frame.
+
+\subsection{The treatment of the kaons}
+\label{sec:kaons}
+Contrary to pions and muons, kaons have many decay channels. They are summarized in table~\ref{tab:BRKP0SL}.
+
+%\Table{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%\br
+%\centre{2}{$K^\pm$}         & \centre{2}{$K^0_L$}     & \centre{2}{$K^0_S$}\\
+%\mr
+%$\mu^\pm\nu_\mu$ & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+%$\pi^\pm\pi^0$ & $21.17\%$   & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+%$\pi^\pm\pi^+\pi^-$ & $5.59\%$ & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+%$e^\pm\nu_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+%$\mu^\pm\nu_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+%$\pi^\pm\pi^0\pi^0$ & $1.73\%$ & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+%\br
+%\endTable
+\begin{table}
+\caption{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+\centre{2}{$K^\pm$}         & \centre{2}{$K^0_L$}     & \centre{2}{$K^0_S$}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$\mu^\pm\nu_\mu$ & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+$\pi^\pm\pi^0$ & $21.17\%$   & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+$\pi^\pm\pi^+\pi^-$ & $5.59\%$ & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+$e^\pm\nu_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+$\mu^\pm\nu_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+$\pi^\pm\pi^0\pi^0$ & $1.73\%$ & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+There is a very small amount of kaons produced (section~\ref{sec:algo}), and this number has been artificially increased in order to obtain statistically satisfactory results.  The multiplicity of decay channels makes impossible the method used for the muon case (\ref{sec:Pmu}). The method chosen for the good compromise between the gain in CPU and the statistical uncertaincy of the results, is to duplicate 300 times each kaon exiting the target. 
+
+All the kaons daughter particles are tracked by GEANT until they decay. Three different types of daughter particles are identified in the kaon decays. The first type corresponds to primary neutrinos, the second type concerns charged pions and muons, and the neutral pions are left for the last type.
+
+In the $K^\pm\rightarrow\mu^\pm \nu_\mu(\bar{\nu}_\mu)$ decay modes, the computation of the probability for a neutrino to reach the detector is the same than the 2-body decay formula used to in the pion decay (equation~\ref{probaPi}), where $\beta$ is now the kaon velocity, and $\alpha$ the angle of the kaon with respect to the beam axis. 
+
+When a neutrino is produced by a kaon 3-body decay, the probability to reach the detector is computed using a pure phase space formula. It yields:
+\begin{equation}
+\mathcal{P}_K = \frac{1}{4\pi}\frac{A}{L^2}\frac{1}{m_K-m_\pi-m_l}\frac{1}{\gamma_K(1+\beta_K\cos\theta^*)}\frac{1-\beta_K^2}{(\beta_K\cos\delta-1)^2}
+\label{probaL}
+\end{equation}
+where $m_K$ is the kaon mass (charged or neutral), $m_\pi$ is the pion mass ($\pi^0$ mass in $K^\pm$ decays and $\pi^\pm$ mass in $K_L^0$ decays), and $m_l$ is the mass of the lepton associated with the neutrino. The $\beta_K$ and $\gamma_K$ are the velocity and the Lorentz boost of the kaon, $\theta^*$ is the angle between the neutrino direction and the kaon direction, in the kaon rest frame. Finally, $\delta$ is the angle between the kaon direction and the beam axis in the tunnel frame.
+
+When a $\pi^\pm$ is produced in the kaon decay chain, it is tracked by GEANT until it decays, and the probability of equation~\ref{probaPi} is applied to the produced neutrino. In case of a muon, it is treated as explained in \ref{sec:Pmu}. The muon polarization is computed this time using the kaon decay informations. Finally, when a $\pi^0$ is produced, as it cannot create neutrinos, it is simply discarded.
+
+%
+\section*{References}
+\begin{thebibliography}{99}
+%
+\bibitem{SKNU04}
+E. Kearns [SuperKamiokande Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{K2KNU04}
+T. Nakaya [K2K Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{MINOS}
+T. Thomson [MINOS Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement);
+P. Adamson \etal, NuMi-L-337 (unpublished)
+
+\bibitem{OPERA}
+D. Autiero [OPERA Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement);
+M. Guler  \etal, \textsl{Experiment proposal} CERN/SPSC 2000-028 SPSC/P318 LNGS P25/2000 (unpublished) 
+
+\bibitem{ICARUS}
+M. Guler  [ICARUS Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement);
+P. Aprili \etal, CERN-SPSC-2002-027 (unpublished)
+
+\bibitem{CNGS}
+G. Acquistapace  \etal, CERN-98-02 (unpublished)
+
+\bibitem{LSND}
+A. Athanassopoulos \etal, \PRL {\bf 81}, 1774  (1998);
+A. Aguilar \etal, \PR D {\bf 64}, 112007 (2001) 
+
+\bibitem{MINIBOONE}
+I. Stancu \etal, FERMILAB-TM-2207 (unpublished)
+
+\bibitem{PMNS}
+B. Pontecorvo \textsl{Sov. Phys.--JETP} {\bf 6}, 429 (1957) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{33}, 549 (1957)];
+Z. Maki, M. Nakagawa and S. Sakata \textsl{Prog. Theor. Phys.} \textbf{28}, 870 (1962);
+Pontecorvo B \textsl{Sov. Phys.--JETP} \textbf{26},  984 (1968) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{53}, 1717 (1967)];
+V. N. Gribov and B. Pontecorvo \PL B \textbf{28}, 493 (1969) 
+
+\bibitem{CHOOZ}
+M. Apollonio \etal, \PL B {\bf 466}, 415 (1999);
+M. Apollonio \etal, \EJP C {\bf 27},  331 (2003)
+
+\bibitem{Wpaper}
+K. Anderson \etal, \textsl{White paper report on using nuclear reactors to search for a value of $\theta_{13}$} (2004), http://www.hep.anl.gov/minos/reactor13/reactor13.pdf (unpublished)
+
+\bibitem{BETABEAM}
+P. Zucchelli, \PL B \textbf{532}, 166 (2002) 
+
+\bibitem{NOVA}
+I. Ambats \etal,  NO$\nu$A proposal FNAL P929, 2004 (unpublished)
+
+\bibitem{T2K}
+Y. Itow, KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05 (unpublished),
+see also arXiv:hep-ex/0106019
+
+\bibitem{BNLHS}
+M. V. Diwan, \PR D {\bf 68}, 012002 (2003)
+
+\bibitem{CERN}
+A. Blondel \etal, CERN-2004-002 (unpublished)
+
+\bibitem{DONINI}
+A. Donini \etal, IFT-UAM/CSIC-04-30, 2004 (unpublished);
+see also arXiv:hep-ph/0406132
+
+\bibitem{DOUBLE-CHOOZ}
+F. Dalnoki-Veress, the Double-CHOOZ project arXiv:hep-ex/0406070 (unpublished)
+
+\bibitem{SPL}
+B. Autin \etal, CERN-2000-12 (unpublished)
+
+\bibitem{UNO} 
+The UNO whitepaper, \textsl{Physics Potential and Feasibility of UNO}, SBHEP01-3 (unpublished), see also http://ale.physics.sunysb.edu/uno/
+
+\bibitem{mosca}
+L. Mosca, Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Meer}
+S. van der Meer, CERN-Report No 61-7, 1961 (unpublished)
+
+\bibitem{nuFact134} 
+J.E. Campagne and A. Cazes, CERN-NUFACT-Note-134, 2003 (unpublished), see http://slac.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+
+\bibitem{MMWPSCazes} 
+J.E. Campagne and A. Cazes, Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004,
+see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{JJG}
+J.J. G\'omez Gadenas \etal,  IFIC/01-31, 2001 (unpublished),
+see also arXiv:hep-ph/0105297
+
+\bibitem{Mezzetto}
+M. Mezzetto,  \jpg {\bf 29}, 1781-1784 (2003),
+see also arXiv:hep-ex/0302005
+
+
+\bibitem{nuFact138} 
+J.E. Campagne, CERN-NUFACT-Note-138, 2004 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+
+\bibitem{fluka}
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p159-164 (2001);
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+
+\bibitem{MMWPSGaroby} 
+R. Garoby, Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{harp}
+C. Catanesi \etal, CERN-SPSC 2002/019 (unpublished)
+
+\bibitem{minerva} 
+D. Drakoulakos \etal, Fermilab P-938 (unpublished),
+see also arXiv:hep-ex/405002
+
+\bibitem{MARS}
+N.V. Mokhov \etal, The MARS Code System User Guide, Version 13(95), Fermilab-FN-628 (1995);
+N.V. Mokhov  \etal, MARS oed Develepments, LANL Report LA-UR-98-5716 (1998), nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+
+\bibitem{FLUKAprivate}
+G. Battistoni and A. Ferrari, \textsl{private communication}
+
+\bibitem{geant}
+Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+
+\bibitem{SIMONE1}
+S. Gilardoni, Talk at NuFact03 (2003), see http://www.cap.bnl.gov/nufact03/
+
+\bibitem{donega}
+A. Blondel \etal, CERN-NUFACT-Note-78, 2001 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+
+\bibitem{DONINI-2}
+A. Donini, D. Meloni and S. Rigolin, J. High Energy Phys. \textbf{0406}, 011 (2004),
+see also arXiv:hep-ph/0312072
+
+\bibitem{NUANCE}
+D. Casper, \textsl{ Nucl. Phys. Proc. Suppl.} \textbf{112}, 161-170 (2002),
+see also arXiv:hep-ph/0208030
+
+\bibitem{MEZZETTONUFACT060}
+M. Mezzetto, CERN-NUFACT-Note-60, 2000 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+
+
+\bibitem{KAMLAND}
+G. Gratta, in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{Gaisser}
+T.K. Gaisser, \textsl{Cosmic Rays and Particle Physics} (Cambridge University Press, 1990)  
+
+\bibitem{picasso}
+F. Combley and E. Picasso, \textsl{Phys. Rept.} {\bf 14}, 1 (1974) 
+
+\bibitem{pdg}
+K. Hagiwara \etal,  \PR D {\bf 66},  010001 (2002)
+
+\bibitem{GEANT4}
+A. Agostinelli \etal, \NIM A \textbf{506}, 250-503 (2003) 
+\end{thebibliography}
+
+
+
+
+
+
+
+\end{document}
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.aux
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.aux	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.aux	(revision 392)
@@ -0,0 +1,193 @@
+\relax 
+\citation{SKNU04,K2KNU04}
+\citation{K2KNU04}
+\citation{MINOS}
+\citation{OPERA,ICARUS}
+\citation{CNGS}
+\citation{LSND}
+\citation{MINIBOONE}
+\citation{PMNS}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{BETABEAM}
+\citation{NOVA,T2K}
+\citation{T2K,BNLHS,CERN}
+\citation{CERN}
+\citation{DONINI}
+\citation{DONINI,DOUBLE-CHOOZ}
+\citation{SPL}
+\citation{UNO}
+\citation{mosca}
+\citation{CERN}
+\citation{Meer}
+\citation{nuFact134,MMWPSCazes}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Sketch of the SPL neutrino Superbeam from CERN to the Fr\'ejus tunnel.}}{2}}
+\newlabel{fig:Sbeam}{{1}{2}}
+\citation{DONINI,JJG,Mezzetto}
+\citation{nuFact138}
+\citation{fluka}
+\citation{CERN}
+\citation{SPL}
+\citation{MMWPSGaroby}
+\citation{nuFact134}
+\citation{harp}
+\citation{minerva}
+\citation{MARS}
+\citation{nuFact134}
+\citation{MMWPSGaroby}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Liquid mercury jet parameters.}}{3}}
+\newlabel{tab:targ}{{1}{3}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Target simulation}{3}}
+\newlabel{sec:target}{{2}{3}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Pion momentum distribution at the exit the target (a) and at the exit of the horns (b), simulated by FLUKA (\mbox {- - - -}) and by MARS (\mbox {------}).}}{3}}
+\newlabel{fig:compFlukaMars}{{2}{3}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Kaon production}{3}}
+\newlabel{sec:kaon}{{3}{3}}
+\citation{FLUKAprivate}
+\citation{geant}
+\citation{SIMONE1}
+\citation{nuFact138}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Average number of the most relevant secondary particles exiting the $30$\nobreakspace  {}cm long, $1.5$\nobreakspace  {}cm diameter mercury target per incident proton (FLUKA). The $\mu ^+/\mu ^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}}{4}}
+\newlabel{tab:nbPart}{{2}{4}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Kaon production (a) as a function of the incident proton beam energy ($E_p$) for $500\nobreakspace  {}000$ incident protons with (\mbox {------}) curve for $K^+$, (\mbox {- - - -}) curve for $K^-$ and (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve for $K^o$. Pion production (b) in the same conditions with (\mbox {------}) curve for $\pi ^+$ and (\mbox {- - - -}) curve for $\pi ^-$.}}{4}}
+\newlabel{fig:KaonsPions}{{3}{4}}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Relevant parameters of horns. The shapes of the conductors are not changed by proton beam energy changes, as the focusing has been optimized for a defined pion momentum.}}{4}}
+\newlabel{tab:specif}{{3}{4}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Horn simulation}{4}}
+\newlabel{sec:horn}{{4}{4}}
+\citation{donega}
+\citation{donega}
+\citation{donega}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Design of the Horn and the Reflector conductor shapes implemented in the GEANT simulation. The Hg target is located inside the cylindrical part of the Horn.}}{5}}
+\newlabel{fig:plan}{{4}{5}}
+\@writefile{toc}{\contentsline {section}{\numberline {5}Particle decay treatment and flux calculation}{5}}
+\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Number of protons on target for different beam energy at 4\nobreakspace  {}MW constant power.}}{5}}
+\newlabel{tab:proton}{{4}{5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Algorithm description}{5}}
+\newlabel{sec:algo}{{5.1}{5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Validation of the algorithm}{5}}
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+\citation{MEZZETTONUFACT060}
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+\citation{NUANCE}
+\citation{MEZZETTONUFACT060}
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+\newlabel{fig:compGeantDonega}{{5}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Simulated fluxes}{6}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Sensitivity computation ingredients}{6}}
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+\citation{KAMLAND}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
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+\newlabel{tab:speciesfluxes}{{5}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  Neutrino fluxes $100$\nobreakspace  {}km from the decay region and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$\nobreakspace  {}GeV (4\nobreakspace  {}MW), a decay tunnel with a length of $20$\nobreakspace  {}m and a radius of $1$\nobreakspace  {}m. The (\mbox {------}) curve is the contribution from primary pions and the daughter muons, the (\mbox {- - - -}) curve is the contribution from the charged kaon decay chain, and the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve is the contribution from the $K^0$ decay chain.}}{7}}
+\newlabel{fig:flux22p}{{6}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but the horns are focusing negative particles.}}{7}}
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+\newlabel{fig:flux45m}{{9}{8}}
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+\newlabel{sec:results}{{7}{8}}
+\citation{DONINI}
+\citation{DONINI,JJG,Mezzetto}
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+\newlabel{fig:compSensi}{{13}{9}}
+\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Minimum $\mathop {\mathgroup \symoperators sin}\nolimits ^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for different level of systematics ($\epsilon _{syst}$) and kinetic beam energy ($E_k(proton)$). Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{9}}
+\newlabel{tab:thvseps}{{9}{9}}
+\citation{GEANT4}
+\citation{DONINI}
+\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces $90\%$ CL sensitivity contours obtained with a SPL energy of $4.5$\nobreakspace  {}GeV and default parameters of table\nobreakspace  {}6\hbox {} but for different $\epsilon _{syst}$ values.}}{10}}
+\newlabel{fig:compEpsSyst}{{14}{10}}
+\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Minimum $\mathop {\mathgroup \symoperators sin}\nolimits ^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for different values of sign$(\Delta m^2_{23})$ and $\delta _{CP}$. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{10}}
+\newlabel{tab:sign}{{10}{10}}
+\@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{10}}
+\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Sensitivity contours obtained with SPL beam energy of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) at $90\%$ CL. Default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}}{10}}
+\newlabel{fig:compDeltaTheta}{{15}{10}}
+\citation{donega}
+\citation{Gaisser}
+\citation{picasso}
+\citation{pdg}
+\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha $ is needed.}}{11}}
+\newlabel{fig:pionDecay}{{16}{11}}
+\@writefile{toc}{\contentsline {section}{\numberline {B}Decay probability computations}{11}}
+\newlabel{sec:decayprobcomp}{{B}{11}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {B.1}Pion neutrino probability computation}{11}}
+\newlabel{sec:Ppi}{{B.1}{11}}
+\newlabel{probaPi}{{2}{11}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {B.2}Muon neutrino probability computation}{11}}
+\newlabel{sec:Pmu}{{B.2}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Flux function in the muon rest frame \cite  {Gaisser}.}}{11}}
+\newlabel{tab:Function}{{11}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Charged and neutral kaon decay channels \cite  {pdg}.}}{11}}
+\newlabel{tab:BRKP0SL}{{12}{11}}
+\newlabel{probaMu}{{3}{11}}
+\newlabel{pola}{{4}{11}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {B.3}The treatment of the kaons}{11}}
+\newlabel{sec:kaons}{{B.3}{11}}
+\bibcite{SKNU04}{1}
+\bibcite{K2KNU04}{2}
+\bibcite{MINOS}{3}
+\bibcite{OPERA}{4}
+\bibcite{ICARUS}{5}
+\bibcite{CNGS}{6}
+\bibcite{LSND}{7}
+\bibcite{MINIBOONE}{8}
+\bibcite{PMNS}{9}
+\bibcite{CHOOZ}{10}
+\bibcite{Wpaper}{11}
+\bibcite{BETABEAM}{12}
+\bibcite{NOVA}{13}
+\bibcite{T2K}{14}
+\bibcite{BNLHS}{15}
+\bibcite{CERN}{16}
+\bibcite{DONINI}{17}
+\bibcite{DOUBLE-CHOOZ}{18}
+\bibcite{SPL}{19}
+\bibcite{UNO}{20}
+\bibcite{mosca}{21}
+\bibcite{Meer}{22}
+\bibcite{nuFact134}{23}
+\bibcite{MMWPSCazes}{24}
+\bibcite{JJG}{25}
+\bibcite{Mezzetto}{26}
+\bibcite{nuFact138}{27}
+\bibcite{fluka}{28}
+\bibcite{MMWPSGaroby}{29}
+\bibcite{harp}{30}
+\bibcite{minerva}{31}
+\newlabel{probaL}{{5}{12}}
+\bibcite{MARS}{32}
+\bibcite{FLUKAprivate}{33}
+\bibcite{geant}{34}
+\bibcite{SIMONE1}{35}
+\bibcite{donega}{36}
+\bibcite{DONINI-2}{37}
+\bibcite{NUANCE}{38}
+\bibcite{MEZZETTONUFACT060}{39}
+\bibcite{KAMLAND}{40}
+\bibcite{Gaisser}{41}
+\bibcite{picasso}{42}
+\bibcite{pdg}{43}
+\bibcite{GEANT4}{44}
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.blg
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.blg	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.blg	(revision 392)
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.log
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.log	(revision 392)
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.tps
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.tps	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC-old/SPLFrejus.tps	(revision 392)
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus-EPJC041122-25Oct05.aux
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus-EPJC041122-25Oct05.aux	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus-EPJC041122-25Oct05.aux	(revision 392)
@@ -0,0 +1,222 @@
+\relax 
+\citation{SKNU04,K2KNU04}
+\citation{K2KNU04}
+\citation{MINOS}
+\citation{OPERA,ICARUS}
+\citation{CNGS}
+\citation{LSND}
+\citation{MINIBOONE}
+\citation{PMNS}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{BETABEAM}
+\citation{NOVA,T2K}
+\citation{T2K,BNLHS,CERN}
+\citation{CERN}
+\citation{DONINI}
+\citation{DONINI,DOUBLE-CHOOZ}
+\citation{SPL}
+\citation{UNO}
+\citation{mosca}
+\citation{CERN}
+\citation{Meer}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Sketch of the SPL neutrino Superbeam from CERN to the Fr\'ejus tunnel.}}{1}}
+\newlabel{fig:Sbeam}{{1}{1}}
+\citation{nuFact134,MMWPSCazes}
+\citation{DONINI,JJG,Mezzetto}
+\citation{nuFact138}
+\citation{fluka}
+\citation{CERN}
+\citation{JJG}
+\citation{CERN}
+\citation{SPL}
+\citation{MMWPSGaroby}
+\citation{nuFact134}
+\citation{harp}
+\citation{MARS}
+\citation{nuFact134}
+\citation{MMWPSGaroby}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Liquid mercury jet parameters.}}{2}}
+\newlabel{tab:targ}{{1}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Target simulation}{2}}
+\newlabel{sec:target}{{2}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Kaon production}{2}}
+\newlabel{sec:kaon}{{3}{2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  (a) $\pi ^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi ^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$\nobreakspace  {}GeV/c and $0.7$\nobreakspace  {}GeV/c. The different SPL beam kinetic energies presented are (\mbox {------}) $2.2$\nobreakspace  {}GeV, (\mbox {- - - -}) $3.5$\nobreakspace  {}GeV, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) $4.5$\nobreakspace  {}GeV and (\mbox {--- $\cdot $ ---}) $6.5$\nobreakspace  {}GeV.}}{3}}
+\newlabel{fig:compEner2}{{2}{3}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces $\pi ^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\mbox {- - - -}) and by MARS (\mbox {------}).}}{3}}
+\newlabel{fig:compFlukaMars}{{3}{3}}
+\citation{FLUKAprivate}
+\citation{geant}
+\citation{SIMONE1}
+\citation{nuFact138}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Average numbers of the most relevant secondary particles exiting the $30$\nobreakspace  {}cm long, $1.5$\nobreakspace  {}cm diameter mercury target per incident proton (FLUKA). The $\mu ^+/\mu ^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}}{4}}
+\newlabel{tab:nbPart}{{2}{4}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Horns simulation}{4}}
+\newlabel{sec:horn}{{4}{4}}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Relevant parameters of the horns in case of the generation of a $260$\nobreakspace  {}MeV neutrino beam (or $350$\nobreakspace  {}MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$\nobreakspace  {}MeV/c (or $800$\nobreakspace  {}MeV/c) pion momentum.}}{4}}
+\newlabel{tab:specif}{{3}{4}}
+\citation{donega}
+\citation{donega}
+\citation{donega}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).}}{5}}
+\newlabel{fig:KaonsPions}{{4}{5}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350\nobreakspace  {}MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}}{5}}
+\newlabel{fig:plan}{{5}{5}}
+\@writefile{toc}{\contentsline {section}{\numberline {5}Particle decay treatment and flux calculation}{5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Algorithm description}{5}}
+\newlabel{sec:algo}{{5.1}{5}}
+\citation{donega}
+\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Number of protons on target for different beam energy at 4\nobreakspace  {}MW constant power. One year is defined as $10^7$\nobreakspace  {}s.}}{6}}
+\newlabel{tab:proton}{{4}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Validation of the algorithm}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Simulated fluxes}{6}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  Neutrino fluxes, $100$\nobreakspace  {}km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$\nobreakspace  {}GeV (4\nobreakspace  {}MW), a decay tunnel with a length of $20$\nobreakspace  {}m and a radius of $1$\nobreakspace  {}m. The top left panel contains the $\nu _\mu $ fluxes, and the top right panel shows the $\mathaccentV {bar}016{\nu }_\mu $ fluxes. The bottom left panel presents the $\nu _e$ fluxes while the bottom right panel displays the $\mathaccentV {bar}016{\nu }_e$ fluxes. The (\mbox {------}) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\mbox {- - - -}) curve is the contribution from the charged kaon decay chain, and the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}}{7}}
+\newlabel{fig:flux22p}{{6}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but the horns are focusing negative particles.}}{7}}
+\newlabel{fig:flux22m}{{7}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{8}}
+\newlabel{fig:flux45p}{{8}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{8}}
+\newlabel{fig:flux45m}{{9}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{9}}
+\newlabel{fig:flux8p}{{10}{9}}
+\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{9}}
+\newlabel{fig:flux8m}{{11}{9}}
+\citation{UNO}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{Mezzetto}
+\citation{DONINI-2}
+\citation{NUANCE}
+\citation{MEZZETTONUFACT060}
+\citation{mosca}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Integral of the total flux of the different species with different settings. The $\nu _\mu $ and $\mathaccentV {bar}016{\nu }_\mu $ fluxes are expressed in $10^{13}/100\@mathrm {m}^2/y$ unit while the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes are expressed in $10^{11}/100\@mathrm {m}^2/y$ unit. The positive focusing and negative focusing are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. }}{10}}
+\newlabel{tab:speciesfluxes}{{5}{10}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Sensitivity computation ingredients}{10}}
+\@writefile{toc}{\contentsline {section}{\numberline {7}Results}{10}}
+\newlabel{sec:results}{{7}{10}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}The positive only focusing scenario}{10}}
+\citation{DONINI}
+\citation{DONINI,JJG,Mezzetto}
+\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Comparison between the probability method, (\mbox {------}) curve, and the full GEANT simulation method, (\mbox {- - - -}) curve, for the $\nu _\mu $ from $\pi ^+$ flux (a) and the $\mathaccentV {bar}016{\nu }_\mu $ from $\pi ^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes contrary to the former simulation.}}{11}}
+\newlabel{fig:compGeantDonega}{{12}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Default parameters used to compute the sensitivity curves \cite  {MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite  {KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite  {JJG}.}}{11}}
+\newlabel{tab:param}{{6}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Number of events for 5 years positive focusing scenario with default parameters of table\nobreakspace  {}6\hbox {}. Other backgrounds are $\pi ^0$, $\nu _\mu $-elast., $\mu /e$-missId. }}{12}}
+\newlabel{tab:nbvsE}{{7}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Sensitivity contours obtained with a SPL energy of $3.5$\nobreakspace  {}GeV and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m. (\mbox {------}), (\mbox {- - - -}) and (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}}{12}}
+\newlabel{fig:sensi45}{{13}{12}}
+\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{12}}
+\newlabel{tab:thvsE}{{8}{12}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Mixed positive/negative focusing scenario}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{12}}
+\newlabel{fig:compSensi}{{14}{12}}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Study of the sensitivity of different beam energy, decay tunnel length ($L_T$) at and radius ($R_T$), and horn design in two different scenarios. First scenario is 5 years of positive focusing, in wich sensitivity is given as the minimum of $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL ($\delta _{CP} = 0$). Second scenario is 2 years of positive focusing plus 8 years of negative focusing, in wich sensitivity is given as the minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta _{CP}$ case. A star $^{(*)}$ indicates the use of the the horn geometry producing a $350$\nobreakspace  {}MeV neutrino beam. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:thvsE_3545}{{9}{13}}
+\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV, and either a $260$\nobreakspace  {}MeV (default) neutrino beam or a $350$\nobreakspace  {}MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$\nobreakspace  {}m and $R_T = 2$\nobreakspace  {}m. The (\mbox {--- $\cdot $ ---}) curve corresponds to a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV (neutrino beam/SPL beam energy) setting; the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve corresponds to a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting; the (\mbox {- - - -}) curve corresponds to a $260$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting and the (\mbox {------}) curve corresponds to a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting.}}{13}}
+\newlabel{fig:comp5year}{{15}{13}}
+\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon _{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:thvseps}{{10}{13}}
+\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$\nobreakspace  {}GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta _{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:sign}{{11}{13}}
+\@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{13}}
+\citation{GEANT4}
+\citation{BIGICARUS}
+\citation{DONINI}
+\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces 90\% sensitivity contours obtained with SPL beam energy of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) at $90\%$ CL. Default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{14}}
+\newlabel{fig:compDeltaTheta}{{16}{14}}
+\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces 90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$\nobreakspace  {}m and $R_T=2$\nobreakspace  {}m and different SPL beam energies ($3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV) and different horn designs ($260$\nobreakspace  {}MeV or $350$\nobreakspace  {}MeV neutrino beams): (\mbox {------}) curve for a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve for a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting, (\mbox {- - - -}) curve for a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting. Other default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}}{14}}
+\newlabel{fig:sensiDeltaTheta}{{17}{14}}
+\@writefile{toc}{\contentsline {section}{\numberline {A}Decay probability computations}{14}}
+\newlabel{sec:decayprobcomp}{{A}{14}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}Pion neutrino probability computation}{14}}
+\newlabel{sec:Ppi}{{A.1}{14}}
+\newlabel{probaPi}{{1}{14}}
+\citation{donega}
+\citation{Gaisser}
+\citation{picasso}
+\citation{pdg}
+\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces 90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite  {CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite  {Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite  {MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite  {KOBAYASHI}. The BNL contour has been obtained from reference \cite  {BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta $ beam was analysed like a reactor experiment with 1\% systematic error \cite  {MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$\nobreakspace  {}GeV beam and a decay tunnel of $40$\nobreakspace  {}m length, and $2$\nobreakspace  {}m radius.}}{15}}
+\newlabel{fig:deltathetaFinal}{{18}{15}}
+\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha $ is needed.}}{15}}
+\newlabel{fig:pionDecay}{{19}{15}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Muon neutrino probability computation}{15}}
+\newlabel{sec:Pmu}{{A.2}{15}}
+\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Flux function in the muon rest frame \cite  {Gaisser}.}}{15}}
+\newlabel{tab:Function}{{12}{15}}
+\newlabel{probaMu}{{2}{15}}
+\newlabel{pola}{{3}{15}}
+\bibcite{SKNU04}{1}
+\bibcite{K2KNU04}{2}
+\bibcite{MINOS}{3}
+\bibcite{OPERA}{4}
+\bibcite{ICARUS}{5}
+\bibcite{CNGS}{6}
+\bibcite{LSND}{7}
+\bibcite{MINIBOONE}{8}
+\bibcite{PMNS}{9}
+\bibcite{CHOOZ}{10}
+\bibcite{Wpaper}{11}
+\bibcite{BETABEAM}{12}
+\bibcite{NOVA}{13}
+\bibcite{T2K}{14}
+\bibcite{BNLHS}{15}
+\bibcite{CERN}{16}
+\bibcite{DONINI}{17}
+\bibcite{DOUBLE-CHOOZ}{18}
+\bibcite{SPL}{19}
+\bibcite{UNO}{20}
+\bibcite{mosca}{21}
+\bibcite{Meer}{22}
+\bibcite{nuFact134}{23}
+\bibcite{MMWPSCazes}{24}
+\bibcite{JJG}{25}
+\@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces Charged and neutral kaon decay channels \cite  {pdg}.}}{16}}
+\newlabel{tab:BRKP0SL}{{13}{16}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.3}The treatment of the kaons}{16}}
+\newlabel{sec:kaons}{{A.3}{16}}
+\newlabel{probaL}{{4}{16}}
+\bibcite{Mezzetto}{26}
+\bibcite{nuFact138}{27}
+\bibcite{fluka}{28}
+\bibcite{MMWPSGaroby}{29}
+\bibcite{harp}{30}
+\bibcite{minerva}{31}
+\bibcite{MARS}{32}
+\bibcite{FLUKAprivate}{33}
+\bibcite{geant}{34}
+\bibcite{SIMONE1}{35}
+\bibcite{donega}{36}
+\bibcite{MEZZETTONUFACT060}{37}
+\bibcite{DONINI-2}{38}
+\bibcite{NUANCE}{39}
+\bibcite{KAMLAND}{40}
+\bibcite{MIGLIOZZITERANOVA}{41}
+\bibcite{KOBAYASHI}{42}
+\bibcite{BNL}{43}
+\bibcite{MAOROPRIVATE}{44}
+\bibcite{GEANT4}{45}
+\bibcite{BIGICARUS}{46}
+\bibcite{Gaisser}{47}
+\bibcite{picasso}{48}
+\bibcite{pdg}{49}
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus-EPJC041122-25Oct05.blg
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--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus-EPJC041122-25Oct05.blg	(revision 392)
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus-EPJC041122-25Oct05.tex
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--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus-EPJC041122-25Oct05.tex	(revision 392)
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+%
+%
+%----------------------------------------------------------------------------
+\begin{document}
+%
+\title{The $\theta_{13}$ and $\delta_{CP}$ sensitivities of the SPL-Fréjus project revisited}
+\author{Jean Eric Campagne, Antoine Cazes}
+\institute{ Laboratoire de l'Accélérateur Linéaire -
+Université Paris-Sud - B\^at. 200 - BP 34 -
+91898 Orsay Cedex, France}
+\mail{campagne@lal.in2p3.fr}
+\date{\today}
+%
+%
+%
+%\selectlanguage{francais}
+%
+\abstract{
+An optimization of the CERN SPL beam line has been performed guided by the sensitivities to the $\theta_{13}$ mixing angle and to the $\delta_{CP}$ Dirac CP violating phase. A UNO-like 440 ktons water \v{C}erenkov detector located at 130~km from the target in a new foreseen Fréjus laboratory has been used as a generic detector. Concerning the $\delta_{CP}$ independent $\theta_{13}$ sensitivity, a gain of about $20\%$ may be reached using a $3.5$~GeV proton beam with a 40~m long, 2~m radius decay tunnel compared to the up to now considered $2.2$~GeV beam energy and 20~m long, 1~m radius decay tunnel. This may motivate new machine developments to upgrade the nominal SPL proton beam energy.}
+%\pacs{14.60.Pq, 14.60.Lm}
+
+\maketitle
+
+
+\section{Introduction}
+The very near future of the neutrino long baseline experiments is devoted to the study of the oscillation mechanism in the range of $\Delta m^2 = \Delta m^2_{atm} \approx 2.4\times10^{-3}\mathrm{eV}^2$ \cite{SKNU04,K2KNU04}
+ using conventional $\nu_\mu$ beams. The current K2K experiment in Japan \cite{K2KNU04}, and the forthcoming MINOS in the USA \cite{MINOS} take benefit of low energy beam to measure the $\Delta m^2$ parameter using the disappearance mode $\nu_\mu\rightarrow\nu_\mu$, while OPERA/ICARUS experiments \cite{OPERA,ICARUS} using the high energy CNGS beam \cite{CNGS} will be able to detect $\nu_\tau$ appearance. If we do not consider the LSND anomaly \cite{LSND} that will be further studied soon by MiniBooNE experiment \cite{MINIBOONE}, the three flavor family scenario will be confirmed and accommodated by a $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix \cite{PMNS} with three angles ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase $\delta_{CP}$.  
+
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/cernSuperBeam_English}
+\caption{\label{fig:Sbeam}Sketch of the SPL neutrino Superbeam from CERN to the Fréjus tunnel.}	
+\end{figure}
+
+Beyond this medium term plan, two of the next future tasks of neutrino physics are to improve the sensitivity of the last unknown mixing angle parameter, the so-called $\theta_{13}$, and to explore the CP violation mechanism in the leptonic sector. The present upper bound on $\theta_{13}$ is $\sin^22\theta_{13}<0.14$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$~CL) \cite{CHOOZ}. This sensitivity can be improved using reactor and accelerator experiments. In reactor experiments, one uses $\bar{\nu}_e$ in disappearance mode and may reach $\sin^22\theta_{13}<0.024$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$CL) \cite{Wpaper}. In accelerator experiments, one can use $\nu_e$ and $\bar{\nu}_e$ from $\beta$ beams \cite{BETABEAM} in both  disappearance and appearance modes (\textit{i.e.} $\stackrel{\scriptscriptstyle (-)}{\nu}_e\rightarrow \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$), and also $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu$ in appearance mode (\textit{i.e.} $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu\rightarrow\stackrel{\scriptscriptstyle(-)}{\nu}_e$) with conventional beams either with sub-mega watt proton drivers \cite{NOVA,T2K} or with multi-mega watt proton drivers \cite{T2K,BNLHS,CERN}. The later neutrino beam type, called Superbeam, is foreseen to be extended to produce $\nu_\mu$ beam and $\bar{\nu}_\mu$ beam from muon decays, the so-called Neutrino Factory, in order to study the eventual leptonic CP violation. Such Neutrino Complex is under study in Japan, in USA and also in Europe at CERN and details may be found in reference \cite{CERN}. A comparison of the performances of $\beta$ beam and Superbeam may be found for instance in reference \cite{DONINI}.  The reactor experiment result on $\theta_{13}$ is straight forward as compared to Superbeam and Neutrino Factory results that are on one hand reacher but in an other hand more complex to analyse due to the interplay between the different physics factors $\theta_{13}$, $\delta_{CP}$, sign$(\Delta m^2_{23})$, sign$(\tan(2\theta_{23}))$ \cite{DONINI,DOUBLE-CHOOZ}. 
+
+This paper presents results of a new simulation of the SPL (Super Proton Linac) Superbeam that could take place at CERN \cite{SPL}, using for definitiveness a UNO-like 440kT fiducial water \v{C}erenkov detector \cite{UNO} located in a new enlarged underground laboratory under study in the Fréjus tunnel, $130$~km away from CERN \cite{mosca}. The SPL neutrino beam is created by  decays of pions, muons and kaons produced by the interactions of a $4$~MW proton beam impinging a liquid mercury jet \cite{CERN}. Pions, muons and kaons are collected using two concentric electromagnetic lenses (horns), the inner one and the outer one are hereafter called "Horn" and "Reflector" respectively \cite{Meer}. The horns are followed by a decay tunnel where most of the neutrinos are produced. A sketch of the beam line is shown on figure~\ref{fig:Sbeam}.  
+
+
+The analysis chain consists of different stages: the simulation of the interactions between the proton beam and the mercury target, the propagation of the resulting secondary particles through the magnetic field and the materials of the horns, the tracking of $\pi^\pm$, $K^{\pm,0}$ and $\mu^\pm$ until they decay, the computation of the neutrino flux at the detector site, and finally the statistical analysis. A part of the simulation chain has already been described in reference \cite{nuFact134,MMWPSCazes}. 
+
+
+Compared to recent papers on the same subject \cite{DONINI,JJG,Mezzetto}, we have reoptimized the Horn and Reflector shapes \cite{nuFact138}, and introduced the kaon background simulation which allows us to update the SPL beam energy. The organization of this document follows the simulation chain: the interaction between the proton beam and the mercury target is presented in the second section. The kaon production is detailed in the third section. The simulation of the horns is described in the forth section, while the algorithms used to compute the neutrino fluxes are explained in the fifth section. Then, the sensitivities to $\theta_{13}$ and $\delta_{CP}$ are revisited with new studies about the optimization of the proton beam energy, the pion collection and the decay tunnel geometry.
+
+\section{Target simulation}
+\label{sec:target}
+Since hadronic processes are crucial to describe the interactions of the proton beam on the target, the FLUKA simulator \cite{fluka} has been chosen for this first step of the simulation. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:targ}Liquid mercury jet parameters.}
+\begin{tabular}{ll}
+\hline\noalign{\smallskip}
+    \centre{2}{Hg target}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+      Hg jet speed & $20$~m/s \\
+      density & $13.546$ \\
+      Length, radius & $30$~cm, $7.5$~mm \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+The target used in the present study is a mercury liquid jet \cite{CERN} simulated for a sake of simplicity by a cylinder $30$~cm long (representing two hadronic lengths) and $1.5$~cm diameter (see table~\ref{tab:targ}) \cite{JJG}. Other types of target are under study \cite{CERN}. The pencil like simulated proton beam is composed with  $10^6$ mono-energetic protons, and no beam-target dynamical effects are taken into account. The beam axis is also the symmetry axis of the target and the horns and the decay tunnel. Simulations have been performed for $2.2$~GeV proton kinetic energy, the up to now nominal design \cite{SPL}, as well as for $3.5$~GeV, $4.5$~GeV, $6.5$~GeV and $8$~GeV according to possible new designs \cite{MMWPSGaroby}.
+
+Particle production yields are summarized in table~\ref{tab:nbPart}. The pion momentum spectra obtained at different energies and normalized to a 4MW SPL beam power are presented in figure~\ref{fig:compEner2}(a). At low energy, pions come from $\Delta$ decays while the high energy part is dominated with multi pion production. At very mow energy, for $P<200$~MeV/c, pions come from $\Delta$ produced by protons of the target excited by the beam interactions, while for  higher energy, pion production is due to transformation of protons of the beam into $\Delta$.
+
+The horns are designed to focus the $600$~MeV/c pions (see section~\ref{sec:horn}) and the variation of the number of such pions is rather smooth with respect to the beam energy considering a 4MW fixed beam power: $4.19\times10^{13}\pi$/s for the $2.2$~GeV beam, $4.91\times10^{13}\pi$/s for the $3.5$~GeV beam, $5.14\times10^{13}\pi$/s for the $4.5$~GeV beam, and $4.92\times10^{13}\pi$/s for the $6.5$~GeV beam. The main difference is made by the angular distribution. Figure~\ref{fig:compEner2}(b) shows this distribution for the $\pi^+$ exiting the target with a momentum between $500$~MeV/c and $700$~MeV/c. The acceptance of the horns is limited to the pion below $25^\circ$, and we see that more pions are accepted by the horns for the $3.5$~GeV and $4.5$~GeV proton beams compared to other beam energies.
+
+
+
+The secondary proton and neutron rates induce important radiation damages and power dissipation in the horns which have been addressed in reference \cite{nuFact134}, and which will require specific R\&D effort. At $2.2$~GeV, kaon yields are very low, but it has a dramatic energy dependence as further studied in section~\ref{sec:kaon}. It is worth to mention that the numbers in table~\ref{tab:nbPart} are not to be taken as face values, because the cross sections of pion and kaon productions using proton beam are still under studies as for instance by the HARP experiment \cite{harp}.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbPart}Average numbers of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA). The $\mu^+/\mu^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+$E_k$ (GeV) & p & n & $\gamma$ & $e^+$ & $e^-$ & $\pi^+$ & $\pi^-$ & $\mu^+$ & $\mu^-$ & $K^+$ & $K^0$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$2.2$ & $1.4$     &  $17$   & $5.0$  &   $0.08$  &  $0.17$    &  $0.24$   &  $0.18$ & $4$ & $1$ & $7$ & $6$ \\
+
+$3.5$ & $1.8$    &  $23$  & $7.0$   &  $0.15$  &  $0.28$    &  $0.41$   &  $0.37$ & $10$ & $3$ & $35$ & $30$ \\
+
+$4.5$ &  $2.3$  &  $25$ & $7.7$  & $0.21$  &  $0.35$    &  $0.57$ & $0.39$&  $11$ & $3.3$  &  $93$ &  $68$       \\
+
+$8$   &  $3.1$  &  $33$ & $11.0$ & $0.41$ & $0.63$    &  $1.00$  &  $0.85$ &  $30$ &  $9.5$ &  $413$ &    $340$         \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compEner2.eps}
+\caption{\label{fig:compEner2} (a) $\pi^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$~GeV/c and $0.7$~GeV/c. The different SPL beam kinetic energies presented are (\full) $2.2$~GeV, (\dashed) $3.5$~GeV, (\dotted) $4.5$~GeV and (\chain) $6.5$~GeV.}
+\end{figure*}
+%
+The cross section uncertainties are the main source of discrepancy between simulator programs. Some comparisons between FLUKA and MARS \cite{MARS} have already been presented in the same context \cite{nuFact134}. The energy distribution of the pions exiting the target, computed with the two simulator programs FLUKA and MARS, is shown on figure~\ref{fig:compFlukaMars}(a).  The discrepancy is quite large for the low energy part. However, the horns are designed to focus the high energy part of the spectrum (see section~\ref{sec:horn}), and therefore, MARS and FLUKA are in better agreement for the energy spectrum computed at the entrance of the decay tunnel, as shows figure~\ref{fig:compFlukaMars}(b). 
+%A difference of $10\%$ has been found between the  $\theta_{13}$ sensitivity computed with the two generators (see section~\ref{sec:results}), that can be taken as systematic error. 
+For a 2.2~GeV beam and a positive focusing,  $27\%$ more $\nu_\mu$ and $6\%$ more $\nu_e$ neutrinos are produced around the oscillation probability maximum with the FLUKA generator. It turns out that 
+a sensitivity $10\%$ better for FLUKA compared to MARS has been found for the $\sin^2(2\theta_{13})$ sensitivity
+(see section~\ref{sec:results}). So, the discrepancy  at low energy between MARS and FLUKA does not matter too much for the present application, and the sensitivity difference can be taken as a systematic error. 
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compMarsFlukav2.eps}
+\caption{\label{fig:compFlukaMars}$\pi^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\dashed) and by MARS (\full).}
+\end{figure*}
+%
+\section{Kaon production}
+\label{sec:kaon}
+The possibility to increase the SPL energy in order to study the optimization of the physics program has been recently pointed out \cite{MMWPSGaroby}. Then, the kaon production should be clearly addressed because it is a source of $\nu_e$ and $\bar{\nu}_e$ background events. The kaon decay channels and branching ratios are presented in table~\ref{tab:BRKP0SL} in \ref{sec:kaons}.
+
+The target simulation described in section~\ref{sec:target} has been used with $10^6$ p.o.t with kinetic energy uniformly distributed between $2.2$~GeV and $5$~GeV. The momentum of outgoing pions and kaons are recorded when they exit the target. The number of produced $K^{o,\pm}$ at different proton beam energies are presented on figure~\ref{fig:KaonsPions} (left). In one hand the $K^o$ production rate is similar to the $K^+$ production rate, but in an other hand the $K^-$ production rate is almost forty times smaller. For comparison, the numbers of $\pi^+$ and $\pi^-$  produced in the same conditions are presented on figure~\ref{fig:KaonsPions} (right). Pion production rate is about two orders of magnitude greater than the kaon production rate.
+%
+\begin{figure*}
+\centering
+%\includegraphics[height=95mm]{../picts/KaonProd.eps}
+\includegraphics[height=95mm]{../picts/KaonPionProdFluka2003v2.eps}
+%\caption{\label{fig:KaonsPions}Kaon production (a) as a function of the incident proton beam kinetic energy ($E_k$) for $10^6$ incident protons with (\full) curve for $K^+$, (\dashed) curve for $K^-$ and (\dotted) curve for $K^0$. Pion production (b) in the same conditions with (\full) curve for $\pi^+$ and (\dashed) curve for $\pi^-$.}
+\caption{\label{fig:KaonsPions} Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).} 
+\end{figure*}
+%
+The behavior of the two pion and kaon production rates are quite different. The $\pi^+$ yield grows smoothly with the proton energy while the production of kaons seams to have two origins, which has been confirmed by FLUKA's authors \cite{FLUKAprivate}. For beam energy below approximatively $4$~GeV, the resonance production model is used, and one notices a low production rate with a maximum at about $3.4$~GeV. For beam energy above  $4$~GeV, the dual parton model is used, and the production rate experiences a threshold effect with a rapid rise. The ratio between positive kaon and pion production rates is about $0.5\%$ between $2.2$~GeV and $4$~GeV and grow up to $2.3\%$ at $5$~GeV. One notices that the transition between the two kaon production models may not be optimal.
+%
+\section{Horns simulation}
+\label{sec:horn}
+The simulation code of the electromagnetic horns is written using GEANT 3.2.1 \cite{geant} for convenience and since electromagnetic processes are dominant, FLUKA has not been considered as mandatory, but this may be revised in a future work. The geometry of the horns has been inspired by an existing CERN prototype and a Reflector design proposed in reference \cite{SIMONE1}. Depending of the current injection, only positive secondary particles or negative secondary particles are focused. The relevant parameters are detailed in table~\ref{tab:specif}.
+
+The mercury target is localized inside the Horn because of the low energy and the large emittance of the secondary pions produced: $$<P_{\pi T}>/<P_\pi> \approx 240~\mathrm{MeV}/400~\mathrm{MeV}$$ ($2.2$~GeV proton beam energy). This explains the Horn design (figure~\ref{fig:plan}), with a cylindrical part around the target, called the neck, which is larger than the transversal size of the target to simulate the room for target handling, and a conic part designed such that the relevant pions are focused as much as possible to exit the magnetic field parallel to the beam axis.
+
+\begin{table}
+\centering
+\caption{\label{tab:specif}Relevant parameters of the horns in case of the generation of a $260$~MeV neutrino beam (or $350$~MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$~MeV/c (or $800$~MeV/c) pion momentum.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+ & Horn & Reflector \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+  neck inner radius & $3.7$~cm &  $20.3$~cm \\
+  neck length & $40$~cm        &  $120 (140)$~cm \\ 
+  end cone inner radius & $16$~cm        &  $35.7$~cm \\
+  outer radius & $20.3$~cm      & $40$~cm \\ 
+  total length & $120 (140)$~cm       & $190 (220)$~cm \\  
+  Alu thickness  & $3$~mm       & $3$~mm \\            
+  Peak current & $300$~kA       & $600$~kA \\
+  Frequency & $50$~Hz            & $50$~Hz \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The shape of the horn conductors is a crucial point since it determines the energy spectrum of the neutrino at the detector site. The details of the conductor shape optimization for the present context may be found in reference \cite{nuFact138}. We just recall here some ingredients. For a $\theta_{13}$ driven $\nu_\mu \rightarrow \nu_e$ oscillation, a $\Delta m^2_{23}$ parameter value of $2.4\times10^{-3}\mathrm{eV}^2$, and a baseline distance of $130$~km, the first oscillation maximum occurs for a neutrino energy of $260$~MeV. The   optimization of the physics potential depends at first approximation on the pion neutrino characteristics, which energy is fully determined by the pion 2-body decay and boost. To reach an energy of $260$~MeV, the pion needs a $\beta=0.97$, which in turn induces a pion momentum of $600$~MeV/c. Then, the shape of the conic part of the horns is determined such that these $600$~MeV/c pions exit parallel to the beam axis. 
+
+An other shape of the horn conductors has been used to produce a $350$~MeV neutrino beam to compare the sensitivity potential (see section \ref{sec:results}). In that case, keeping the current intensity unchanged ($300/600$~kA), the lengths of the Horn and the Reflector should be increased by $16$\% and $18.5$\%, respectively (see table~\ref{tab:specif}).
+
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/corne350.eps}
+\caption{\label{fig:plan}Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350~MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}
+\end{figure}
+
+Before closing this section, it is worth to quote that the Horn/Reflector conductor shapes optimized in the present study to focus a given pion momentum value, is not affected at first order by a proton beam energy change. What is affected is the production rate of the relevant pions. This Horn/Reflector design consideration would be different if one wishes to focus as much as possible all the pions produced for which the mean energy is of course affected by a proton beam energy change.    
+%
+\section{Particle decay treatment and flux calculation}
+%
+The decay tunnel representation is a simple cylinder with variable length ($L_T$) and radius ($R_T$) filled with "vacuum" and located right after the horns. The default design is a $20$~m long and $1$~m radius cylinder, but simulations have also been conducted with lengths of $10$~m, $40$~m and $60$~m, and radius of $1.5$~m and $2$~m in the spirit of reference \cite{donega}. In the GEANT simulation, to gain in CPU time, only pions, muons and kaons are tracked in the volume of the tunnel, and all particles exiting this volume are discarded. 
+
+Beyond the $1/L^2$ solid angle factor due to the source-detector distance ($L$) which decreases dramatically the fluxes, the neutrino beam focusing is very limited due to the small pion boost factor ($\approx 4$). Therefore, computational algorithms have been used to avoid a too prohibitive CPU time resulting from the simulation of each secondary particle decay. Otherwise, about $10^{15}$ p.o.t would have been necessary to obtain reliable statistics for the estimation of the $\bar{\nu}_e$ flux for instance.
+
+It is worth to mention that the particle decays occurring before the entrance of the decay tunnel are also taken into account and treated in the same manner, which is not the case in reference \cite{donega}. 
+%
+\subsection{Algorithm description}
+\label{sec:algo}
+The decay code has been included in the GEANT code. The basic idea of this algorithm is to compute the neutrino fluxes using the probability of reaching the detector for each neutrino produced by a $\pi$ or a $K$ or a $\mu$ particle (on-axis neutrino beam). This method has already been used in reference \cite{donega} and has been modified and extended to the kaon decay chain for the present study. 
+
+Muon neutrino comes mostly from pion decay. In a first stage, each pion is tracked by GEANT until it decays. Then, the probability for the produced muon neutrino to reach the detector is computed. The flux is obtained applying the probability as a weight for each neutrino. All the pions produced in the simulation are therefore useful to compute the flux, and this allows to reduce the number of events in the simulation to $10^6$ p.o.t. In this computation, the decay region (horns and tunnel) is considered as point like compared to the source-detector distance. 
+
+The same method is applied for neutrino coming from muons and kaons with some modifications  because most of the muons do not decay, and there are very few kaons produced (see table~\ref{tab:nbPart}).
+The probability computation is presented in appendix~\ref{sec:decayprobcomp}. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:proton}Number of protons on target for different beam energy at 4~MW constant power. One year is defined as $10^7$~s.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			Beam energy  & Number of proton \\
+			  (GeV)      & per year ($10^{23}$ p.o.t/y) \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			2.2 & 1.10 \\
+			3.5 & 0.70 \\
+			4.5 & 0.56 \\
+			6.5 & 0.40 \\
+			8.0 & 0.30 \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22p.eps}
+\caption{	\label{fig:flux22p}Neutrino fluxes, $100$~km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$~GeV (4~MW), a decay tunnel with a length of $20$~m and a radius of $1$~m. The top left panel contains the $\nu_\mu$ fluxes, and the top right panel shows the $\bar{\nu}_\mu$ fluxes. The bottom left panel presents the $\nu_e$ fluxes while the bottom right panel displays the $\bar{\nu}_e$ fluxes. The (\full) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\dashed) curve is the contribution from the charged kaon decay chain, and the (\dotted) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22m.eps}
+\caption{\label{fig:flux22m}Same legend as for figure~\ref{fig:flux22p} but the horns are focusing negative particles.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35p.eps}
+\caption{\label{fig:flux45p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35m.eps}
+\caption{\label{fig:flux45m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8p.eps}
+\caption{\label{fig:flux8p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8m.eps}
+\caption{\label{fig:flux8m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{table*}
+\centering
+\caption{\label{tab:speciesfluxes}Integral of the total flux of the different species with different settings. The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are expressed in $10^{13}/100\mathrm{m}^2/y$ unit while the $\nu_e$ and $\bar{\nu}_e$ fluxes are expressed in $10^{11}/100\mathrm{m}^2/y$ unit. The positive focusing  and negative focusing  are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. %Setting (1) means $L_T = 10$~m and $R_T = 1$~m. Setting (2) is the default option and means $L_T = 20$~m and $R_T = 1$~m. Setting (3) means $L_T = 20$~m and $R_T = 1.5$~m. Setting (4) means $L_T = 30$~m and $R_T = 1$~m. Setting (5) means $L_T = 40$~m and $R_T = 1$~m. Setting (6) means $L_T = 40$~m and $R_T = 1.5$~m. Setting (7) means $L_T = 40$~m and $R_T = 2$~m.  Setting (8) means $L_T = 60$~m and $R_T = 1$~m, and finally, setting (9) means $L_T = 60$~m and $R_T = 1.5$~m.
+}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+
+			\centre{3}{Settings}  & \centre{2}{$\nu_\mu$} & \centre{2}{$\nu_e$} 
+								&	\centre{2}{$\bar{\nu}_\mu$} & \centre{2}{$\bar{\nu}_e$} \\
+								$E_p$ & $L_T$ & $R_T$ & $+$ & $-$ & $+$ & $-$ & $+$ & $-$ 
+								& $+$ & $-$ \\ 
+\noalign{\smallskip}\hline\noalign{\smallskip}
+
+$2.2$~GeV & $10$~m &  $1$~m 
+	& $5.5$          & $0.4$ 
+	& $1.7$          & $0.2$
+	& $0.3$          & $4.3$  
+	& $0.1$ 	 & $0.8$ \\		
+
+$3.5$~GeV  & $10$~m &  $1$~m  
+	& $7.7$          & $0.7$ 
+	& $2.6$          & $0.6$
+	& $0.6$          & $6.6$  
+	& $0.3$ 	 & $1.3$ \\		
+	
+$4.5$~GeV  & $10$~m &  $1$~m  
+	& $7.1$          & $1.0$ 
+	& $2.8$          & $0.9$
+	& $0.5$          & $5.2$  
+	& $0.3$ 	 & $1.1$ \\		  
+
+$6.5$~GeV  & $10$~m &  $1$~m  
+	& $8.3$          & $1.2$ 
+	& $4.7$          & $1.9$
+	& $0.8$          & $5.6$  
+	& $0.9$          & $1.8$ \\
+
+$8.0$~GeV  & $10$~m &  $1$~m  
+	& $7.7$          & $1.2$ 
+	& $5.1$          & $2.2$
+	& $0.9$          & $5.6$  
+	& $1.1$ 	 & $2.1$ \\
+
+$2.2$~GeV & $20$~m &  $1$~m   
+	& $7.6$         & $0.4$ 
+	& $3.2$ 	& $0.2$
+	& $0.3$ 	& $5.8$  
+	& $0.1$ 	& $1.6$ \\		  
+
+$3.5$~GeV & $20$~m &  $1$~m    
+	& $10.0$          & $0.9$ 
+	& $4.4$           & $0.6$
+	& $0.7$ 	  & $8.5$  
+	& $0.3$ 	  & $2.2$ \\		  
+
+$4.5$~GeV & $20$~m &  $1$~m    
+	& $10.9$          & $1.1$ 
+	& $5.1$           & $1.0$
+	& $0.7$ 	  & $6.7$  
+	& $0.4$ 	  & $1.8$ \\		  
+
+$6.5$~GeV & $20$~m &  $1$~m    
+	& $10.4$          & $1.4$ 
+	& $6.4$           & $2.0$
+	& $1.0$           & $7.1$  
+	& $0.9$ 	  & $2.5$ \\	
+
+$8.0$~GeV & $20$~m &  $1$~m    
+	& $9.7$           & $1.5$ 
+	& $6.7$           & $2.3$
+	& $1.2$           & $7.1$  
+	& $1.1$ 	  & $2.8$ \\
+
+$2.2$~GeV & $20$~m &  $1.5$~m    
+	& $9.0$           & $0.6$ 
+	& $4.4$           & $0.4$
+	& $0.4$           & $6.7$  
+	& $0.2$  	  & $2.2$ \\
+
+$4.5$~GeV & $20$~m &  $1.5$~m    
+	& $13.2$          & $1.5$ 
+	& $6.9$           & $1.4$
+	& $0.9$           & $8.1$  
+	& $0.6$  	  & $2.7$ \\
+
+$3.5$~GeV & $30$~m &  $1$~m    
+	& $10.9$          & $0.9$ 
+	& $5.7$           & $0.7$
+	& $0.7$           & $9.4$  
+	& $0.3$  	  & $2.9$ \\
+
+$4.5$~GeV & $30$~m &  $1$~m   
+	& $11.6$          & $1.2$ 
+	& $6.3$           & $1.0$
+	& $0.7$           & $7.1$  
+	& $0.4$    	  & $2.3$ \\
+
+$2.2$~GeV & $40$~m &  $1$~m    
+	& $8.9$           & $0.5$ 
+	& $5.1$           & $0.3$
+	& $0.5$           & $6.7$  
+	& $0.1$   	  & $2.4$ \\	
+
+$3.5$~GeV & $40$~m &  $1$~m  
+	& $11.3$          & $0.9$ 
+	& $6.5$           & $0.6$
+	& $0.8$           & $9.7$  
+	& $0.3$ 	  & $3.3$ \\	
+
+$4.5$~GeV & $40$~m &  $1$~m  
+	& $12.3$          & $1.2$ 
+	& $7.2$           & $1.0$
+	& $0.8$           & $7.5$  
+	& $0.4$   	  & $2.6$ \\	
+
+$6.5$~GeV & $40$~m &  $1$~m  
+	& $11.7$          & $1.6$ 
+	& $8.3$           & $2.2$
+	& $1.1$           & $8.0$  
+	& $0.9$   	  & $3.3$ \\	
+
+$8.0$~GeV & $40$~m &  $1$~m  
+	& $10.9$          & $1.7$ 
+	& $8.5$           & $2.4$
+	& $1.3$           & $8.0$  
+	& $1.2$    	  & $3.6$ \\	
+
+$3.5$~GeV & $40$~m &  $1.5$~m  
+	& $14.5$          & $1.3$ 
+	& $10.0$          & $1.0$
+	& $1.0$           & $12.3$  
+	& $0.5$  	  & $5.3$ \\
+	
+$4.5$~GeV & $40$~m &  $1.5$~m 
+	& $15.5$          & $1.7$ 
+	& $10.8$          & $1.5$
+	& $1.0$           & $9.5$  
+	& $0.6$  	  & $4.2$ \\
+		
+$3.5$~GeV & $40$~m &  $2$~m 
+	& $16.6$          & $1.5$ 
+	& $12.9$          & $1.3$
+	& $1.3$           & $13.9$  
+	& $0.7$  	  & $6.9$ \\
+	
+$4.5$~GeV & $40$~m &  $2$~m 
+	& $18.2$          & $2.1$ 
+	& $14.3$          & $1.9$
+	& $1.3$           & $11.1$  
+	& $0.8$  	  & $5.6$ \\
+	
+$3.5$~GeV & $60$~m &  $1$~m 
+	& $11.7$          & $0.9$ 
+	& $7.6$           & $0.7$
+	& $0.7$           & $10.1$  
+	& $0.3$      	  & $3.7$ \\
+	
+$4.5$~GeV & $60$~m &  $1$~m 
+	& $12.5$          & $1.3$ 
+	& $8.1$           & $1.1$
+	& $0.7$           & $7.7$  
+	& $0.4$ 	  & $2.9$ \\
+	
+$3.5$~GeV & $60$~m &  $1.5$~m 
+	& $15.1$          & $1.3$ 
+	& $12.2$          & $1.0$
+	& $1.0$           & $12.8$  
+	& $0.5$  	  & $6.3$ \\
+	
+$4.5$~GeV & $60$~m &  $1.5$~m 
+	& $16.2$          & $1.8$ 
+	& $13.1$          & $1.6$
+	& $1.0$           & $9.9$  
+	& $0.6$ 	  & $4.9$ \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\subsection{Validation of the algorithm}
+The validity of the method presented in the previous section have been tested against a straight forward  algorithm consisting of decaying each pion $N$ times ($N \approx 10^6$) in a full GEANT simulation of the event (decays included). Such method presents the advantage to keep all the information of the neutrino available for further studies. It can be a good approach to compute the muon neutrino flux coming from pion decays. It can also provide the beam profile, but it shows its limits for the muon induced fluxes, especially the $\bar{\nu}_e$ flux. Indeed, this means that each muon is duplicated $N$ times and when a muon decays, it must decay $N$ times again. For $N\approx 10^6$, this is a prohibitive CPU time consuming.
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compGeantDonega.eps}
+\caption{\label{fig:compGeantDonega}Comparison between the probability method, (\full) curve, and the full GEANT simulation method, (\dashed) curve, for the $\nu_\mu$ from $\pi^+$ flux (a) and the $\bar{\nu}_\mu$ from $\pi^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu_e$ and $\bar{\nu}_e$ fluxes contrary to the former simulation.}
+\end{figure*}
+%
+The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are displayed on figure~\ref{fig:compGeantDonega} for both methods. The two spectra shows a clear agreement, and this makes confidence on the probability method.
+%
+\subsection{Simulated fluxes}
+The fluxes are computed at a distance of $100$~km from the source by convention and can be rescaled at any desired distance. They provide the number of the four neutrino species ($\nu_\mu$, $\bar{\nu}_\mu$, $\nu_e$, $\bar{\nu}_e$) passing through a $100$~m$^2$ fiducial area during $1$~year.
+
+In practice, the fluxes are given as a function of the neutrino energy via histograms composed of $20$~MeV bin width.  These histograms are filled with the energy of each neutrino weighted by the probability to reach the detector (section~\ref{sec:algo}). To obtain the fluxes, the histograms are rescaled to the number of p.o.t per year depending on the beam energy. Table~\ref{tab:proton} reports on the number of p.o.t per year for the different energies studied using the definition of one year being $10^7$~s and keeping the beam power constant (\textit{i.e.} $4$~MW).
+
+Three origins are identified in the composition of each neutrino flux:
+\begin{description}
+	\item[-] neutrinos from pions, which includes neutrinos created by primary pion decays and neutrinos coming from the muons produced by pion decays or muons directly exiting the target. This is the component studied in reference \cite{donega} but with different settings and event generator;
+	\item[-] neutrinos emitted during the decay chain of the charged kaons, either by direct production, or produced by the daughter pions and muons;
+	\item[-] neutrinos coming from the decay chain of the neutral kaons.
+\end{description}
+
+The three components of the fluxes for the four neutrino species are presented on figure~\ref{fig:flux22p} for positive particle focusing and a proton beam kinetic energy of $2.2$~GeV. The $\nu_\mu$ flux is dominated by the neutrinos of pion decays, but a tail above $500$~MeV (insert on the top left part) is created by the $K^+\rightarrow \mu^+\nu_\mu$ channel, which is anyway at least three order of magnitude below the flux maximum. The $\bar{\nu}_\mu$ flux is mostly due to the decays of $\pi^-$ that are not unfocused by the horns, but the higher energy part comes from $\mu^+$ decays. It is noticable that the $\nu_e$ and $\bar{\nu}_e$ fluxes are respectively more than $200$ and more than $7000$ times smaller than the $\nu_\mu$ flux. The $\bar{\nu}_e$ are produced in a large part by the $K^0_L\rightarrow\pi^+e^-\bar{\nu}_e$ decay channel and by $\mu^-$ decays, while the  $\nu_e$ flux is dominated by the $\mu^+$ decays.
+
+On figure~\ref{fig:flux22m}, the horns are set to focus negative particles keeping other parameters identical. By comparison with positive focusing, one can at first approximation translate the results by exchanging particles and anti-particles, except that the $K^+/K^-$ ratio is about 50 in the beam-target interactions (see table~\ref{tab:nbPart}).
+
+On figures~\ref{fig:flux45p} and \ref{fig:flux8p}, one observes the evolution of figure~\ref{fig:flux22p} when the proton beam kinetic energy increases to $3.5$~GeV and $8$~GeV, respectively. Correspondingly, the results for negative particle focusing are presented on figures~\ref{fig:flux45m} and \ref{fig:flux8m}. One clearly notices the increase of the kaon induced neutrino contents as the beam energy grows.
+%
+On table~\ref{tab:speciesfluxes} are reported the integral of the fluxes when one modifies the decay tunnel length and radius, as well as the beam kinetic energy. Changing the length from $10$~m to $40$~m will increase the $\nu_\mu$ flux by $50\%$ to $70\%$ and in the same time, the number of $\nu_e$ will be multiply by a factor $1.5$ to $2$. One can notice that going from $40$~m to $60$~m does not increase the signal-like events but increase the background-like events. For a $40$~m length of the decay tunnel, the increase of the radius improve the number of signal-like events by $50\%$, and the backgroud increase by $70\%$ to $100\%$. Notice that the $\nu_\mu/\bar{\nu}_\mu$ flux ratio is rather insensitive to the decay tunnel length. The feeling that $L_T = 40$~m and $R_T = 2$~m is a good signal over background compromise is confirmed by sensitivity quantitative studies reported in section~\ref{sec:results}.
+
+Looking at the evolution of $\nu_\mu$ flux with respect to the beam energy, one notices that a maximum is reached around $4.5$~GeV. This is due to the competition between the cross section rise with respect to the energy and the decrease of the number of p.o.t due to the constant SPL power ($4$~MW).
+%
+\section{Sensitivity computation ingredients}
+%
+The sensitivity to $\theta_{13}$ and $\delta_{CP}$ is computed for a $\nu_\mu\rightarrow\nu_e$ appearance experiment. The detector considered for definitiveness is similar to the UNO detector, \textit{i.e.} a $440$~kt fiducial water \v{C}erenkov detector \cite{UNO}. The detector simulation has been presented in reference \cite{JJG} and the analysis program described in reference \cite{MEZZETTONUFACT060} has been used for sensitivity computation following previous work of reference \cite{Mezzetto}. See table~\ref{tab:param} for the default user parameter values used in this paper. We just remind here some key points of the sensitivity analysis program. 
+
+It is included a full 3-flavors oscillation probability computation with matter effects, but no ambiguities are taken into account. This latest point may be revisited in a future work using reference \cite{DONINI-2}. Concerning the background events, the $\nu_e/\bar{\nu}_e$ from the beam, the $\nu_\mu e^-$ elastic scattering process, the $\pi^o$ production as well as the $\mu/e$ misidentification are taken into account. The cross-sections from the NUANCE program are used \cite{NUANCE}. The systematics error on the total $\nu_e$ and $\bar{\nu}_e$ fluxes determination is a user parameter and we have used the $2\%$ value considered as a final goal, but also $5\%$ and $10\%$ \cite{MEZZETTONUFACT060}. The detector is located at $L = 130$~km from CERN, in the foreseen new Fréjus laboratory \cite{mosca}. It is worth to mention that if one wants to evaluate the influence of $L$ on the sensitivity, it would mean a re-optimization of the horns for each $L$ envisaged (see section~\ref{sec:horn}).  
+%
+\begin{table}
+\centering
+\caption{\label{tab:param}Default parameters used to compute the sensitivity curves \cite{MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite{KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite{JJG}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			$\Delta m^2_{12} = 8.2 (0.5)\times 10^{-5}~\mathrm{eV}^2$ & $\sin^22\theta_{12} = 0.82 (9\%)$ \\
+			$\Delta m^2_{23} = 2.5 (0.1)\times 10^{-3}~\mathrm{eV}^2$ & $\sin^22\theta_{23} = 1.0 (1\%)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		  $L_T = 20$~m & $R_T = 1$~m \\ 
+		  $M=440$~kT   & $\epsilon_{syst}=2\%$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+\centre{2}{Horn/Reflector shapes to produce a $260$~MeV neutrino beam} \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The running time scenario has been fixed either by focusing positive particles during 5 years, either  by focusing positive particles during 1 (or 2) year(s) followed by focusing negative particles during 4 (or 8) years.
+%
+\section{Results}
+\label{sec:results}
+\subsection{The positive only focusing scenario}
+The $\theta_{13}$ and $\delta_{CP}$ sensitivities are computed with $\theta_{13} = 0^\circ$ and $\delta_{CP} = 0^\circ$ if not explicitly mentioned. It is worth to stress that the default parameters of table~\ref{tab:param} are used if not contrary mentioned, in particular, the decay tunnel geometry parameters ($L_T=20$~m and $R_T=1$~m), and the horn design to generate a $260$~MeV neutrino beam. 
+
+Table~\ref{tab:nbvsE} presents the number of signal and background events for a $5$ years positive focusing experiment, but with different beam energy settings. 
+%The quality factor ($S$) is defined in reference \cite{MEZZETTONUFACT060} as\footnote{Contrary to the definition of the significance of reference \cite{MEZZETTONUFACT060}, the systematical factor is applied to the total $\nu_e$ flux in agreement with the sensitivity contour computation.}:
+%\begin{equation}
+%\begin{aligned}
+%\mathcal{S} &= \frac{N^{osc}_{\nu_e}}{\sqrt{ N^{tot}_{\nu_e} + \left(N^{tot}_{\nu_e}\times\epsilon_{syst}\right)^2}}\\
+%\mathrm{with}\quad N^{tot}_{\nu_e} &= N^{osc}_{\nu_e} + N^{beam}_{\nu_e} + N^{oth. bkg}
+%\label{eq:significance}
+%\end{aligned}
+%\end{equation}
+%and $N^{osc}_{\nu_e}$ the number of $\nu_e$ events due to $\nu_\mu$ oscillations, $N^{beam}_{\nu_e}$ the number of background events coming from the $\nu_e+\bar{\nu}_e$ contamination of the beam, $N^{oth. bkg}$ the other kinds of background events and $\epsilon_{syst}$ the systematical factor.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbvsE}Number of events for 5 years positive focusing scenario with default parameters of table~\ref{tab:param}. Other backgrounds are $\pi^0$, $\nu_\mu$-elast., $\mu/e$-missId. 
+%The $S$ factor is defined by equation~\ref{eq:significance}.
+}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		 & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			non oscillated $\nu_\mu$       & $36917$  & $60969$  & $73202$  & $78024$ & $76068$ \\ 
+			oscillated $\nu_e$             & $43$     & $60$     & $64$     & $61$    & $56$ \\
+			beam $\nu_e$                   & $165$    & $222$    & $242$    & $288$   & $299$ \\
+			other background               & $70$     & $105$    & $127$    & $148$   & $152$ \\
+%			S factor                       & $1.88$   & $2.16$   & $2.17$   & $1.87$  & $1.69$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+The contours at $90\%$, $95\%$ and $99\%$~CL of the $\theta_{13}$ sensitivity are presented in the ($\sin^22\theta_{13}$, $\Delta m^2_{23}$) plane on figure~\ref{fig:sensi45} for $3.5$~GeV proton beam kinetic energy. 
+The comparison between the contours at $90\%$~CL with $2.2$~GeV, $3.5$~GeV, $4.5$~GeV and $8$~GeV beam energies is shown on figure~\ref{fig:compSensi}. One notices in this scenario a better perfomence reached with a $4.5$~GeV energy beam. 
+%as a confirmation of significance parameter value. 
+But, in fact there is not much visual difference between a sensitivity obtained with $3.5$~GeV and $4.5$~GeV, even if one should keep in mind that kaon production models are different at these two energies (see section~\ref{sec:kaon}). These two energy settings have been studied with different decay tunnel geometries and minimum values of $\sin^22\theta_{13}$ observable at $90\%$~CL are reported on table~\ref{tab:thvsE_3545}. One notice that similar results can be reached with a $3.5$~GeV beam, compared to a $4.5$~GeV beam.
+
+Quantitative studies of the minimum $\sin^22\theta_{13}$ with respect to the kinetic beam energy $E_k(proton)$, and the decay length $L_T$, and the systematics $\epsilon_{syst}$ are presented in tables~\ref{tab:thvsE} and \ref{tab:thvseps}. One notices that for $\epsilon_{syst} = 5\%$ there is no difference between a $3.5$~GeV and a $4.5$~GeV beam.
+%
+We have also considered the $3.5$~GeV and $4.5$~GeV beam energies with the tunnel geometry parameters $L_T=40$~m and $R_T=2$~m, and the horn design producing a $350$~MeV neutrino beam (see section~\ref{sec:horn}). In table~\ref{tab:thvsE_3545} are reported numerical values, and on figure~\ref{fig:comp5year} are shown the $90$\% CL sensitivity contours. With the $350$~MeV neutrino beam, one can expect a $16$\% improvment with respect to the $260$~MeV neutrino beam. One notices also that there is marginal gain to increase the beam energy from $3.5$~GeV to $4.5$~GeV, as already mentioned. 
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensi35.eps}
+\caption{\label{fig:sensi45}Sensitivity contours obtained with a SPL energy of $3.5$~GeV and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m. (\full), (\dashed) and (\dotted) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compSensi.eps}
+\caption{\label{fig:compSensi}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comp5year.eps}
+\caption{\label{fig:comp5year}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$~GeV or $4.5$~GeV, and either a $260$~MeV (default) neutrino beam or a $350$~MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$~m and $R_T = 2$~m. The (\chain) curve corresponds to a $350$~MeV/$4.5$~GeV (neutrino beam/SPL beam energy) setting; the (\dotted) curve corresponds to a $350$~MeV/$3.5$~GeV setting; the (\dashed) curve corresponds to a $260$~MeV/$4.5$~GeV setting and the (\full) curve corresponds to a  $260$~MeV/$3.5$~GeV setting.}
+\end{figure}
+%
+\begin{table}
+\centering
+\caption{\label{tab:thvsE}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		        & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV  \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$10$~m & $1.10$ & $0.92$ & $1.04$ & $1.07$ & $1.16$ \\
+			$20$~m & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$40$~m & $1.23$ & $1.00$ & $0.99$ & $1.08$ & $1.19$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+
+There are also variations on the minimum $\sin^22\theta_{13}$ value that may be reached in a $\nu_\mu \rightarrow \nu_e$ experiment which are due to the $\mathrm{sign}(\Delta m^2_{23})$ ambiguity and the $\delta_{CP}$ value. On table~\ref{tab:sign} are presented these kind of variations. Other ambiguities coming from the sign$(\tan(2\theta_{23}))$ ignorance also take place as studied in reference \cite{DONINI}. From figure~9 of this reference, we estimate a 30\% effect on $\sin^2(2\theta_{13})$ sensivity due to these ambiguities.
+%
+\subsection{Mixed positive/negative focusing scenario}
+%
+The combined $\sin^22\theta_{13}$ and $\delta_{CP}$ sensitivity for the 5 years positive focusing scenario and the default parameters of table~\ref{tab:param} is presented on figure~\ref{fig:compDeltaTheta}(a). The results obtained with a $3.5$~GeV and $4.5$~GeV SPL beam are similar and better than with the other energy settings. On figure~\ref{fig:sensiDeltaTheta}(a) the results obtained with a $260$~MeV neutrino beam and a $350$~MeV neutrino beam are presented with a $40$~m long, $2$~m radius decay tunnel. With the $350$~MeV neutrino beam, one can reached better sensitivity results in the range $|\delta_{CP}| < 120^o$, and comparatively the gain obtained when switching from a $3.5$~GeV proton beam to a $4.5$~GeV proton beam is marginal. 
+%
+To improve the $\delta_{CP}$-independent limit on $\sin^22\theta_{13}$, especially around $\delta_{CP}=90^\circ$, one may envisaged a combination of 2 years with positive focusing and 8 years negative focusing as in references \cite{DONINI,JJG,Mezzetto}. The comparison of the results obtained with different SPL beam energies on the combined sensitivity contours are presented in figure~\ref{fig:compDeltaTheta}(b). %Quantitative results  with this kind of mixed focusing scenario are reported table \ref{tab:thvsE_3545}.
+Sensitivities to $\sin^22\theta_{13}$ observable at $90\%$~CL in the worse $\delta_{CP}$ case are reported table \ref{tab:thvsE_3545} for this kind of mixed focusing scenario.
+ One generally gets $10\%$ to $20\%$ better limit on $\sin^22\theta_{13}$ independently of $\delta_{CP}$ with a $3.5$~GeV kinetic energy beam compare to a $2.2$~GeV beam. Doubling the length and the radius of the decay tunnel allows to reach a $10\%$ better limit.
+
+On figure~\ref{fig:sensiDeltaTheta}(b) are presented the results considering the effects of a $350$~MeV neutrino beam obtained either with a $3.5$~GeV proton beam or a $4.5$~GeV proton beam compared to a $260$~MeV neutrino beam obtained with a $4.5$~GeV proton beam. The tunnel geometry parameters are $L_T=40$~m and $R_T=2$~m (other tunnel geometry have been studied but the results are worse and so are not reported). Except in the region $|\delta_{CP}|>150^o$, the results obtained with the $350$~MeV neutrino beam ($3.5$~GeV proton beam) are somewhat better, even if a $11\%$ improvement of the $\delta_{CP}$-independent $\sin^22\theta_{13}$ limit can be reached with the $260$~MeV neutrino beam obtained with the $3.5$~GeV proton beam.
+\begin{table*}
+\centering
+%\caption{\label{tab:thvsE_3545}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) at and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings in parenthesis are identical to those of table~\ref{tab:speciesfluxes}, except that the setting (7b) corresponds to the tunnel geometry of setting (7) but the horn geometry producing a $350$~MeV neutrino beam is used. We remind that the setting (2) is the default one, and the settings (7) and (7b) corresponds to $L_T = 40$~m and $R_T = 2$~m.}
+\caption{\label{tab:thvsE_3545}Study of the sensitivity of different beam energy, decay tunnel length ($L_T$) at and radius ($R_T$), and horn design in two different scenarios. First scenario is 5 years of positive focusing, in wich sensitivity is given as the minimum of $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL ($\delta_{CP} = 0$). Second scenario is 2 years of positive focusing plus 8 years of negative focusing, in wich sensitivity is given as the minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta_{CP}$ case. A star $^{(*)}$ indicates the use of the the horn geometry producing a $350$~MeV neutrino beam. Other parameters are fixed to default values (table~\ref{tab:param}).}
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+setting & $L_T$ & $10$~m & $20$~m &  $20$~m & $30$~m & $40$~m &  $40$~m & $40$~m & $40$~m$^{(*)}$ & $60$~m &  $60$~m\\
+        & $R_T$ & $1$~m  & $1$~m & $1.5$~m &  $1$~m &  $1$~m & $1.5$~m &  $2$~m &  $2$~m$^{(*)}$ &  $1$~m & $1.5$~m\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+5 years of positive &
+    $3.5$~GeV   & $0.92$ & $0.92$ & $0.83$ & $0.98$ & $1.00$ & $0.93$ & $0.91$ & $0.76$ & $1.05$ & $1.01$ \\
+focusing scenario &
+    $4.5$~GeV   & $1.04$ & $0.89$ & $0.82$ & $0.94$ & $0.99$ & $0.92$ & $0.87$ & $0.71$ & $1.03$ & $1.00$ \\
+\noalign{\smallskip}\hline
+ 2 years of positive  &
+    $2.2$~GeV &        & $2.52$ &        &        & $2.58$ &        & $2.30$ &        &         &       \\
+focusing $+$ 8 year of &
+    $3.5$~GeV & $2.34$ & $2.22$ & $2.10$ & $2.13$ & $2.09$ & $2.08$ & $2.02$ & $2.28$ &  $2.16$ & $2.09$\\
+negative focusing scenario &
+    $4.5$~GeV & $2.91$ & $2.60$ & $2.43$ & $2.48$ & $2.52$ & $2.39$ & $2.34$ & $2.55$ &  $2.53$ & $2.47$\\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{table}
+\centering
+\caption{\label{tab:thvseps}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon_{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			      & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$2\%$ & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$5\%$ & $1.48$ & $1.25$ & $1.25$ & $1.48$ & $1.64$ \\
+			$10\%$ & $2.40$ & $2.14$ & $2.21$ & $2.72$ & $3.09$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table}
+\centering
+\caption{\label{tab:sign}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$~GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta_{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			    & $-180^\circ$ & $-90^\circ$ & $0^\circ$ & $90^\circ$ & $180^\circ$\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$+$ & $1.40$ & $0.43$ & $1.16$ & $11.48$ & $1.40$\\
+			$-$ & $1.45$ & $11.75$& $1.11$ & $0.43$  & $1.45$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compDeltaTheta.eps}
+\caption{\label{fig:compDeltaTheta}90\% sensitivity contours obtained with SPL beam energy of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) at $90\%$ CL. Default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensiDeltaTheta.eps}
+\caption{\label{fig:sensiDeltaTheta}90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$~m and $R_T=2$~m and different SPL beam energies ($3.5$~GeV or $4.5$~GeV) and different horn designs ($260$~MeV or $350$~MeV neutrino beams): (\full) curve for a $350$~MeV/$4.5$~GeV setting, (\dotted) curve for a $350$~MeV/$3.5$~GeV setting, (\dashed) curve for a $260$~MeV/$3.5$~GeV setting. Other default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}
+\end{figure}
+%
+%\begin{table*}
+%\centering
+%\caption{\label{tab:thvsE_td}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta_{CP}$ case, and for different decay tunnel length ($L_T$) and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 2 years of positive focusing plus 8 years of negative focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings are identical to those of table~\ref{tab:speciesfluxes}.}
+%
+%\begin{tabular}{@{}l*{15}{l}}
+%\hline\noalign{\smallskip}
+%setting & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (7b) & (8) & (9)\\
+%\noalign{\smallskip}\hline\noalign{\smallskip}
+%$2.2$~GeV &        & $2.52$ &        &        & $2.58$ &        & $2.30$ &        &         &       \\
+%$3.5$~GeV & $2.34$ & $2.22$ & $2.10$ & $2.13$ & $2.09$ & $2.08$ & $2.02$ & $2.28$ &  $2.16$ & $2.09$\\
+%$4.5$~GeV & $2.91$ & $2.60$ & $2.43$ & $2.48$ & $2.52$ & $2.39$ & $2.34$ & $2.55$ &  $2.53$ & $2.47$\\
+%\noalign{\smallskip}\hline
+%\end{tabular}
+%\end{table*}
+%
+\section{Summary and outlook}
+A complete chain of simulation has been set up for the SPL-Fréjus project. The neutrino production has been extended to the kaon decay contribution, which is important to test SPL energy scenario above $2.2$~GeV.
+The beam line optimization has been performed using the sensitivity to $\sin^22\theta_{13}$ and $\delta_{CP}$. The shape of the focusing system has been updated to obtain a neutrino beam energy around $260$~MeV or $350$~MeV.
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comparaisonFinale.eps}
+\caption{\label{fig:deltathetaFinal}90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite{CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite{Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite{MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite{KOBAYASHI}. The BNL contour has been obtained from reference \cite{BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu_e$ and $\bar{\nu}_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta$ beam was analysed like a reactor experiment with 1\% systematic error \cite{MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$~GeV beam and a decay tunnel of $40$~m length, and $2$~m radius.}
+\end{figure}
+
+In a positive only focusing scenario, the best limit on $\sin^22\theta_{13}$ is $0.82\times10^{-3}$
+ ($90\%$ CL, $\delta_{CP}=0$), with a $4.5$~GeV beam energy and a $20$~m long, $1.5$~m radius decay tunnel. However, the $3.5$~GeV beam may also obtain rather similar limit with $0.83\times10^{-3}$ ($90\%$ CL) with the same tunnel parameters. The $\delta_{CP}$ independant $\sin^22\theta_{13}$ sensitivity is limited to $\approx 10^{-2}$ due to the $\delta_{CP} \approx 90^o$ region.
+ 
+In a mixed focusing scenario, the best limit on $\sin^22\theta_{13}$ independent of $\delta_{CP}$ is $2.02\times10^{-3}$ ($90\%$ CL) obtained with a $3.5$~GeV beam energy and a $40$~m long, $2$~m radius decay tunnel.
+
+The comparison of the optimization presented in this paper with the results obtained by other projects is displayed on figure \ref{fig:deltathetaFinal}. It is presented the 5 years positive focusing scenario, and two versions of a mixed scenario using positive and negative focusing: one scenario duration is 5 years in total and the other one is 10 years running in total and has been used in the previous section. It shows the complementarity of the SPL-Fr\'ejus project with the beta beam-Fr\'ejus project. Especially when considering the sensitivity to $\sin^22\theta_{13}$ for $\delta_{CP}<0$. 
+
+%
+The authors think that the present study may be extended in many respects. The beam line simulation part may be performed with a single simulator as FLUKA (or GEANT4 \cite{GEANT4} for comparison). Other targets may be envisaged (tantalum, carbon) as well as other detector types as a Large Liquid Argon detector \cite{BIGICARUS}. The baseline length may also be revisited as well as the off axis option. The sensitivity analysis may be deeper investigated using the complete set of possible ambiguities as in reference \cite{DONINI}, and the $\theta_{13}$ or $\delta_{CP}$ measurement accuracy with new beam energy scenario may be investigated too.     
+%
+\begin{acknowledgement}
+The authors would like to thank M.~Mezzetto to have expressed his interest since the early stage of this work and to have provided us with his sensitivity computation program. Also the authors thank S.~Gilardoni for fruitful discussions.
+\end{acknowledgement}
+%
+\appendix
+\setcounter{section}{0}
+\section{Decay probability computations}
+\label{sec:decayprobcomp}
+This appendix contains the probability formulas and the algorithms used in the flux computation (see section~\ref{sec:algo}).
+
+\subsection{Pion neutrino probability computation}
+\label{sec:Ppi}
+Pions decay only as $\pi^+\rightarrow \mu^+ + \nu_\mu$ or $\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$ and the neutrinos are emitted isotropically in the pion rest frame, with an energy of about $30$~MeV given by the 2-body decay kinematics. Applying a Lorentz boost knowing the pion momentum and direction, it is possible to compute the probability to reach the detector for the neutrinos. Only neutrino parallel to the beam axis are supposed to pass through the detector fiducial area, and therefore, the neutrino must be emitted by the pion with an angle opposite to the angle between the pion and the beam axis (see figure~\ref{fig:pionDecay}). This gives:
+\begin{equation}
+\mathcal{P}_\pi = \frac{1}{4\pi}\frac{A}{L^2}\frac{1-\beta^2}{(\beta\cos\alpha-1)^2}
+\label{probaPi}
+\end{equation}
+where $\beta$ is the velocity of the pion in the tunnel frame, $A$ is the fiducial detector surface, $L$ the distance between the neutrino source and the detector, and $\alpha$ the angle between the pion direction and the beam axis in the laboratory frame.
+
+\begin{figure}
+\centering
+\includegraphics{../picts/pionDecay.eps}
+\caption{\label{fig:pionDecay}Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha$ is needed.}
+\end{figure}
+
+\subsection{Muon neutrino probability computation}
+\label{sec:Pmu}
+Muons decay only as $\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_\mu$ or $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$, and will produce background events. The mean decay length of the muons is $2$~km, therefore, most of them do not decay in the tunnel. This induces a lack of statistics to estimate the corresponding level of background. This problem has been solved using each muon appearing in the simulation in the following steps:
+\begin{enumerate}
+	\item the probability for the muon to decay into the tunnel has been computed using a straight line propagation;
+	\item the available energy for the neutrino in the tunnel frame has been divided in $20$~MeV energy bins; 
+	% (the number of bin depending of the muon energy).
+	\item one $\nu_e$ and one $\nu_\mu$ have been simulated in each of the energy bins (step 2). Then, the probability to reach the detector has been computed, and multiplied by the probability computed at step (1).%the neutrino energy is stored in an histogram, weighted with this probability and 
+\end{enumerate}
+After the probability computation, the non useful muon is discarded by GEANT to gain in CPU time. 
+
+The probability for the muon neutrino and the electron neutrino to be emitted parallel to the beam axis is \cite{donega}:
+\begin{multline}
+\frac{d\mathcal{P}_\mu}{dE_\nu} = \frac{1}{4\pi}\frac{A}{L^2}\frac{2}{m_\mu}\frac{1}{\gamma_\mu(1+\beta_\mu\cos\theta^*)}\\ \times \frac{1-\beta_\mu^2}{(\beta_\mu\cos\rho-1)^2}\left[f_0(x)\mp \Pi_\mu^L f_1(x)\cos\theta^*\right]
+\label{probaMu}
+\end{multline}
+where $\beta_\mu$ and $\gamma_\mu$ are the velocity and the Lorentz boost of the muon in the tunnel frame, $\theta^*$ is the angle with respect to the beam axis of the muon in the muon rest frame, $\rho$ is the corresponding angle in the tunnel frame. Like in the pion case, this angle appears because the neutrino must be parallel to the beam axis. $\Pi_\mu^L$ is the muon longitudinal polarization, the parameter $x$ is defined as $x=2E_\nu^*/m_\mu$ where $E_\nu^*$ is the neutrino energy in the muon rest frame, and the function $f_0(x)$ and $f_1(x)$ coming from the matrix element of the muon decay are given in table~\ref{tab:Function}. The sign in front of $\Pi_\mu^L$ in equation~\ref{probaMu} is $(-)$ for the $\mu^+$ decays and $(+)$ for the $\mu^-$ decays, respectively.
+
+%\Table{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%\br
+%		      &  $f_0(x)$ & $f_1(x)$ \\
+%\mr
+%		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+%		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		      &  $f_0(x)$ & $f_1(x)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+Muon polarization is computed using the conservation of the transverse component of the velocity four-vector $\gamma(1,\beta)$ between the muon rest frame (where the polarization is computed) and the pion rest frame, where the muon helicity is $-1$, due to the parity non conservation. It yields \cite{picasso}:
+\begin{equation}
+\Pi_\mu^T = \frac{\gamma_\pi\beta_\pi}{\gamma_\mu\beta_\mu}\sin\theta^*
+\mbox{ and }\Pi_\mu^L = \sqrt{1-\Pi_\mu^{T2}}
+\label{pola}
+\end{equation}
+where $\gamma_\pi$, $\beta_\pi$, $\gamma_\mu$, and $\beta_\mu$ are the Lorentz boost and velocity of the pion and of the muon in the tunnel frame, and $\theta^*$ the angle with respect to the beam axis of the muon in the pion rest frame.
+
+\subsection{The treatment of the kaons}
+\label{sec:kaons}
+Contrary to pions and muons, kaons have many decay channels. They are summarized in table~\ref{tab:BRKP0SL}.
+
+%\Table{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%\br
+%\centre{2}{$K^\pm$}                                               & \centre{2}{$K^0_L$}     &          \centre{2}{$K^0_S$}\\
+%\mr
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu$   & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+%$\pi^\pm\pi^0$ & $21.17\%$                                        & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+%$\pi^\pm\pi^+\pi^-$ & $5.59\%$                                    & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+%$e^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+%$\pi^\pm\pi^0\pi^0$ & $1.73\%$                                    & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+\centre{2}{$K^\pm$}         & \centre{2}{$K^0_L$}     & \centre{2}{$K^0_S$}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$\mu^\pm\nu_\mu$ & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+$\pi^\pm\pi^0$ & $21.17\%$   & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+$\pi^\pm\pi^+\pi^-$ & $5.59\%$ & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+$e^\pm\nu_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+$\mu^\pm\nu_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+$\pi^\pm\pi^0\pi^0$ & $1.73\%$ & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+There is a very small amount of kaons produced (section~\ref{sec:kaon}), and this number has been artificially increased in order to obtain statistically significant results.  The multiplicity of decay channels makes impossible the method used for the muon case (\ref{sec:Pmu}). The method chosen for the good compromise between the gain in CPU and the statistical uncertainty of the results, is to duplicate many times each kaon exiting the target. The number of duplication varies between 10 and 300. It depends on the initial kaon rate and therefore on the beam energy.
+
+All the kaons daughter particles are tracked by GEANT until they decay. Three different types of daughter particles are identified in the kaon decays. The first type corresponds to primary neutrinos, the second type concerns charged pions and muons, and the neutral pions are left for the last type.
+
+In the $K^\pm\rightarrow\mu^\pm \nu_\mu(\bar{\nu}_\mu)$ decay modes, the computation of the probability for a neutrino to reach the detector is the same than the 2-body decay formula used to in the pion decay (equation~\ref{probaPi}), where $\beta$ is now the kaon velocity, and $\alpha$ the angle of the kaon with respect to the beam axis. 
+
+When a neutrino is produced by a kaon 3-body decay, the probability to reach the detector is computed using a pure phase space formula. It yields:
+\begin{multline}
+\mathcal{P}_K = \frac{1}{4\pi}\frac{A}{L^2}\frac{1}{m_K-m_\pi-m_l} \\ \times \frac{1}{\gamma_K(1+\beta_K\cos\theta^*)}
+\frac{1-\beta_K^2}{(\beta_K\cos\delta-1)^2}
+\label{probaL}
+\end{multline}
+where $m_K$ is the kaon mass (charged or neutral), $m_\pi$ is the pion mass ($\pi^0$ mass in $K^\pm$ decays and $\pi^\pm$ mass in $K_L^0$ decays), and $m_l$ is the mass of the lepton associated with the neutrino. The $\beta_K$ and $\gamma_K$ are the velocity and the Lorentz boost of the kaon, $\theta^*$ is the angle between the neutrino direction and the kaon direction, in the kaon rest frame. Finally, $\delta$ is the angle between the kaon direction and the beam axis in the tunnel frame.
+
+When a $\pi^\pm$ is produced in the kaon decay chain, it is tracked by GEANT until it decays, and the probability of equation~\ref{probaPi} is applied to the produced neutrino. In case of a muon, it is treated as explained in \ref{sec:Pmu}. The muon polarization is computed this time using the kaon decay informations. Finally, when a $\pi^0$ is produced, as it cannot create neutrinos, it is simply discarded.
+
+%
+%\section*{References}
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+%
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+%
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+%Pontecorvo B  1957 \textit{Sov. Phys.--JETP} {\bf 6} 429 [1957 \textit{Zh. Eksp. Teor. Fiz.} \textbf{33} 549]
+%\nonum Maki Z, Nakagawa M and Sakata S 1962 \textit{Prog. Theor. Phys.} \textbf{28} 870\\
+%Pontecorvo B 1968 \textit{Sov. Phys.--JETP} \textbf{26}  984 [1967 \textit{Zh. Eksp. Teor. Fiz.} \textbf{53} 1717]
+%\nonum Gribov V N and Pontecorvo B 1969 \PL B \textbf{28} 493
+%
+%\bibitem{CHOOZ}
+%Apollonio M \etal  [CHOOZ Collaboration] 1999 \PL B {\bf 466} 415
+%\nonum Apollonio M \etal  [CHOOZ Collaboration] 2003 \EJP C {\bf 27}  331
+%
+%\bibitem{Wpaper}
+%Anderson K \etal 2004 \textit{White paper report on using nuclear reactors to search for a value of $\theta_{13}$} http://www.hep.anl.gov/minos/reactor13/reactor13.pdf
+%
+%\bibitem{BETABEAM}
+%Zucchelli P 2002 \PL B \textbf{532} 166
+%
+%\bibitem{NOVA}
+%Ambats I \etal 2004 NO$\nu$A proposal FNAL P929
+%
+%\bibitem{T2K}
+%Itow Y 2001 KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05 \\
+%see also arXiv:hep-ex/0106019
+%
+%\bibitem{BNLHS}
+%Diwan M V 2003 \PR D {\bf 68} 012002
+%
+%\bibitem{CERN}
+%Blondel A \etal CERN-2004-002
+%
+%\bibitem{DONINI}
+%Donini A \etal 2004 IFT-UAM/CSIC-04-30\\
+%see also arXiv:hep-ph/0406132.
+%
+%\bibitem{DOUBLE-CHOOZ}
+%Dalnoki-Veress F for the Double-CHOOZ project arXiv:hep-ex/0406070
+%
+%\bibitem{SPL}
+%Autin B \etal CERN-2000-12
+%
+%\bibitem{UNO} 
+%The UNO whitepaper \textit{Physics Potential and Feasibility of UNO} (preprint SBHEP01-3) (see also http://ale.physics.sunysb.edu/uno/)
+%
+%\bibitem{mosca}
+%Mosca L 2004 Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+%
+%\bibitem{Meer}
+%van der Meer S 1961 CERN-Report No 61-7
+%
+%\bibitem{nuFact134} 
+%Campagne J E and Cazes A 2003 CERN-NUFACT-Note-134\\ http://slac.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{MMWPSCazes} 
+%Campagne J E and Cazes A 2004 Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 \\
+%http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+%
+%\bibitem{JJG}
+%G\'omez Gadenas J J \etal 2001 IFIC/01-31 \\
+%see also arXiv:hep-ph/0105297
+%
+%\bibitem{Mezzetto}
+%Mezzetto M 2003 \jpg {\bf 29} 1781-1784\\
+%see also arXiv:hep-ex/0302005
+%
+%
+%\bibitem{nuFact138} 
+%Campagne J E 2004 CERN-NUFACT-Note-138\\
+% http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{fluka}
+%Fasso A \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, Kling A \etal - eds., Springer-Verlag Berlin, p159-164 (2001);
+%\nonum Fasso A \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, Kling A \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+%
+%\bibitem{MMWPSGaroby} 
+%Garoby R 2004 Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+%
+%\bibitem{harp}
+%Catanesi C \etal [HARP Collaboration] CERN-SPSC 2002/019
+%
+%\bibitem{MARS}
+%Mokhov N V \etal 1995 The MARS Code System User Guide, Version 13(95), Fermilab-FN-628
+%\nonum Mokhov N V \etal 1998 MARS oed Develepments; LANL Report LA-UR-98-5716, nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+%
+%\bibitem{FLUKAprivate}
+%Battistoni G and Ferrari A \textit{private communication}
+%
+%\bibitem{geant}
+%Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+%
+%\bibitem{SIMONE1}
+%Gilardoni S 2003 Talk at NuFact03 http://www.cap.bnl.gov/nufact03/
+%
+%\bibitem{donega}
+%Blondel A \etal 2001 CERN-NUFACT-Note-78\\
+% http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{MEZZETTONUFACT060}
+%Mezzetto M 2000 CERN-NUFACT-Note-60\\
+% http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{DONINI-2}
+%Donini A, Meloni D and Rigolin S 2004 J. High Energy Phys. \textbf{0406} 011\\
+%see also arXiv:hep-ph/0312072
+%
+%\bibitem{NUANCE}
+%Casper D  2002\textit{ Nucl. Phys. Proc. Suppl.} \textbf{112} 161-170\\
+%see also arXiv:hep-ph/0208030
+%
+%
+%\bibitem{KAMLAND}
+%Gratta G [KamLAND Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%
+%\bibitem{GEANT4}
+%Agostinelli A \etal [GEANT4 Collaboration] 2003 \NIM A \textbf{506} 250-503
+%
+%\bibitem{Gaisser}
+%Gaisser T K 1990 \textit{Cosmic Rays and Particle Physics} Cambridge University Press 
+%
+%\bibitem{picasso}
+%Combley F and Picasso E 1974 \textit{Phys. Rept.} {\bf 14} 1
+%
+%\bibitem{pdg}
+%Hagiwara K \etal 2002 \PR D {\bf 66}  010001
+%
+\bibitem{SKNU04}
+E. Kearns [SuperKamiokande Collaboration], talk at the International Conference NEUTRINO 2004, 14-19 June 2004, http://neutrino2004.in2p3.fr/
+
+\bibitem{K2KNU04}
+T. Nakaya [K2K Collaboration], \NP B (Proceedings Supplement) {\bf 143}, 96 (2005)
+
+\bibitem{MINOS}
+T. Thomson [MINOS Collaboration], \NP B (Proceedings Supplement) {\bf 143}, 249 (2005);
+P. Adamson \etal, NuMi-L-337 (unpublished)
+
+\bibitem{OPERA}
+D. Autiero [OPERA Collaboration], \NP B (Proceedings Supplement) {\bf 143}, 257 (2005);
+M. Guler  \etal, \textsl{Experiment proposal} CERN/SPSC 2000-028 SPSC/P318 LNGS P25/2000 (unpublished) 
+
+\bibitem{ICARUS}
+A. Bueno  [ICARUS Collaboration], \NP B (Proceedings Supplement) {\bf 143}, 262 (2005);
+P. Aprili \etal, CERN-SPSC-2002-027 (unpublished)
+
+\bibitem{CNGS}
+G. Acquistapace  \etal, CERN-98-02 (unpublished)
+
+\bibitem{LSND}
+A. Athanassopoulos \etal, \PRL {\bf 81}, 1774  (1998);
+A. Aguilar \etal, \PR D {\bf 64}, 112007 (2001) 
+
+\bibitem{MINIBOONE}
+I. Stancu \etal, FERMILAB-TM-2207 (unpublished)
+
+\bibitem{PMNS}
+B. Pontecorvo \textsl{Sov. Phys.--JETP} {\bf 6}, 429 (1957) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{33}, 549 (1957)];
+Z. Maki, M. Nakagawa and S. Sakata \textsl{Prog. Theor. Phys.} \textbf{28}, 870 (1962);
+Pontecorvo B \textsl{Sov. Phys.--JETP} \textbf{26},  984 (1968) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{53}, 1717 (1967)];
+V. N. Gribov and B. Pontecorvo \PL B \textbf{28}, 493 (1969) 
+
+\bibitem{CHOOZ}
+M. Apollonio \etal, \PL B {\bf 466}, 415 (1999);
+M. Apollonio \etal, \EJP C {\bf 27},  331 (2003)
+
+\bibitem{Wpaper}
+K. Anderson \etal, \textsl{White paper report on using nuclear reactors to search for a value of $\theta_{13}$} (2004), http://www.hep.anl.gov/minos/reactor13/reactor13.pdf (unpublished); 
+F.~Arbelier \etal, \textsl{Letter of Intend for Double-CHOOZ}, arXiv:hep-ex/0405032 (unpublished)
+
+\bibitem{BETABEAM}
+P. Zucchelli, \PL B \textbf{532}, 166 (2002) 
+
+\bibitem{NOVA}
+I. Ambats \etal,  NO$\nu$A proposal FNAL P929, 2004 (unpublished)
+
+\bibitem{T2K}
+Y. Itow, KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05 (unpublished),
+see also arXiv:hep-ex/0106019
+
+\bibitem{BNLHS}
+M. V. Diwan, \PR D {\bf 68}, 012002 (2003)
+
+\bibitem{CERN}
+A. Blondel \etal, CERN-2004-002 (unpublished)
+
+\bibitem{DONINI}
+A. Donini \etal, IFT-UAM/CSIC-04-30, 2004 (unpublished);
+see also arXiv:hep-ph/0406132
+
+\bibitem{DOUBLE-CHOOZ}
+F. Dalnoki-Veress, the Double-CHOOZ project arXiv:hep-ex/0406070 (unpublished)
+
+\bibitem{SPL}
+B. Autin \etal, CERN-2000-12 (unpublished)
+
+\bibitem{UNO} 
+The UNO whitepaper, \textsl{Physics Potential and Feasibility of UNO}, SBHEP01-3 (unpublished), see also http://ale.physics.sunysb.edu/uno/
+
+\bibitem{mosca}
+L. Mosca, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Meer}
+S. van der Meer, CERN-Report No 61-7, 1961 (unpublished)
+
+\bibitem{nuFact134} 
+J.E. Campagne and A. Cazes, CERN-NUFACT-Note-134, 2003 (unpublished), see http://slac.web.cern.ch/slap/NuFact/NuFact/\\
+NFNotes.html
+
+\bibitem{MMWPSCazes} 
+J.E. Campagne and A. Cazes, Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004,
+see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{JJG}
+J.J. G\'omez Gadenas \etal,  IFIC/01-31, Proceedings of Venice 2001, Neutrino telescopes, vol. 2, p463-481;
+see also arXiv:hep-ph/0105297; A. Blondel \etal, \NIM A {\bf 503} 173 (2001);
+A. Blondel \etal, CERN-2004-002
+
+\bibitem{Mezzetto}
+M. Mezzetto,  \jpg {\bf 29}, 1781-1784 (2003),
+see also arXiv:hep-ex/0302005
+
+
+\bibitem{nuFact138} 
+J.E. Campagne, CERN-NUFACT-Note-138, 2004 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{fluka}
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p159-164 (2001);
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+
+\bibitem{MMWPSGaroby} 
+R. Garoby, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{harp}
+C. Catanesi \etal, CERN-SPSC 2002/019 (unpublished)
+
+\bibitem{minerva} 
+D. Drakoulakos \etal, Fermilab P-938 (unpublished),
+see also arXiv:hep-ex/405002
+
+\bibitem{MARS}
+N.V. Mokhov \etal, The MARS Code System User Guide, Version 13(95), Fermilab-FN-628 (1995);
+N.V. Mokhov  \etal, MARS oed Develepments, LANL Report LA-UR-98-5716 (1998), nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+
+\bibitem{FLUKAprivate}
+G. Battistoni and A. Ferrari, \textsl{private communication}
+
+\bibitem{geant}
+Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+
+\bibitem{SIMONE1}
+S. Gilardoni, Talk at NuFact03 (2003), see http://www.cap.bnl.gov/nufact03/
+
+\bibitem{donega}
+A. Blondel \etal, CERN-NUFACT-Note-78, 2001 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{MEZZETTONUFACT060}
+M. Mezzetto, CERN-NUFACT-Note-60, 2000 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{DONINI-2}
+A. Donini, D. Meloni and S. Rigolin, J. High Energy Phys. \textbf{0406}, 011 (2004),
+see also arXiv:hep-ph/0312072
+
+\bibitem{NUANCE}
+D. Casper, \textsl{ Nucl. Phys. Proc. Suppl.} \textbf{112}, 161-170 (2002),
+see also arXiv:hep-ph/0208030
+
+\bibitem{KAMLAND}
+G. Gratta,  talk at the International Conference NEUTRINO 2004, 14-19 June 2004, http://neutrino2004.in2p3.fr/
+
+\bibitem{MIGLIOZZITERANOVA}
+M. Komatsu, P Migliozzi and F. Terranova,  \jpg {\bf 29}, 443 (2003); see also arXiv:hep-ph/0210043
+
+\bibitem{KOBAYASHI}
+T. Kobayashi, \NP B (Proceedings Supplement) {\bf 143}, 303 (2005)
+
+\bibitem{BNL}
+ M.V. Diwan \etal, \PR D \textbf{68}, 012002 (2003); see also figure~8 of 
+arXiv:hep-ph/0303081
+
+\bibitem{MAOROPRIVATE}
+M. Mezzetto, \textsl{private communication}: the corresponding $\theta_{13}$ limit is $3.4^o$.
+
+\bibitem{GEANT4}
+A. Agostinelli \etal, \NIM A \textbf{506}, 250-503 (2003) 
+
+\bibitem{BIGICARUS}
+A. Ereditato and A. Rubia, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Gaisser}
+T.K. Gaisser, \textsl{Cosmic Rays and Particle Physics} (Cambridge University Press, 1990)  
+
+\bibitem{picasso}
+F. Combley and E. Picasso, \textsl{Phys. Rept.} {\bf 14}, 1 (1974) 
+
+\bibitem{pdg}
+K. Hagiwara \etal,  \PR D {\bf 66},  010001 (2002)
+
+
+%
+\end{thebibliography}
+%
+\end{document}
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus.tcp
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+
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+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus.tex
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--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus.tex	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus.tex	(revision 392)
@@ -0,0 +1,1191 @@
+%\documentclass[epj,nopacs,referee]{svjour}
+%remove referee for final version
+\documentclass[epj,nopacs]{svjour}
+%----------------------------------------------------------------------------
+%
+\usepackage[T1]{fontenc}
+\usepackage[latin1]{inputenc}
+\usepackage{graphicx}
+\usepackage{epsfig}
+\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage{latexsym}
+%
+\newcommand{\centre}[2]{\multispan{#1}{\hfill #2\hfill}}
+\newcommand{\dotted}{\protect\mbox{${\mathinner{\cdotp\cdotp\cdotp\cdotp\cdotp\cdotp}}$}}
+\newcommand{\dashed}{\protect\mbox{- - - -}}
+\newcommand{\broken}{\protect\mbox{-- -- --}}
+\newcommand{\longbroken}{\protect\mbox{--- --- ---}}
+\newcommand{\chain}{\protect\mbox{--- $\cdot$ ---}}
+\newcommand{\dashddot}{\protect\mbox{--- $\cdot$ $\cdot$ ---}}
+\newcommand{\full}{\protect\mbox{------}}
+%
+% abbreviations for IOPP journals
+%
+\newcommand{\CQG}{{\it Class. Quantum Grav.} }
+\newcommand{\CTM}{{\it Combust. Theory Modelling\/} }
+\newcommand{\DSE}{{\it Distrib. Syst. Engng\/} }
+\newcommand{\EJP}{{\it Eur. J. Phys.} } 
+\newcommand{\HPP}{{\it High Perform. Polym.} }              % added 4/5/93
+\newcommand{\IP}{{\it Inverse Problems\/} }
+\newcommand{\JHM}{{\it J. Hard Mater.} }                    % added 4/5/93
+\newcommand{\JO}{{\it J. Opt.} }
+\newcommand{\JOA}{{\it J. Opt. A: Pure Appl. Opt.} }
+\newcommand{\JOB}{{\it J. Opt. B: Quantum Semiclass. Opt.} }
+\newcommand{\JPA}{{\it J. Phys. A: Math. Gen.} }
+\newcommand{\JPB}{{\it J. Phys. B: At. Mol. Phys.} }      %1968-87
+\newcommand{\jpb}{{\it J. Phys. B: At. Mol. Opt. Phys.} } %1988 and onwards
+\newcommand{\JPC}{{\it J. Phys. C: Solid State Phys.} }   %1968--1988
+\newcommand{\JPCM}{{\it J. Phys.: Condens. Matter\/} }    %1989 and onwards
+\newcommand{\JPD}{{\it J. Phys. D: Appl. Phys.} }
+\newcommand{\JPE}{{\it J. Phys. E: Sci. Instrum.} }
+\newcommand{\JPF}{{\it J. Phys. F: Met. Phys.} }
+\newcommand{\JPG}{{\it J. Phys. G: Nucl. Phys.} }         %1975--1988
+\newcommand{\jpg}{{\it J. Phys. G: Nucl. Part. Phys.} }   %1989 and onwards
+\newcommand{\MSMSE}{{\it Modelling Simulation Mater. Sci. Eng.} }
+\newcommand{\MST}{{\it Meas. Sci. Technol.} }                 %1990 and onwards
+\newcommand{\NET}{{\it Network: Comput. Neural Syst.} }
+\newcommand{\NJP}{{\it New J. Phys.} }
+\newcommand{\NL}{{\it Nonlinearity\/} }
+\newcommand{\NT}{{\it Nanotechnology} }
+\newcommand{\PAO}{{\it Pure Appl. Optics\/} }
+\newcommand{\PM}{{\it Physiol. Meas.} }                        % added 4/5/93
+\newcommand{\PMB}{{\it Phys. Med. Biol.} }
+\newcommand{\PPCF}{{\it Plasma Phys. Control. Fusion\/} }      % added 4/5/93
+\newcommand{\PSST}{{\it Plasma Sources Sci. Technol.} }
+\newcommand{\PUS}{{\it Public Understand. Sci.} }
+\newcommand{\QO}{{\it Quantum Opt.} }
+\newcommand{\QSO}{{\em Quantum Semiclass. Opt.} }
+\newcommand{\RPP}{{\it Rep. Prog. Phys.} }
+\newcommand{\SLC}{{\it Sov. Lightwave Commun.} }               % added 4/5/93 
+\newcommand{\SST}{{\it Semicond. Sci. Technol.} }
+\newcommand{\SUST}{{\it Supercond. Sci. Technol.} }
+\newcommand{\WRM}{{\it Waves Random Media\/} }
+\newcommand{\JMM}{{\it J. Micromech. Microeng.\/} }
+%
+% Other commonly quoted journals
+%
+\newcommand{\AC}{{\it Acta Crystallogr.} }
+\newcommand{\AM}{{\it Acta Metall.} }
+\newcommand{\AP}{{\it Ann. Phys., Lpz.} }
+\newcommand{\APNY}{{\it Ann. Phys., NY\/} }
+\newcommand{\APP}{{\it Ann. Phys., Paris\/} }
+\newcommand{\CJP}{{\it Can. J. Phys.} }
+\newcommand{\JAP}{{\it J. Appl. Phys.} }
+\newcommand{\JCP}{{\it J. Chem. Phys.} }
+\newcommand{\JJAP}{{\it Japan. J. Appl. Phys.} }
+\newcommand{\JP}{{\it J. Physique\/} }
+\newcommand{\JPhCh}{{\it J. Phys. Chem.} }
+\newcommand{\JMMM}{{\it J. Magn. Magn. Mater.} }
+\newcommand{\JMP}{{\it J. Math. Phys.} }
+\newcommand{\JOSA}{{\it J. Opt. Soc. Am.} }
+\newcommand{\JPSJ}{{\it J. Phys. Soc. Japan\/} }
+\newcommand{\JQSRT}{{\it J. Quant. Spectrosc. Radiat. Transfer\/} }
+\newcommand{\NC}{{\it Nuovo Cimento\/} }
+\newcommand{\NIM}{{\it Nucl. Instrum. Methods\/} }
+\newcommand{\NP}{{\it Nucl. Phys.} }
+\newcommand{\PL}{{\it Phys. Lett.} }
+\newcommand{\PR}{{\it Phys. Rev.} }
+\newcommand{\PRL}{{\it Phys. Rev. Lett.} }
+\newcommand{\PRS}{{\it Proc. R. Soc.} }
+\newcommand{\PS}{{\it Phys. Scr.} }
+\newcommand{\PSS}{{\it Phys. Status Solidi\/} }
+\newcommand{\PTRS}{{\it Phil. Trans. R. Soc.} }
+\newcommand{\RMP}{{\it Rev. Mod. Phys.} }
+\newcommand{\RSI}{{\it Rev. Sci. Instrum.} }
+\newcommand{\SSC}{{\it Solid State Commun.} }
+\newcommand{\ZP}{{\it Z. Phys.} }
+
+\newcommand{\etal}{{et al.\/}}
+%
+%
+%----------------------------------------------------------------------------
+\begin{document}
+%
+\title{The $\theta_{13}$ and $\delta_{CP}$ sensitivities of the SPL-Fréjus project revisited}
+\author{Jean Eric Campagne, Antoine Cazes}
+\institute{ Laboratoire de l'Accélérateur Linéaire -
+Université Paris-Sud - B\^at. 200 - BP 34 -
+91898 Orsay Cedex, France}
+\mail{campagne@lal.in2p3.fr}
+\date{\today}
+%
+%
+%
+%\selectlanguage{francais}
+%
+\abstract{
+An optimization of the CERN SPL beam line has been performed guided by the sensitivities to the $\theta_{13}$ mixing angle and to the $\delta_{CP}$ Dirac CP violating phase. A UNO-like 440 ktons water \v{C}erenkov detector located at 130~km from the target in a new foreseen Fréjus laboratory has been used as a generic detector. Concerning the $\delta_{CP}$ independent $\theta_{13}$ sensitivity, a gain of about $20\%$ may be reached using a $3.5$~GeV proton beam with a 40~m long, 2~m radius decay tunnel compared to the up to now considered $2.2$~GeV beam energy and 20~m long, 1~m radius decay tunnel. This may motivate new machine developments to upgrade the nominal SPL proton beam energy.}
+%\pacs{14.60.Pq, 14.60.Lm}
+
+\maketitle
+
+
+\section{Introduction}
+The very near future of the neutrino long baseline experiments is devoted to the study of the oscillation mechanism in the range of $\Delta m^2 = \Delta m^2_{atm} \approx 2.4\times10^{-3}\mathrm{eV}^2$ \cite{SKNU04,K2KNU04}
+ using conventional $\nu_\mu$ beams. The current K2K experiment in Japan \cite{K2KNU04}, and the forthcoming MINOS in the USA \cite{MINOS} take benefit of low energy beam to measure the $\Delta m^2$ parameter using the disappearance mode $\nu_\mu\rightarrow\nu_\mu$, while OPERA/ICARUS experiments \cite{OPERA,ICARUS} using the high energy CNGS beam \cite{CNGS} will be able to detect $\nu_\tau$ appearance. If we do not consider the LSND anomaly \cite{LSND} that will be further studied soon by MiniBooNE experiment \cite{MINIBOONE}, the three flavor family scenario will be confirmed and accommodated by a $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix \cite{PMNS} with three angles ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase $\delta_{CP}$.  
+
+Beyond this medium term plan, two of the next future tasks of neutrino physics are to improve the sensitivity of the last unknown mixing angle parameter, the so-called $\theta_{13}$, and to explore the CP violation mechanism in the leptonic sector. The present upper bound on $\theta_{13}$ is $\sin^22\theta_{13}<0.14$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$~CL) \cite{CHOOZ}. This sensitivity can be improved using reactor and accelerator experiments. In reactor experiments, one uses $\bar{\nu}_e$ in disappearance mode and may reach $\sin^22\theta_{13}<0.024$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$CL) \cite{Wpaper}. In accelerator experiments, one can use $\nu_e$ and $\bar{\nu}_e$ from $\beta$ beams \cite{BETABEAM} in both  disappearance and appearance modes (\textit{i.e.} $\stackrel{\scriptscriptstyle (-)}{\nu}_e\rightarrow \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$), and also $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu$ in appearance mode (\textit{i.e.} $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu\rightarrow\stackrel{\scriptscriptstyle(-)}{\nu}_e$) with conventional beams either with sub-mega watt proton drivers \cite{NOVA,T2K} or with multi-mega watt proton drivers \cite{T2K,BNLHS,CERN}. The later neutrino beam type, called Superbeam, is foreseen to be extended to produce $\nu_\mu$ beam and $\bar{\nu}_\mu$ beam from muon decays, the so-called Neutrino Factory, in order to study the eventual leptonic CP violation. Such Neutrino Complex is under study in Japan, in USA and also in Europe at CERN and details may be found in reference \cite{CERN}. A comparison of the performances of $\beta$ beam and Superbeam may be found for instance in reference \cite{DONINI}.  The reactor experiment result on $\theta_{13}$ is straight forward as compared to Superbeam and Neutrino Factory results that are on one hand reacher but in an other hand more complex to analyse due to the interplay between the different physics factors $\theta_{13}$, $\delta_{CP}$, sign$(\Delta m^2_{23})$, sign$(\tan(2\theta_{23}))$ \cite{DONINI,DOUBLE-CHOOZ}. 
+
+This paper presents results of a new simulation of the SPL (Super Proton Linac) Superbeam that could take place at CERN \cite{SPL}, using for definitiveness a UNO-like 440kT fiducial water \v{C}erenkov detector \cite{UNO} located in a new enlarged underground laboratory under study in the Fréjus tunnel, $130$~km away from CERN \cite{mosca}. The SPL neutrino beam is created by  decays of pions, muons and kaons produced by the interactions of a $4$~MW proton beam impinging a liquid mercury jet \cite{CERN}. Pions, muons and kaons are collected using two concentric electromagnetic lenses (horns), the inner one and the outer one are hereafter called "Horn" and "Reflector" respectively \cite{Meer}. The horns are followed by a decay tunnel where most of the neutrinos are produced. A sketch of the beam line is shown on figure~\ref{fig:Sbeam}.  
+
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/cernSuperBeam_English}
+\caption{\label{fig:Sbeam}Sketch of the SPL neutrino Superbeam from CERN to the Fréjus tunnel.}	
+\end{figure}
+
+The analysis chain consists of different stages: the simulation of the interactions between the proton beam and the mercury target, the propagation of the resulting secondary particles through the magnetic field and the materials of the horns, the tracking of $\pi^\pm$, $K^{\pm,0}$ and $\mu^\pm$ until they decay, the computation of the neutrino flux at the detector site, and finally the statistical analysis. A part of the simulation chain has already been described in reference \cite{nuFact134,MMWPSCazes}. 
+
+
+Compared to recent papers on the same subject \cite{DONINI,JJG,Mezzetto}, we have reoptimized the Horn and Reflector shapes \cite{nuFact138}, and introduced the kaon background simulation which allows us to update the SPL beam energy. The organization of this document follows the simulation chain: the interaction between the proton beam and the mercury target is presented in the second section. The kaon production is detailed in the third section. The simulation of the horns is described in the forth section, while the algorithms used to compute the neutrino fluxes are explained in the fifth section. Then, the sensitivities to $\theta_{13}$ and $\delta_{CP}$ are revisited with new studies about the optimization of the proton beam energy, the pion collection and the decay tunnel geometry.
+
+\section{Target simulation}
+\label{sec:target}
+Since hadronic processes are crucial to describe the interactions of the proton beam on the target, the FLUKA simulator \cite{fluka} has been chosen for this first step of the simulation. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:targ}Liquid mercury jet parameters.}
+\begin{tabular}{ll}
+\hline\noalign{\smallskip}
+    \centre{2}{Hg target}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+      Hg jet speed & $20$~m/s \\
+      density & $13.546$ \\
+      Length, radius & $30$~cm, $7.5$~mm \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+The target used in the present study is a mercury liquid jet \cite{CERN} simulated by a cylinder $30$~cm long (representing two hadronic lengths) and $1.5$~cm diameter (see table~\ref{tab:targ}). Other types of target are under study \cite{CERN}. The pencil like simulated proton beam is composed with  $10^6$ mono-energetic protons. The beam axis is also the symmetry axis of the target and the horns and the decay tunnel. Simulations have been performed for $2.2$~GeV proton kinetic energy, the up to now nominal design \cite{SPL}, as well as for $3.5$~GeV, $4.5$~GeV, $6.5$~GeV and $8$~GeV according to possible new designs \cite{MMWPSGaroby}.
+
+Particle production yields are summarized in table~\ref{tab:nbPart}. The pion momentum spectra obtained at different energies and normalized to a 4MW SPL beam power are presented in figure~\ref{fig:compEner2}(a). At low energy, pions come from $\Delta$ decays while the high energy part is dominated with multi pion production. At very mow energy, for $P<200$~MeV/c, pions come from $\Delta$ produced by protons of the target excited by the beam interactions, while for  higher energy, pion production is due to transformation of protons of the beam into $\Delta$.
+
+The horns are designed to focus the $600$~MeV/c pions (see section~\ref{sec:horn}) and the variation of the number of such pion is rather smooth with respect to the beam energy considering a 4MW fixed beam power: $4.19\times10^{13}\pi$/s for the $2.2$~GeV beam, $4.91\times10^{13}\pi$/s for the $3.5$~GeV beam, $5.14\times10^{13}\pi$/s for the $4.5$~GeV beam, and $4.92\times10^{13}\pi$/s for the $6.5$~GeV beam. The main difference is made by the angular distribution. Figure~\ref{fig:compEner2}(b) shows this distribution for the $\pi^+$ exiting the target with a momentum between $500$~MeV/c and $700$~MeV/c. The acceptance of the horns is limited to the pion below $25^\circ$, and we see that more pions are accepted by the horns for the $3.5$~GeV and $4.5$~GeV proton beams compared to other beam energies.
+
+The secondary proton and neutron rates induce important radiation damages and power dissipation in the horns which have been addressed in reference \cite{nuFact134}, and which will require specific R\&D effort. At $2.2$~GeV, kaon yields are very low, but it has a dramatic energy dependence as further studied in section~\ref{sec:kaon}. It is worth to mention that the numbers in table~\ref{tab:nbPart} are not to be taken as face values, because the cross sections of pion and kaon productions using proton beam are still under studies as for instance by the HARP experiment \cite{harp}.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbPart}Average numbers of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA). The $\mu^+/\mu^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+$E_k$ (GeV) & p & n & $\gamma$ & $e^+$ & $e^-$ & $\pi^+$ & $\pi^-$ & $\mu^+$ & $\mu^-$ & $K^+$ & $K^0$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$2.2$ & $1.4$     &  $17$   & $5.0$  &   $0.08$  &  $0.17$    &  $0.24$   &  $0.18$ & $4$ & $1$ & $7$ & $6$ \\
+
+$3.5$ & $1.8$    &  $23$  & $7.0$   &  $0.15$  &  $0.28$    &  $0.41$   &  $0.37$ & $10$ & $3$ & $35$ & $30$ \\
+
+$4.5$ &  $2.3$  &  $25$ & $7.7$  & $0.21$  &  $0.35$    &  $0.57$ & $0.39$&  $11$ & $3.3$  &  $93$ &  $68$       \\
+
+$8$   &  $3.1$  &  $33$ & $11.0$ & $0.41$ & $0.63$    &  $1.00$  &  $0.85$ &  $30$ &  $9.5$ &  $413$ &    $340$         \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compEner2.eps}
+\caption{\label{fig:compEner2} (a) $\pi^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$~GeV/c and $0.7$~GeV/c. The different SPL beam kinetic energies presented are (\full) $2.2$~GeV, (\dashed) $3.5$~GeV, (\dotted) $4.5$~GeV and (\chain) $6.5$~GeV.}
+\end{figure*}
+%
+The cross section uncertainties are the main source of discrepancy between simulator programs. Some comparisons between FLUKA and MARS \cite{MARS} have already been presented in the same context \cite{nuFact134}. The energy distribution of the pions exiting the target, computed with the two simulator programs FLUKA and MARS, is shown on figure~\ref{fig:compFlukaMars}(a).  The discrepancy is quite large for the low energy part. However, the horns are designed to focus the high energy part of the spectrum (see section~\ref{sec:horn}), and therefore, MARS and FLUKA are in better agreement for the energy spectrum computed at the entrance of the decay tunnel, as shows figure~\ref{fig:compFlukaMars}(b). So,  the discrepancy  at low energy between MARS and FLUKA does not matter too much for the present application. A difference of $10\%$ has been found between the  $\theta_{13}$ sensitivity computed with the two generators (see section~\ref{sec:results}), that can be taken as systematic error. 
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compMarsFluka.eps}
+\caption{\label{fig:compFlukaMars}$\pi^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\dashed) and by MARS (\full).}
+\end{figure*}
+%
+\section{Kaon production}
+\label{sec:kaon}
+The possibility to increase the SPL energy in order to study the optimization of the physics program has been recently pointed out \cite{MMWPSGaroby}. Then, the kaon production should be clearly addressed because it is a source of $\nu_e$ and $\bar{\nu}_e$ background events. The kaon decay channels and branching ratios are presented in table~\ref{tab:BRKP0SL} in \ref{sec:kaons}.
+
+The target simulation described in section~\ref{sec:target} has been used with $10^6$ p.o.t with kinetic energy uniformly distributed between $2.2$~GeV and $5$~GeV. The momentum of outgoing pions and kaons are recorded when they exit the target. The number of produced $K^{o,\pm}$ at different proton beam energies are presented on figure~\ref{fig:KaonsPions}(a). In one hand the $K^o$ production rate is similar to the $K^+$ production rate, but in an other hand the $K^-$ production rate is almost forty times smaller. For comparison, the numbers of $\pi^+$ and $\pi^-$  produced in the same conditions are presented on figure~\ref{fig:KaonsPions}(b). Pion production rate is about two orders of magnitude greater than the kaon production rate.
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/KaonProd.eps}
+\caption{\label{fig:KaonsPions}Kaon production (a) as a function of the incident proton beam kinetic energy ($E_k$) for $10^6$ incident protons with (\full) curve for $K^+$, (\dashed) curve for $K^-$ and (\dotted) curve for $K^0$. Pion production (b) in the same conditions with (\full) curve for $\pi^+$ and (\dashed) curve for $\pi^-$.}
+\end{figure*}
+%
+The behavior of the two pion and kaon production rates are quite different. The $\pi^+$ yield grows smoothly with the proton energy while the production of kaons seams to have two origins, which has been confirmed by FLUKA's authors \cite{FLUKAprivate}. For beam energy below approximatively $4$~GeV, the resonance production model is used, and one notices a low production rate with a maximum at about $3.4$~GeV. For beam energy above  $4$~GeV, the dual parton model is used, and the production rate experiences a threshold effect with a rapid rise. The ratio between positive kaon and pion production rates is about $0.5\%$ between $2.2$~GeV and $4$~GeV and grow up to $2.3\%$ at $5$~GeV. One notices that the transition between the two kaon production models may not be optimal.
+%
+\section{Horns simulation}
+\label{sec:horn}
+The simulation code of the electromagnetic horns is written using GEANT 3.2.1 \cite{geant} for convenience and since electromagnetic processes are dominant, FLUKA has not been considered as mandatory, but this may be revised in a future work. The geometry of the horns has been inspired by an existing CERN prototype and a Reflector design proposed in reference \cite{SIMONE1}. Depending of the current injection, only positive secondary particles or negative secondary particles are focused. The relevant parameters are detailed in table~\ref{tab:specif}.
+
+The mercury target is localized inside the Horn because of the low energy and the large emittance of the secondary pions produced: $$<P_{\pi T}>/<P_\pi> \approx 240~\mathrm{MeV}/400~\mathrm{MeV}$$ ($2.2$~GeV proton beam energy). This explains the Horn design (figure~\ref{fig:plan}), with a cylindrical part around the target, called the neck, which is larger than the transversal size of the target to simulate the room for target handling, and a conic part designed such that the relevant pions are focused as much as possible to exit the magnetic field parallel to the beam axis.
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/corne350.eps}
+\caption{\label{fig:plan}Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350~MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}
+\end{figure}
+
+\begin{table}
+\centering
+\caption{\label{tab:specif}Relevant parameters of the horns in case of the generation of a $260$~MeV neutrino beam (or $350$~MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$~MeV/c (or $800$~MeV/c) pion momentum.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+ & Horn & Reflector \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+  neck inner radius & $3.7$~cm &  $20.3$~cm \\
+  neck length & $40$~cm        &  $120 (140)$~cm \\ 
+  end cone inner radius & $16$~cm        &  $35.7$~cm \\
+  outer radius & $20.3$~cm      & $40$~cm \\ 
+  total length & $120 (140)$~cm       & $190 (220)$~cm \\  
+  Alu thickness  & $3$~mm       & $3$~mm \\            
+  Peak current & $300$~kA       & $600$~kA \\
+  Frequency & $50$~Hz            & $50$~Hz \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The shape of the horn conductors is a crucial point since it determines the energy spectrum of the neutrino at the detector site. The details of the conductor shape optimization for the present context may be found in reference \cite{nuFact138}. We just recall here some ingredients. For a $\theta_{13}$ driven $\nu_\mu \rightarrow \nu_e$ oscillation, a $\Delta m^2_{23}$ parameter value of $2.4\times10^{-3}\mathrm{eV}^2$, and a baseline distance of $130$~km, the first oscillation maximum occurs for a neutrino energy of $260$~MeV. The   optimization of the physics potential depends at first approximation on the pion neutrino characteristics, which energy is fully determined by the pion 2-body decay and boost. To reach an energy of $260$~MeV, the pion needs a $\beta=0.97$, which in turn induces a pion momentum of $600$~MeV/c. Then, the shape of the conic part of the horns is determined such that these $600$~MeV/c pions exit parallel to the beam axis. 
+
+An other shape of the horn conductors has been used to produce a $350$~MeV neutrino beam to compare the sensitivity potential (see section \ref{sec:results}). In that case, keeping the current intensity unchanged ($300/600$~kA), the lengths of the Horn and the Reflector should be increased by $16$\% and $18.5$\%, respectively (see table~\ref{tab:specif}).
+
+Before closing this section, it is worth to quote that the Horn/Reflector conductor shapes optimized in the present study to focus a given pion momentum value, is not affected at first order by a proton beam energy change. What is affected is the production rate of the relevant pions. This Horn/Reflector design consideration would be different if one wishes to focus as much as possible all the pions produced for which the mean energy is of course affected by a proton beam energy change.    
+%
+\section{Particle decay treatment and flux calculation}
+%
+The decay tunnel representation is a simple cylinder with variable length ($L_T$) and radius ($R_T$) filled with "vacuum" and located right after the horns. The default design is a $20$~m long and $1$~m radius cylinder, but simulations have also been conducted with lengths of $10$~m, $40$~m and $60$~m, and radius of $1.5$~m and $2$~m in the spirit of reference \cite{donega}. In the GEANT simulation, to gain in CPU time, only pions, muons and kaons are tracked in the volume of the tunnel, and all particles exiting this volume are discarded. 
+
+Beyond the $1/L^2$ solid angle factor due to the source-detector distance ($L$) which decreases dramatically the fluxes, the neutrino beam focusing is very limited due to the small pion boost factor ($\approx 4$). Therefore, computational algorithms have been used to avoid a too prohibitive CPU time resulting from the simulation of each secondary particle decay. Otherwise, about $10^{15}$ p.o.t would have been necessary to obtain reliable statistics for the estimation of the $\bar{\nu}_e$ flux for instance.
+
+It is worth to mention that the particle decays occurring before the entrance of the decay tunnel are also taken into account and treated in the same manner, which is not the case in reference \cite{donega}. 
+%
+\subsection{Algorithm description}
+\label{sec:algo}
+The decay code has been included in the GEANT code. The basic idea of this algorithm is to compute the neutrino fluxes using the probability of reaching the detector for each neutrino produced by a $\pi$ or a $K$ or a $\mu$ particle (on-axis neutrino beam). This method has already been used in reference \cite{donega} and has been modified and extended to the kaon decay chain for the present study. 
+
+Muon neutrino comes mostly from pion decay. In a first stage, each pion is tracked by GEANT until it decays. Then, the probability for the produced muon neutrino to reach the detector is computed. The flux is obtained applying the probability as a weight for each neutrino. All the pions produced in the simulation are therefore useful to compute the flux, and this allows to reduce the number of events in the simulation to $10^6$ p.o.t. In this computation, the decay region (horns and tunnel) is considered as point like compared to the source-detector distance. 
+
+The same method is applied for neutrino coming from muons and kaons with some modifications  because most of the muons do not decay, and there are very few kaons produced (see table~\ref{tab:nbPart}).
+The probability computation is presented in appendix~\ref{sec:decayprobcomp}. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:proton}Number of protons on target for different beam energy at 4~MW constant power. One year is defined as $10^7$~s.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			Beam energy  & Number of proton \\
+			  (GeV)      & per year ($10^{23}$ p.o.t/y) \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			2.2 & 1.10 \\
+			3.5 & 0.70 \\
+			4.5 & 0.56 \\
+			6.5 & 0.40 \\
+			8.0 & 0.30 \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table*}
+\centering
+\caption{\label{tab:speciesfluxes}Integral of the total flux of the different species with different settings. The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are expressed in $10^{13}/100\mathrm{m}^2/y$ unit while the $\nu_e$ and $\bar{\nu}_e$ fluxes are expressed in $10^{11}/100\mathrm{m}^2/y$ unit. The positive focusing  and negative focusing  are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. Setting (1) means $L_T = 10$~m and $R_T = 1$~m. Setting (2) is the default option and means $L_T = 20$~m and $R_T = 1$~m. Setting (3) means $L_T = 20$~m and $R_T = 1.5$~m. Setting (4) means $L_T = 30$~m and $R_T = 1$~m. Setting (5) means $L_T = 40$~m and $R_T = 1$~m. Setting (6) means $L_T = 40$~m and $R_T = 1.5$~m. Setting (7) means $L_T = 40$~m and $R_T = 2$~m.  Setting (8) means $L_T = 60$~m and $R_T = 1$~m, and finally, setting (9) means $L_T = 60$~m and $R_T = 1.5$~m.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+
+			Settings  & \centre{2}{$\nu_\mu$} & \centre{2}{$\nu_e$} 
+								&	\centre{2}{$\bar{\nu}_\mu$} & \centre{2}{$\bar{\nu}_e$} \\
+								\cline{2-9}
+								& $+$ & $-$ & $+$ & $-$ & $+$ & $-$ 
+								& $+$ & $-$ \\ 
+\noalign{\smallskip}\hline\noalign{\smallskip}
+
+(1): $2.2$~GeV  
+	& $5.5$          & $0.4$ 
+	& $1.7$          & $0.2$
+	& $0.3$          & $4.3$  
+	& $0.1$ 				 & $0.8$ \\		
+
+(1): $3.5$~GeV  
+	& $7.7$          & $0.7$ 
+	& $2.6$          & $0.6$
+	& $0.6$          & $6.6$  
+	& $0.3$ 				 & $1.3$ \\		
+	
+(1): $4.5$~GeV  
+	& $7.1$          & $1.0$ 
+	& $2.8$          & $0.9$
+	& $0.5$          & $5.2$  
+	& $0.3$ 			   & $1.1$ \\		  
+
+(1): $6.5$~GeV  
+	& $8.3$          & $1.2$ 
+	& $4.7$          & $1.9$
+	& $0.8$          & $5.6$  
+	& $0.9$ 			   & $1.8$ \\
+
+(1): $8.0$~GeV  
+	& $7.7$          & $1.2$ 
+	& $5.1$          & $2.2$
+	& $0.9$          & $5.6$  
+	& $1.1$ 				 & $2.1$ \\
+
+(2): $2.2$~GeV  
+	& $7.6$         & $0.4$ 
+	& $3.2$ 				& $0.2$
+	& $0.3$ 				& $5.8$  
+	& $0.1$ 				& $1.6$ \\		  
+
+(2): $3.5$~GeV  
+	& $10.0$          & $0.9$ 
+	& $4.4$           & $0.6$
+	& $0.7$ 					& $8.5$  
+	& $0.3$ 					& $2.2$ \\		  
+
+(2): $4.5$~GeV  
+	& $10.9$          & $1.1$ 
+	& $5.1$           & $1.0$
+	& $0.7$ 					& $6.7$  
+	& $0.4$ 					& $1.8$ \\		  
+
+(2): $6.5$~GeV  
+	& $10.4$          & $1.4$ 
+	& $6.4$           & $2.0$
+	& $1.0$           & $7.1$  
+	& $0.9$ 					& $2.5$ \\	
+
+(2): $8.0$~GeV  
+	& $9.7$          & $1.5$ 
+	& $6.7$           & $2.3$
+	& $1.2$           & $7.1$  
+	& $1.1$ 					& $2.8$ \\
+
+
+(3): $2.2$~GeV  
+	& $9.0$           & $0.6$ 
+	& $4.4$           & $0.4$
+	& $0.4$           & $6.7$  
+	& $0.2$  					& $2.2$ \\
+
+(3): $4.5$~GeV  
+	& $13.2$          & $1.5$ 
+	& $6.9$           & $1.4$
+	& $0.9$           & $8.1$  
+	& $0.6$  					& $2.7$ \\
+
+(4): $3.5$~GeV  
+	& $10.9$          & $0.9$ 
+	& $5.7$           & $0.7$
+	& $0.7$           & $9.4$  
+	& $0.3$  					& $2.9$ \\
+
+(4): $4.5$~GeV  
+	& $11.6$          & $1.2$ 
+	& $6.3$           & $1.0$
+	& $0.7$           & $7.1$  
+	& $0.4$  					& $2.3$ \\
+
+(5): $2.2$~GeV  
+	& $8.9$           & $0.5$ 
+	& $5.1$           & $0.3$
+	& $0.5$           & $6.7$  
+	& $0.1$ 					& $2.4$ \\	
+
+(5): $3.5$~GeV  
+	& $11.3$          & $0.9$ 
+	& $6.5$           & $0.6$
+	& $0.8$           & $9.7$  
+	& $0.3$ 					& $3.3$ \\	
+
+(5): $4.5$~GeV  
+	& $12.3$          & $1.2$ 
+	& $7.2$           & $1.0$
+	& $0.8$           & $7.5$  
+	& $0.4$ 					& $2.6$ \\	
+
+(5): $6.5$~GeV  
+	& $11.7$          & $1.6$ 
+	& $8.3$           & $2.2$
+	& $1.1$           & $8.0$  
+	& $0.9$ 					& $3.3$ \\	
+
+(5): $8.0$~GeV  
+	& $10.9$          & $1.7$ 
+	& $8.5$           & $2.4$
+	& $1.3$           & $8.0$  
+	& $1.2$ 					& $3.6$ \\	
+
+(6): $3.5$~GeV  
+	& $14.5$          & $1.3$ 
+	& $10.0$          & $1.0$
+	& $1.0$           & $12.3$  
+	& $0.5$  					& $5.3$ \\
+	
+(6): $4.5$~GeV  
+	& $15.5$          & $1.7$ 
+	& $10.8$          & $1.5$
+	& $1.0$           & $9.5$  
+	& $0.6$  					& $4.2$ \\
+		
+(7): $3.5$~GeV  
+	& $16.6$          & $1.5$ 
+	& $12.9$          & $1.3$
+	& $1.3$           & $13.9$  
+	& $0.7$  					& $6.9$ \\
+	
+(7): $4.5$~GeV  
+	& $18.2$          & $2.1$ 
+	& $14.3$          & $1.9$
+	& $1.3$           & $11.1$  
+	& $0.8$  					& $5.6$ \\
+	
+(8): $3.5$~GeV  
+	& $11.7$          & $0.9$ 
+	& $7.6$           & $0.7$
+	& $0.7$          & $10.1$  
+	& $0.3$  					& $3.7$ \\
+	
+(8): $4.5$~GeV  
+	& $12.5$          & $1.3$ 
+	& $8.1$           & $1.1$
+	& $0.7$          & $7.7$  
+	& $0.4$  					& $2.9$ \\
+	
+(9): $3.5$~GeV  
+	& $15.1$          & $1.3$ 
+	& $12.2$          & $1.0$
+	& $1.0$           & $12.8$  
+	& $0.5$  					& $6.3$ \\
+	
+(9): $4.5$~GeV  
+	& $16.2$          & $1.8$ 
+	& $13.1$          & $1.6$
+	& $1.0$           & $9.9$  
+	& $0.6$  					& $4.9$ \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\subsection{Validation of the algorithm}
+The validity of the method presented in the previous section have been tested against a straight forward  algorithm consisting of decaying each pion $N$ times ($N \approx 10^6$) in a full GEANT simulation of the event (decays included). Such method presents the advantage to keep all the information of the neutrino available for further studies. It can be a good approach to compute the muon neutrino flux coming from pion decays. It can also provide the beam profile, but it shows its limits for the muon induced fluxes, especially the $\bar{\nu}_e$ flux. Indeed, this means that each muon is duplicated $N$ times and when a muon decays, it must decay $N$ times again. For $N\approx 10^6$, this is a prohibitive CPU time consuming.
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compGeantDonega.eps}
+\caption{\label{fig:compGeantDonega}Comparison between the probability method, (\full) curve, and the full GEANT simulation method, (\dashed) curve, for the $\nu_\mu$ from $\pi^+$ flux (a) and the $\bar{\nu}_\mu$ from $\pi^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu_e$ and $\bar{\nu}_e$ fluxes contrary to the former simulation.}
+\end{figure*}
+%
+The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are displayed on figure~\ref{fig:compGeantDonega} for both methods. The two spectra shows a clear agreement, and this makes confidence on the probability method.
+%
+\subsection{Simulated fluxes}
+The fluxes are computed at a distance of $100$~km from the source by convention and can be rescaled at any desired distance. They provide the number of the four neutrino species ($\nu_\mu$, $\bar{\nu}_\mu$, $\nu_e$, $\bar{\nu}_e$) passing through a $100$~m$^2$ fiducial area during $1$~year.
+
+In practice, the fluxes are given as a function of the neutrino energy via histograms composed of $20$~MeV bin width.  These histograms are filled with the energy of each neutrino weighted by the probability to reach the detector (section~\ref{sec:algo}). To obtain the fluxes, the histograms are rescaled to the number of p.o.t per year depending on the beam energy. Table~\ref{tab:proton} reports on the number of p.o.t per year for the different energies studied using the definition of one year being $10^7$~s and keeping the beam power constant (\textit{i.e.} $4$~MW).
+
+Three origins are identified in the composition of each neutrino flux:
+\begin{description}
+	\item[-] neutrinos from pions, which includes neutrinos created by primary pion decays and neutrinos coming from the muons produced by pion decays or muons directly exiting the target. This is the component studied in reference \cite{donega} but with different settings and event generator;
+	\item[-] neutrinos emitted during the decay chain of the charged kaons, either by direct production, or produced by the daughter pions and muons;
+	\item[-] neutrinos coming from the decay chain of the neutral kaons.
+\end{description}
+
+The three components of the fluxes for the four neutrino species are presented on figure~\ref{fig:flux22p} for positive particle focusing and a proton beam kinetic energy of $2.2$~GeV. The $\nu_\mu$ flux is dominated by the neutrinos of pion decays, but a tail above $500$~MeV (insert on the top left part) is created by the $K^+\rightarrow \mu^+\nu_\mu$ channel, which is anyway at least three order of magnitude below the flux maximum. The $\bar{\nu}_\mu$ flux is mostly due to the decays of $\pi^-$ that are not unfocused by the horns, but the higher energy part comes from $\mu^+$ decays. It is noticable that the $\nu_e$ and $\bar{\nu}_e$ fluxes are respectively more than $200$ and more than $7000$ times smaller than the $\nu_\mu$ flux. The $\bar{\nu}_e$ are produced in a large part by the $K^0_L\rightarrow\pi^+e^-\bar{\nu}_e$ decay channel and by $\mu^-$ decays, while the  $\nu_e$ flux is dominated by the $\mu^+$ decays.
+
+On figure~\ref{fig:flux22m}, the horns are set to focus negative particles keeping other parameters identical. By comparison with positive focusing, one can at first approximation translate the results by exchanging particles and anti-particles, except that the $K^+/K^-$ ratio is about 50 in the beam-target interactions (see table~\ref{tab:nbPart}).
+
+On figures~\ref{fig:flux45p} and \ref{fig:flux8p}, one observes the evolution of figure~\ref{fig:flux22p} when the proton beam kinetic energy increases to $3.5$~GeV and $8$~GeV, respectively. Correspondingly, the results for negative particle focusing are presented on figures~\ref{fig:flux45m} and \ref{fig:flux8m}. One clearly notices the increase of the kaon induced neutrino contents as the beam energy grows.
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22p.eps}
+\caption{	\label{fig:flux22p}Neutrino fluxes, $100$~km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$~GeV (4~MW), a decay tunnel with a length of $20$~m and a radius of $1$~m. The top left panel contains the $\nu_\mu$ fluxes, and the top right panel shows the $\bar{\nu}_\mu$ fluxes. The bottom left panel presents the $\nu_e$ fluxes while the bottom right panel displays the $\bar{\nu}_e$ fluxes. The (\full) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\dashed) curve is the contribution from the charged kaon decay chain, and the (\dotted) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22m.eps}
+\caption{\label{fig:flux22m}Same legend as for figure~\ref{fig:flux22p} but the horns are focusing negative particles.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35p.eps}
+\caption{\label{fig:flux45p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35m.eps}
+\caption{\label{fig:flux45m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8p.eps}
+\caption{\label{fig:flux8p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8m.eps}
+\caption{\label{fig:flux8m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+On table~\ref{tab:speciesfluxes} are reported the integral of the fluxes when one modifies the decay tunnel length and radius, as well as the beam kinetic energy. Changing the length from $10$~m to $40$~m will increase the $\nu_\mu$ flux by $50\%$ to $70\%$ and in the same time, the number of $\nu_e$ will be multiply by a factor $1.5$ to $2$. One can notice that going from $40$~m to $60$~m does not increase the signal-like events but increase the background-like events. For a $40$~m length of the decay tunnel, the increase of the radius improve the number of signal-like events by $50\%$, and the backgroud increase by $70\%$ to $100\%$. Notice that the $\nu_\mu/\bar{\nu}_\mu$ flux ratio is rather insensitive to the decay tunnel length. The feeling that $L_T = 40$~m and $R_T = 2$~m is a good signal over background compromise is confirmed by sensitivity quantitative studies reported in section~\ref{sec:results}.
+
+Looking at the evolution of $\nu_\mu$ flux with respect to the beam energy, one notices that a maximum is reached around $4.5$~GeV. This is due to the competition between the cross section rise with respect to the energy and the decrease of the number of p.o.t due to the constant SPL power ($4$~MW).
+%
+\section{Sensitivity computation ingredients}
+%
+The sensitivity to $\theta_{13}$ and $\delta_{CP}$ is computed for a $\nu_\mu\rightarrow\nu_e$ appearance experiment. An analysis program described in reference \cite{MEZZETTONUFACT060} has been used for such sensitivity computation. See table~\ref{tab:param} for the default user parameter values used in this paper. We just remind here some key points of the program. 
+
+It is included a full 3-flavors oscillation probability computation with matter effects, but no ambiguities are taken into account. This latest point may be revisited in a future work using reference \cite{DONINI-2}. Concerning the background events, the $\nu_e/\bar{\nu}_e$ from the beam, the $\nu_\mu e^-$ elastic scattering process, the $\pi^o$ production as well as the $\mu/e$ misidentification are taken into account. The cross-sections from the NUANCE program are used \cite{NUANCE}. The systematics error on the total $\nu_e$ and $\bar{\nu}_e$ fluxes determination is a user parameter and we have used the $2\%$ value considered as a final goal, but also $5\%$ and $10\%$ \cite{MEZZETTONUFACT060}. The detector considered for definitiveness is similar to the UNO detector, \textit{i.e.} a $440$~kt fiducial water \v{C}erenkov detector \cite{UNO}. It is located at $L = 130$~km from CERN, in the foreseen new Fréjus laboratory \cite{mosca}. It is worth to mention that if one wants to evaluate the influence of $L$ on the sensitivity, it would mean a re-optimization of the horns for each $L$ envisaged (see section~\ref{sec:horn}).  
+%
+\begin{table}
+\centering
+\caption{\label{tab:param}Default parameters used to compute the sensitivity curves \cite{MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite{KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite{JJG}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			$\Delta m^2_{12} = 8.2 (0.5)\times 10^{-5}~\mathrm{eV}^2$ & $\sin^22\theta_{12} = 0.82 (9\%)$ \\
+			$\Delta m^2_{23} = 2.5 (0.1)\times 10^{-3}~\mathrm{eV}^2$ & $\sin^22\theta_{23} = 1.0 (1\%)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		  $L_T = 20$~m & $R_T = 1$~m \\ 
+		  $M=440$~kT   & $\epsilon_{syst}=2\%$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+\centre{2}{Horn/Reflector shapes to produce a $260$~MeV neutrino beam} \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The running time scenario has been fixed either by focusing positive particles during 5 years, either  by focusing positive particles during 1 (or 2) year(s) followed by focusing negative particles during 4 (or 8) years.
+%
+\section{Results}
+\label{sec:results}
+\subsection{The positive only focusing scenario}
+The $\theta_{13}$ and $\delta_{CP}$ sensitivities are computed with $\theta_{13} = 0^\circ$ and $\delta_{CP} = 0^\circ$ if not explicitly mentioned. It is worth to stress that the default parameters of table~\ref{tab:param} are used if not contrary mentioned, in particular, the decay tunnel geometry parameters ($L_T=20$~m and $R_T=1$~m), and the horn design to generate a $260$~MeV neutrino beam. 
+
+Table~\ref{tab:nbvsE} presents the number of signal and background events for a $5$ years positive focusing experiment, but with different beam energy settings. The significance parameter is defined in reference \cite{MEZZETTONUFACT060} as\footnote{Contrary to the definition of the significance of reference \cite{MEZZETTONUFACT060}, the systematical factor is applied to the total $\nu_e$ flux in agreement with the sensitivity contour computation.}:
+\begin{equation}
+\begin{aligned}
+\mathcal{S} &= \frac{N^{osc}_{\nu_e}}{\sqrt{ N^{tot}_{\nu_e} + \left(N^{tot}_{\nu_e}\times\epsilon_{syst}\right)^2}}\\
+\mathrm{with}\quad N^{tot}_{\nu_e} &= N^{osc}_{\nu_e} + N^{beam}_{\nu_e} + N^{oth. bkg}
+\label{eq:significance}
+\end{aligned}
+\end{equation}
+and $N^{osc}_{\nu_e}$ the number of $\nu_e$ events due to $\nu_\mu$ oscillations, $N^{beam}_{\nu_e}$ the number of background events coming from the $\nu_e+\bar{\nu}_e$ contamination of the beam, $N^{oth. bkg}$ the other kinds of background events and $\epsilon_{syst}$ the systematical factor.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbvsE}Number of events for 5 years positive focusing scenario with default parameters of table~\ref{tab:param}. Other backgrounds are $\pi^0$, $\nu_\mu$-elast., $\mu/e$-missId. The significance parameter is defined by equation~\ref{eq:significance}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		 & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			non oscillated $\nu_\mu$       & $36917$  & $60969$  & $73202$  & $78024$ & $76068$ \\ 
+			oscillated $\nu_e$             & $43$     & $60$     & $64$     & $61$    & $56$ \\
+			beam $\nu_e$                   & $165$    & $222$    & $242$    & $288$   & $299$ \\
+			other background               & $70$     & $105$    & $127$    & $148$   & $152$ \\
+			Significance                   & $1.88$   & $2.16$   & $2.17$   & $1.87$  & $1.69$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+The contours at $90\%$, $95\%$ and $99\%$~CL of the $\theta_{13}$ sensitivity are presented in the ($\sin^22\theta_{13}$, $\Delta m^2_{23}$) plane on figure~\ref{fig:sensi45} for $3.5$~GeV proton beam kinetic energy. 
+The comparison between the contours at $90\%$~CL with $2.2$~GeV, $3.5$~GeV, $4.5$~GeV and $8$~GeV beam energies is shown on figure~\ref{fig:compSensi}. One notices in this scenario a better perfomence reached with a $4.5$~GeV energy beam as a confirmation of significance parameter value. But, in fact there is not much visual difference between a sensitivity obtained with $3.5$~GeV and $4.5$~GeV, even if one should keep in mind that kaon production models are different at these two energies (see section~\ref{sec:kaon}). These two energy settings have been studied with different decay tunnel geometry and  results are reported on table~\ref{tab:thvsE_3545}. One notice that similar results can be reached with a $3.5$~GeV beam, compared to a $4.5$~GeV beam.
+
+Quantitative studies of the minimum $\sin^22\theta_{13}$ with respect to the kinetic beam energy $E_k(proton)$, and the decay length $L_T$, and the systematics $\epsilon_{syst}$ are presented in tables~\ref{tab:thvsE} and \ref{tab:thvseps}. One notices that for $\epsilon_{syst} = 5\%$ there is no difference between a $3.5$~GeV and a $4.5$~GeV beam.
+\begin{table}
+\centering
+\caption{\label{tab:thvsE}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		        & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV  \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$10$~m & $1.10$ & $0.92$ & $1.04$ & $1.07$ & $1.16$ \\
+			$20$~m & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$40$~m & $1.23$ & $1.00$ & $0.99$ & $1.08$ & $1.19$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table*}
+\centering
+\caption{\label{tab:thvsE_3545}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) at and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings in parenthesis are identical to those of table~\ref{tab:speciesfluxes}, except that the setting (7b) corresponds to the tunnel geometry of setting (7) but the horn geometry producing a $350$~MeV neutrino beam is used. We remind that the setting (2) is the default one, and the settings (7) and (7b) corresponds to $L_T = 40$~m and $R_T = 2$~m.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+setting & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (7b) & (8) & (9)\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$3.5$~GeV   & $0.92$ & $0.92$ & $0.83$ & $0.98$ & $1.00$ & $0.93$ & $0.91$ & $0.76$ & $1.05$ & $1.01$ \\
+$4.5$~GeV   & $1.04$ & $0.89$ & $0.82$ & $0.94$ & $0.99$ & $0.92$ & $0.87$ & $0.71$ & $1.03$ & $1.00$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensi35.eps}
+\caption{\label{fig:sensi45}Sensitivity contours obtained with a SPL energy of $3.5$~GeV and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m. (\full), (\dashed) and (\dotted) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compsensi.eps}
+\caption{\label{fig:compSensi}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+We have also considered the $3.5$~GeV and $4.5$~GeV beam energies with the tunnel geometry parameters $L_T=40$~m and $R_T=2$~m, and the horn design producing a $350$~MeV neutrino beam (see section~\ref{sec:horn}). In table~\ref{tab:thvsE_3545} are reported numerical values, and on figure~\ref{fig:comp5year} are shown the $90$\% CL sensitivity contours. With the $350$~MeV neutrino beam, one can expect a $16$\% improvment with respect to the $260$~MeV neutrino beam. One notices also that there is marginal gain to increase the beam energy from $3.5$~GeV to $4.5$~GeV, as already mentioned. 
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comp5year.eps}
+\caption{\label{fig:comp5year}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$~GeV or $4.5$~GeV, and either a $260$~MeV (default) neutrino beam or a $350$~MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$~m and $R_T = 2$~m. The (\chain) curve corresponds to a $350$~MeV/$4.5$~GeV (neutrino beam/SPL beam energy) setting; the (\dotted) curve corresponds to a $350$~MeV/$3.5$~GeV setting; the (\dashed) curve corresponds to a $260$~MeV/$4.5$~GeV setting and the (\full) curve corresponds to a  $260$~MeV/$3.5$~GeV setting.}
+\end{figure}
+%
+
+There are also variations on the minimum $\sin^22\theta_{13}$ value that may be reached in a $\nu_\mu \rightarrow \nu_e$ experiment which are due to the $\mathrm{sign}(\Delta m^2_{23})$ ambiguity and the $\delta_{CP}$ value. On table~\ref{tab:sign} are presented these kind of variations. Other ambiguities coming from the sign$(\tan(2\theta_{23}))$ ignorance also take place as studied in reference \cite{DONINI}. From figure~9 of this reference, we estimate a 30\% effect on $\sin^2(2\theta_{13})$ sensivity due to these ambiguities.
+%
+\subsection{Mixed positive/negative focusing scenario}
+%
+The combined $\sin^22\theta_{13}$ and $\delta_{CP}$ sensitivity for the 5 years positive focusing scenario and the default parameters of table~\ref{tab:param} is presented on figure~\ref{fig:compDeltaTheta}(a). The results obtained with a $3.5$~GeV and $4.5$~GeV SPL beam are similar and better than with the other energy settings. On figure~\ref{fig:sensiDeltaTheta}(a) the results obtained with a $260$~MeV neutrino beam and a $350$~MeV neutrino beam are presented with a $40$~m long, $2$~m radius decay tunnel. With the $350$~MeV neutrino beam, one can reached better sensitivity results in the range $|\delta_{CP}| < 120^o$, and comparatively the gain obtained when switching from a $3.5$~GeV proton beam to a $4.5$~GeV proton beam is marginal. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:thvseps}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon_{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			      & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$2\%$ & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$5\%$ & $1.48$ & $1.25$ & $1.25$ & $1.48$ & $1.64$ \\
+			$10\%$ & $2.40$ & $2.14$ & $2.21$ & $2.72$ & $3.09$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table}
+\centering
+\caption{\label{tab:sign}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$~GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta_{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			    & $-180^\circ$ & $-90^\circ$ & $0^\circ$ & $90^\circ$ & $180^\circ$\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$+$ & $1.40$ & $0.43$ & $1.16$ & $11.48$ & $1.40$\\
+			$-$ & $1.45$ & $11.75$& $1.11$ & $0.43$  & $1.45$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+To improve the $\delta_{CP}$-independent limit on $\sin^22\theta_{13}$, especially around $\delta_{CP}=90^\circ$, one may envisaged a combination of 2 years with positive focusing and 8 years negative focusing as in references \cite{DONINI,JJG,Mezzetto}. The comparison of the results obtained with different SPL beam energies on the combined sensitivity contours are presented in figure~\ref{fig:compDeltaTheta}(b). Quantitative results with this kind of mixed focusing scenario are reported table \ref{tab:thvsE_td}. One generally gets $10\%$ to $20\%$ better limit on $\sin^22\theta_{13}$ independently of $\delta_{CP}$ with a $3.5$~GeV kinetic energy beam compare to a $2.2$~GeV beam. Doubling the length and the radius of the decay tunnel allows to reach a $10\%$ better limit.
+
+On figure~\ref{fig:sensiDeltaTheta}(b) are presented the results considering the effects of a $350$~MeV neutrino beam obtained either with a $3.5$~GeV proton beam or a $4.5$~GeV proton beam compared to a $260$~MeV neutrino beam obtained with a $4.5$~GeV proton beam. The tunnel geometry parameters are $L_T=40$~m and $R_T=2$~m (other tunnel geometry have been studied but the results are worse and so are not reported). Except in the region $|\delta_{CP}|>150^o$, the results obtained with the $350$~MeV neutrino beam ($3.5$~GeV proton beam) are somewhat better, even if a $11\%$ improvement of the $\delta_{CP}$-independent $\sin^22\theta_{13}$ limit can be reached with the $260$~MeV neutrino beam obtained with the $3.5$~GeV proton beam.
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compDeltaTheta.eps}
+\caption{\label{fig:compDeltaTheta}90\% sensitivity contours obtained with SPL beam energy of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) at $90\%$ CL. Default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensiDeltaTheta.eps}
+\caption{\label{fig:sensiDeltaTheta}90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$~m and $R_T=2$~m and different SPL beam energies ($3.5$~GeV or $4.5$~GeV) and different horn designs ($260$~MeV or $350$~MeV neutrino beams): (\full) curve for a $350$~MeV/$4.5$~GeV setting, (\dotted) curve for a $350$~MeV/$3.5$~GeV setting, (\dashed) curve for a $260$~MeV/$3.5$~GeV setting. Other default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comparaisonFinale.eps}
+\caption{\label{fig:deltathetaFinal}90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite{CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite{Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite{MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite{KOBAYASHI}. The BNL contour has been obtained from reference \cite{BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu_e$ and $\bar{\nu}_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta$ beam was analysed like a reactor experiment with 1\% systematic error \cite{MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$~GeV beam and a decay tunnel of $40$~m length, and $2$~m radius.}
+\end{figure}
+%
+\section{Summary and outlook}
+A complete chain of simulation has been set up for the SPL-Fréjus project. The neutrino production has been extended to the kaon decay contribution, which is important to test SPL energy scenario above $2.2$~GeV.
+
+The beam line optimization has been performed using the sensitivity to $\sin^22\theta_{13}$ and $\delta_{CP}$. The shape of the focusing system has been updated to obtain a neutrino beam energy around $260$~MeV or $350$~MeV.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:thvsE_td}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta_{CP}$ case, and for different decay tunnel length ($L_T$) and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 2 years of positive focusing plus 8 years of negative focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings are identical to those of table~\ref{tab:speciesfluxes}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+setting & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (7b) & (8) & (9)\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$2.2$~GeV &        & $2.52$ &        &        & $2.58$ &        & $2.30$ &        &         &       \\
+$3.5$~GeV & $2.34$ & $2.22$ & $2.10$ & $2.13$ & $2.09$ & $2.08$ & $2.02$ & $2.28$ &  $2.16$ & $2.09$\\
+$4.5$~GeV & $2.91$ & $2.60$ & $2.43$ & $2.48$ & $2.52$ & $2.39$ & $2.34$ & $2.55$ &  $2.53$ & $2.47$\\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+
+In a positive only focusing scenario, the best limit on $\sin^22\theta_{13}$ is $0.82\times10^{-3}$
+ ($90\%$ CL, $\delta_{CP}=0$), with a $4.5$~GeV beam energy and a $20$~m long, $1.5$~m radius decay tunnel. However, the $3.5$~GeV beam may also obtain rather similar limit with $0.83\times10^{-3}$ ($90\%$ CL) with the same tunnel parameters. The $\delta_{CP}$ independant $\sin^22\theta_{13}$ sensitivity is limited to $\approx 10^{-2}$ due to the $\delta_{CP} \approx 90^o$ region.
+ 
+In a mixed focusing scenario, the best limit on $\sin^22\theta_{13}$ independent of $\delta_{CP}$ is $2.02\times10^{-3}$ ($90\%$ CL) obtained with a $3.5$~GeV beam energy and a $40$~m long, $2$~m radius decay tunnel.
+
+The comparison of the optimization presented in this paper with the results obtained by other projects is displayed on figure \ref{fig:deltathetaFinal}. It is presented the 5 years positive focusing scenario, and two versions of a mixed scenario using positive and negative focusing: one scenario duration is 5 years in total and the other one is 10 years running in total and has been used in the previous section. It shows the complementarity of the SPL-Fr\'ejus project with the beta beam-Fr\'ejus project. Especially when considering the sensitivity to $\sin^22\theta_{13}$ for $\delta_{CP}<0$. 
+
+The authors think that the present study may be extended in many respects. The beam line simulation part may be performed with a single simulator as FLUKA (or GEANT4 \cite{GEANT4} for comparison). Other targets may be envisaged (tantalum, carbon) as well as other detector types as a Large Liquid Argon detector \cite{BIGICARUS}. The baseline length may also be revisited as well as the off axis option. The sensitivity analysis may be deeper investigated using the complete set of possible ambiguities as in reference \cite{DONINI}, and the $\theta_{13}$ or $\delta_{CP}$ measurement accuracy with new beam energy scenario may be investigated too.     
+%
+\begin{acknowledgement}
+The authors would like to thank M.~Mezzetto to have expressed his interest since the early stage of this work and to have provided us with his sensitivity computation program. Also the authors thank S.~Gilardoni for fruitful discussions.
+\end{acknowledgement}
+%
+\appendix
+\setcounter{section}{0}
+\section{Decay probability computations}
+\label{sec:decayprobcomp}
+This appendix contains the probability formulas and the algorithms used in the flux computation (see section~\ref{sec:algo}).
+
+\subsection{Pion neutrino probability computation}
+\label{sec:Ppi}
+Pions decay only as $\pi^+\rightarrow \mu^+ + \nu_\mu$ or $\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$ and the neutrinos are emitted isotropically in the pion rest frame, with an energy of about $30$~MeV given by the 2-body decay kinematics. Applying a Lorentz boost knowing the pion momentum and direction, it is possible to compute the probability to reach the detector for the neutrinos. Only neutrino parallel to the beam axis are supposed to pass through the detector fiducial area, and therefore, the neutrino must be emitted by the pion with an angle opposite to the angle between the pion and the beam axis (see figure~\ref{fig:pionDecay}). This gives:
+\begin{equation}
+\mathcal{P}_\pi = \frac{1}{4\pi}\frac{A}{L^2}\frac{1-\beta^2}{(\beta\cos\alpha-1)^2}
+\label{probaPi}
+\end{equation}
+where $\beta$ is the velocity of the pion in the tunnel frame, $A$ is the fiducial detector surface, $L$ the distance between the neutrino source and the detector, and $\alpha$ the angle between the pion direction and the beam axis in the laboratory frame.
+
+\begin{figure}
+\centering
+\includegraphics{../picts/pionDecay.eps}
+\caption{\label{fig:pionDecay}Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha$ is needed.}
+\end{figure}
+
+\subsection{Muon neutrino probability computation}
+\label{sec:Pmu}
+Muons decay only as $\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_\mu$ or $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$, and will produce background events. The mean decay length of the muons is $2$~km, therefore, most of them do not decay in the tunnel. This induces a lack of statistics to estimate the corresponding level of background. This problem has been solved using each muon appearing in the simulation in the following steps:
+\begin{enumerate}
+	\item the probability for the muon to decay into the tunnel has been computed using a straight line propagation;
+	\item the available energy for the neutrino in the tunnel frame has been divided in $20$~MeV energy bins; 
+	% (the number of bin depending of the muon energy).
+	\item one $\nu_e$ and one $\nu_\mu$ have been simulated in each of the energy bins (step 2). Then, the probability to reach the detector has been computed, and multiplied by the probability computed at step (1).%the neutrino energy is stored in an histogram, weighted with this probability and 
+\end{enumerate}
+After the probability computation, the non useful muon is discarded by GEANT to gain in CPU time. 
+
+The probability for the muon neutrino and the electron neutrino to be emitted parallel to the beam axis is \cite{donega}:
+\begin{multline}
+\frac{d\mathcal{P}_\mu}{dE_\nu} = \frac{1}{4\pi}\frac{A}{L^2}\frac{2}{m_\mu}\frac{1}{\gamma_\mu(1+\beta_\mu\cos\theta^*)}\\ \times \frac{1-\beta_\mu^2}{(\beta_\mu\cos\rho-1)^2}\left[f_0(x)\mp \Pi_\mu^L f_1(x)\cos\theta^*\right]
+\label{probaMu}
+\end{multline}
+where $\beta_\mu$ and $\gamma_\mu$ are the velocity and the Lorentz boost of the muon in the tunnel frame, $\theta^*$ is the angle with respect to the beam axis of the muon in the muon rest frame, $\rho$ is the corresponding angle in the tunnel frame. Like in the pion case, this angle appears because the neutrino must be parallel to the beam axis. $\Pi_\mu^L$ is the muon longitudinal polarization, the parameter $x$ is defined as $x=2E_\nu^*/m_\mu$ where $E_\nu^*$ is the neutrino energy in the muon rest frame, and the function $f_0(x)$ and $f_1(x)$ coming from the matrix element of the muon decay are given in table~\ref{tab:Function}. The sign in front of $\Pi_\mu^L$ in equation~\ref{probaMu} is $(-)$ for the $\mu^+$ decays and $(+)$ for the $\mu^-$ decays, respectively.
+
+%\Table{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%\br
+%		      &  $f_0(x)$ & $f_1(x)$ \\
+%\mr
+%		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+%		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		      &  $f_0(x)$ & $f_1(x)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+Muon polarization is computed using the conservation of the transverse component of the velocity four-vector $\gamma(1,\beta)$ between the muon rest frame (where the polarization is computed) and the pion rest frame, where the muon helicity is $-1$, due to the parity non conservation. It yields \cite{picasso}:
+\begin{equation}
+\Pi_\mu^T = \frac{\gamma_\pi\beta_\pi}{\gamma_\mu\beta_\mu}\sin\theta^*
+\mbox{ and }\Pi_\mu^L = \sqrt{1-\Pi_\mu^{T2}}
+\label{pola}
+\end{equation}
+where $\gamma_\pi$, $\beta_\pi$, $\gamma_\mu$, and $\beta_\mu$ are the Lorentz boost and velocity of the pion and of the muon in the tunnel frame, and $\theta^*$ the angle with respect to the beam axis of the muon in the pion rest frame.
+
+\subsection{The treatment of the kaons}
+\label{sec:kaons}
+Contrary to pions and muons, kaons have many decay channels. They are summarized in table~\ref{tab:BRKP0SL}.
+
+%\Table{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%\br
+%\centre{2}{$K^\pm$}                                               & \centre{2}{$K^0_L$}     &          \centre{2}{$K^0_S$}\\
+%\mr
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu$   & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+%$\pi^\pm\pi^0$ & $21.17\%$                                        & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+%$\pi^\pm\pi^+\pi^-$ & $5.59\%$                                    & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+%$e^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+%$\pi^\pm\pi^0\pi^0$ & $1.73\%$                                    & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+\centre{2}{$K^\pm$}         & \centre{2}{$K^0_L$}     & \centre{2}{$K^0_S$}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$\mu^\pm\nu_\mu$ & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+$\pi^\pm\pi^0$ & $21.17\%$   & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+$\pi^\pm\pi^+\pi^-$ & $5.59\%$ & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+$e^\pm\nu_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+$\mu^\pm\nu_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+$\pi^\pm\pi^0\pi^0$ & $1.73\%$ & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+There is a very small amount of kaons produced (section~\ref{sec:kaon}), and this number has been artificially increased in order to obtain statistically significant results.  The multiplicity of decay channels makes impossible the method used for the muon case (\ref{sec:Pmu}). The method chosen for the good compromise between the gain in CPU and the statistical uncertainty of the results, is to duplicate many times each kaon exiting the target. The number of duplication varies between 10 and 300. It depends on the initial kaon rate and therefore on the beam energy.
+
+All the kaons daughter particles are tracked by GEANT until they decay. Three different types of daughter particles are identified in the kaon decays. The first type corresponds to primary neutrinos, the second type concerns charged pions and muons, and the neutral pions are left for the last type.
+
+In the $K^\pm\rightarrow\mu^\pm \nu_\mu(\bar{\nu}_\mu)$ decay modes, the computation of the probability for a neutrino to reach the detector is the same than the 2-body decay formula used to in the pion decay (equation~\ref{probaPi}), where $\beta$ is now the kaon velocity, and $\alpha$ the angle of the kaon with respect to the beam axis. 
+
+When a neutrino is produced by a kaon 3-body decay, the probability to reach the detector is computed using a pure phase space formula. It yields:
+\begin{multline}
+\mathcal{P}_K = \frac{1}{4\pi}\frac{A}{L^2}\frac{1}{m_K-m_\pi-m_l} \\ \times \frac{1}{\gamma_K(1+\beta_K\cos\theta^*)}
+\frac{1-\beta_K^2}{(\beta_K\cos\delta-1)^2}
+\label{probaL}
+\end{multline}
+where $m_K$ is the kaon mass (charged or neutral), $m_\pi$ is the pion mass ($\pi^0$ mass in $K^\pm$ decays and $\pi^\pm$ mass in $K_L^0$ decays), and $m_l$ is the mass of the lepton associated with the neutrino. The $\beta_K$ and $\gamma_K$ are the velocity and the Lorentz boost of the kaon, $\theta^*$ is the angle between the neutrino direction and the kaon direction, in the kaon rest frame. Finally, $\delta$ is the angle between the kaon direction and the beam axis in the tunnel frame.
+
+When a $\pi^\pm$ is produced in the kaon decay chain, it is tracked by GEANT until it decays, and the probability of equation~\ref{probaPi} is applied to the produced neutrino. In case of a muon, it is treated as explained in \ref{sec:Pmu}. The muon polarization is computed this time using the kaon decay informations. Finally, when a $\pi^0$ is produced, as it cannot create neutrinos, it is simply discarded.
+
+%
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+%Agostinelli A \etal [GEANT4 Collaboration] 2003 \NIM A \textbf{506} 250-503
+%
+%\bibitem{Gaisser}
+%Gaisser T K 1990 \textit{Cosmic Rays and Particle Physics} Cambridge University Press 
+%
+%\bibitem{picasso}
+%Combley F and Picasso E 1974 \textit{Phys. Rept.} {\bf 14} 1
+%
+%\bibitem{pdg}
+%Hagiwara K \etal 2002 \PR D {\bf 66}  010001
+%
+\bibitem{SKNU04}
+E. Kearns [SuperKamiokande Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{K2KNU04}
+T. Nakaya [K2K Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{MINOS}
+T. Thomson [MINOS Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement);
+P. Adamson \etal, NuMi-L-337 (unpublished)
+
+\bibitem{OPERA}
+D. Autiero [OPERA Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement);
+M. Guler  \etal, \textsl{Experiment proposal} CERN/SPSC 2000-028 SPSC/P318 LNGS P25/2000 (unpublished) 
+
+\bibitem{ICARUS}
+M. Guler  [ICARUS Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement);
+P. Aprili \etal, CERN-SPSC-2002-027 (unpublished)
+
+\bibitem{CNGS}
+G. Acquistapace  \etal, CERN-98-02 (unpublished)
+
+\bibitem{LSND}
+A. Athanassopoulos \etal, \PRL {\bf 81}, 1774  (1998);
+A. Aguilar \etal, \PR D {\bf 64}, 112007 (2001) 
+
+\bibitem{MINIBOONE}
+I. Stancu \etal, FERMILAB-TM-2207 (unpublished)
+
+\bibitem{PMNS}
+B. Pontecorvo \textsl{Sov. Phys.--JETP} {\bf 6}, 429 (1957) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{33}, 549 (1957)];
+Z. Maki, M. Nakagawa and S. Sakata \textsl{Prog. Theor. Phys.} \textbf{28}, 870 (1962);
+Pontecorvo B \textsl{Sov. Phys.--JETP} \textbf{26},  984 (1968) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{53}, 1717 (1967)];
+V. N. Gribov and B. Pontecorvo \PL B \textbf{28}, 493 (1969) 
+
+\bibitem{CHOOZ}
+M. Apollonio \etal, \PL B {\bf 466}, 415 (1999);
+M. Apollonio \etal, \EJP C {\bf 27},  331 (2003)
+
+\bibitem{Wpaper}
+K. Anderson \etal, \textsl{White paper report on using nuclear reactors to search for a value of $\theta_{13}$} (2004), http://www.hep.anl.gov/minos/reactor13/reactor13.pdf (unpublished); 
+F.~Arbelier \etal, \textsl{Letter of Intend for Double-CHOOZ}, arXiv:hep-ex/0405032 (unpublished)
+
+\bibitem{BETABEAM}
+P. Zucchelli, \PL B \textbf{532}, 166 (2002) 
+
+\bibitem{NOVA}
+I. Ambats \etal,  NO$\nu$A proposal FNAL P929, 2004 (unpublished)
+
+\bibitem{T2K}
+Y. Itow, KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05 (unpublished),
+see also arXiv:hep-ex/0106019
+
+\bibitem{BNLHS}
+M. V. Diwan, \PR D {\bf 68}, 012002 (2003)
+
+\bibitem{CERN}
+A. Blondel \etal, CERN-2004-002 (unpublished)
+
+\bibitem{DONINI}
+A. Donini \etal, IFT-UAM/CSIC-04-30, 2004 (unpublished);
+see also arXiv:hep-ph/0406132
+
+\bibitem{DOUBLE-CHOOZ}
+F. Dalnoki-Veress, the Double-CHOOZ project arXiv:hep-ex/0406070 (unpublished)
+
+\bibitem{SPL}
+B. Autin \etal, CERN-2000-12 (unpublished)
+
+\bibitem{UNO} 
+The UNO whitepaper, \textsl{Physics Potential and Feasibility of UNO}, SBHEP01-3 (unpublished), see also http://ale.physics.sunysb.edu/uno/
+
+\bibitem{mosca}
+L. Mosca, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Meer}
+S. van der Meer, CERN-Report No 61-7, 1961 (unpublished)
+
+\bibitem{nuFact134} 
+J.E. Campagne and A. Cazes, CERN-NUFACT-Note-134, 2003 (unpublished), see http://slac.web.cern.ch/slap/NuFact/NuFact/\\
+NFNotes.html
+
+\bibitem{MMWPSCazes} 
+J.E. Campagne and A. Cazes, Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004,
+see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{JJG}
+J.J. G\'omez Gadenas \etal,  IFIC/01-31, 2001 (unpublished),
+see also arXiv:hep-ph/0105297
+
+\bibitem{Mezzetto}
+M. Mezzetto,  \jpg {\bf 29}, 1781-1784 (2003),
+see also arXiv:hep-ex/0302005
+
+
+\bibitem{nuFact138} 
+J.E. Campagne, CERN-NUFACT-Note-138, 2004 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{fluka}
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p159-164 (2001);
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+
+\bibitem{MMWPSGaroby} 
+R. Garoby, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{harp}
+C. Catanesi \etal, CERN-SPSC 2002/019 (unpublished)
+
+\bibitem{minerva} 
+D. Drakoulakos \etal, Fermilab P-938 (unpublished),
+see also arXiv:hep-ex/405002
+
+\bibitem{MARS}
+N.V. Mokhov \etal, The MARS Code System User Guide, Version 13(95), Fermilab-FN-628 (1995);
+N.V. Mokhov  \etal, MARS oed Develepments, LANL Report LA-UR-98-5716 (1998), nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+
+\bibitem{FLUKAprivate}
+G. Battistoni and A. Ferrari, \textsl{private communication}
+
+\bibitem{geant}
+Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+
+\bibitem{SIMONE1}
+S. Gilardoni, Talk at NuFact03 (2003), see http://www.cap.bnl.gov/nufact03/
+
+\bibitem{donega}
+A. Blondel \etal, CERN-NUFACT-Note-78, 2001 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{MEZZETTONUFACT060}
+M. Mezzetto, CERN-NUFACT-Note-60, 2000 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+
+\bibitem{DONINI-2}
+A. Donini, D. Meloni and S. Rigolin, J. High Energy Phys. \textbf{0406}, 011 (2004),
+see also arXiv:hep-ph/0312072
+
+\bibitem{NUANCE}
+D. Casper, \textsl{ Nucl. Phys. Proc. Suppl.} \textbf{112}, 161-170 (2002),
+see also arXiv:hep-ph/0208030
+
+
+\bibitem{KAMLAND}
+G. Gratta, in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{MIGLIOZZITERANOVA}
+M. Komatsu, P Migliozzi and F. Terranova,  \jpg {\bf 29}, 443 (2003); see also arXiv:hep-ph/0210043
+
+\bibitem{KOBAYASHI}
+T. Kobayashi, in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{BNL}
+ M.V. Diwan \etal, \PR D \textbf{68}, 012002 (2003); see also figure~8 of 
+arXiv:hep-ph/0303081
+
+\bibitem{MAOROPRIVATE}
+M. Mezzetto, \textsl{private communication}: the corresponding $\theta_{13}$ limit is $3.4^o$.
+
+\bibitem{GEANT4}
+A. Agostinelli \etal, \NIM A \textbf{506}, 250-503 (2003) 
+
+\bibitem{BIGICARUS}
+A. Ereditato and A. Rubia, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Gaisser}
+T.K. Gaisser, \textsl{Cosmic Rays and Particle Physics} (Cambridge University Press, 1990)  
+
+\bibitem{picasso}
+F. Combley and E. Picasso, \textsl{Phys. Rept.} {\bf 14}, 1 (1974) 
+
+\bibitem{pdg}
+K. Hagiwara \etal,  \PR D {\bf 66},  010001 (2002)
+
+
+%
+\end{thebibliography}
+%
+\end{document}
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus.tps
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus.tps	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejus.tps	(revision 392)
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv2.aux
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv2.aux	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv2.aux	(revision 392)
@@ -0,0 +1,224 @@
+\relax 
+\citation{SKNU04,K2KNU04}
+\citation{K2KNU04}
+\citation{MINOS}
+\citation{OPERA,ICARUS}
+\citation{CNGS}
+\citation{LSND}
+\citation{MINIBOONE}
+\citation{PMNS}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{BETABEAM}
+\citation{NOVA,T2K}
+\citation{T2K,BNLHS,CERN}
+\citation{CERN}
+\citation{DONINI}
+\citation{DONINI,DOUBLE-CHOOZ}
+\citation{SPL}
+\citation{UNO}
+\citation{mosca}
+\citation{CERN}
+\citation{Meer}
+\citation{nuFact134,MMWPSCazes}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
+\citation{DONINI,JJG,Mezzetto}
+\citation{nuFact138}
+\citation{fluka}
+\citation{CERN}
+\citation{JJG}
+\citation{CERN}
+\citation{SPL}
+\citation{MMWPSGaroby}
+\citation{nuFact134}
+\citation{harp}
+\citation{MARS}
+\citation{nuFact134}
+\citation{MMWPSGaroby}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Sketch of the SPL neutrino Superbeam from CERN to the Fr\'ejus tunnel.}}{2}}
+\newlabel{fig:Sbeam}{{1}{2}}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Liquid mercury jet parameters.}}{2}}
+\newlabel{tab:targ}{{1}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Target simulation}{2}}
+\newlabel{sec:target}{{2}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Kaon production}{2}}
+\newlabel{sec:kaon}{{3}{2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  (a) $\pi ^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi ^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$\nobreakspace  {}GeV/c and $0.7$\nobreakspace  {}GeV/c. The different SPL beam kinetic energies presented are (\mbox {------}) $2.2$\nobreakspace  {}GeV, (\mbox {- - - -}) $3.5$\nobreakspace  {}GeV, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) $4.5$\nobreakspace  {}GeV and (\mbox {--- $\cdot $ ---}) $6.5$\nobreakspace  {}GeV.}}{3}}
+\newlabel{fig:compEner2}{{2}{3}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces $\pi ^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\mbox {- - - -}) and by MARS (\mbox {------}).}}{3}}
+\newlabel{fig:compFlukaMars}{{3}{3}}
+\citation{FLUKAprivate}
+\citation{geant}
+\citation{SIMONE1}
+\citation{nuFact138}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Average numbers of the most relevant secondary particles exiting the $30$\nobreakspace  {}cm long, $1.5$\nobreakspace  {}cm diameter mercury target per incident proton (FLUKA). The $\mu ^+/\mu ^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}}{4}}
+\newlabel{tab:nbPart}{{2}{4}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Horns simulation}{4}}
+\newlabel{sec:horn}{{4}{4}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350\nobreakspace  {}MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}}{4}}
+\newlabel{fig:plan}{{5}{4}}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Relevant parameters of the horns in case of the generation of a $260$\nobreakspace  {}MeV neutrino beam (or $350$\nobreakspace  {}MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$\nobreakspace  {}MeV/c (or $800$\nobreakspace  {}MeV/c) pion momentum.}}{4}}
+\newlabel{tab:specif}{{3}{4}}
+\citation{donega}
+\citation{donega}
+\citation{donega}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).}}{5}}
+\newlabel{fig:KaonsPions}{{4}{5}}
+\@writefile{toc}{\contentsline {section}{\numberline {5}Particle decay treatment and flux calculation}{5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Algorithm description}{5}}
+\newlabel{sec:algo}{{5.1}{5}}
+\citation{donega}
+\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Number of protons on target for different beam energy at 4\nobreakspace  {}MW constant power. One year is defined as $10^7$\nobreakspace  {}s.}}{6}}
+\newlabel{tab:proton}{{4}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Validation of the algorithm}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Simulated fluxes}{6}}
+\citation{UNO}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{Mezzetto}
+\citation{DONINI-2}
+\citation{NUANCE}
+\citation{MEZZETTONUFACT060}
+\citation{mosca}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Integral of the total flux of the different species with different settings. The $\nu _\mu $ and $\mathaccentV {bar}016{\nu }_\mu $ fluxes are expressed in $10^{13}/100\@mathrm {m}^2/y$ unit while the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes are expressed in $10^{11}/100\@mathrm {m}^2/y$ unit. The positive focusing and negative focusing are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. }}{7}}
+\newlabel{tab:speciesfluxes}{{5}{7}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Sensitivity computation ingredients}{7}}
+\@writefile{toc}{\contentsline {section}{\numberline {7}Results}{7}}
+\newlabel{sec:results}{{7}{7}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}The positive only focusing scenario}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Comparison between the probability method, (\mbox {------}) curve, and the full GEANT simulation method, (\mbox {- - - -}) curve, for the $\nu _\mu $ from $\pi ^+$ flux (a) and the $\mathaccentV {bar}016{\nu }_\mu $ from $\pi ^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes contrary to the former simulation.}}{8}}
+\newlabel{fig:compGeantDonega}{{6}{8}}
+\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Default parameters used to compute the sensitivity curves \cite  {MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite  {KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite  {JJG}.}}{8}}
+\newlabel{tab:param}{{6}{8}}
+\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{8}}
+\newlabel{tab:thvsE}{{8}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces  Neutrino fluxes, $100$\nobreakspace  {}km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$\nobreakspace  {}GeV (4\nobreakspace  {}MW), a decay tunnel with a length of $20$\nobreakspace  {}m and a radius of $1$\nobreakspace  {}m. The top left panel contains the $\nu _\mu $ fluxes, and the top right panel shows the $\mathaccentV {bar}016{\nu }_\mu $ fluxes. The bottom left panel presents the $\nu _e$ fluxes while the bottom right panel displays the $\mathaccentV {bar}016{\nu }_e$ fluxes. The (\mbox {------}) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\mbox {- - - -}) curve is the contribution from the charged kaon decay chain, and the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}}{9}}
+\newlabel{fig:flux22p}{{7}{9}}
+\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but the horns are focusing negative particles.}}{9}}
+\newlabel{fig:flux22m}{{8}{9}}
+\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{10}}
+\newlabel{fig:flux45p}{{9}{10}}
+\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Same legend as for figure\nobreakspace  {}8\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{10}}
+\newlabel{fig:flux45m}{{10}{10}}
+\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{11}}
+\newlabel{fig:flux8p}{{11}{11}}
+\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Same legend as for figure\nobreakspace  {}8\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{11}}
+\newlabel{fig:flux8m}{{12}{11}}
+\citation{DONINI}
+\citation{DONINI,JJG,Mezzetto}
+\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Number of events for 5 years positive focusing scenario with default parameters of table\nobreakspace  {}6\hbox {}. Other backgrounds are $\pi ^0$, $\nu _\mu $-elast., $\mu /e$-missId. }}{12}}
+\newlabel{tab:nbvsE}{{7}{12}}
+\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) at and radius ($R_T$) for the $3.5$\nobreakspace  {}GeV and $4.5$\nobreakspace  {}GeV scenarios and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}). Settings in parenthesis are identical to those of table\nobreakspace  {}5\hbox {}, except that the setting (7b) corresponds to the tunnel geometry of setting (7) but the horn geometry producing a $350$\nobreakspace  {}MeV neutrino beam is used. We remind that the setting (2) is the default one, and the settings (7) and (7b) corresponds to $L_T = 40$\nobreakspace  {}m and $R_T = 2$\nobreakspace  {}m.}}{12}}
+\newlabel{tab:thvsE_3545}{{9}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Sensitivity contours obtained with a SPL energy of $3.5$\nobreakspace  {}GeV and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m. (\mbox {------}), (\mbox {- - - -}) and (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}}{12}}
+\newlabel{fig:sensi45}{{13}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{12}}
+\newlabel{fig:compSensi}{{14}{12}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Mixed positive/negative focusing scenario}{12}}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV, and either a $260$\nobreakspace  {}MeV (default) neutrino beam or a $350$\nobreakspace  {}MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$\nobreakspace  {}m and $R_T = 2$\nobreakspace  {}m. The (\mbox {--- $\cdot $ ---}) curve corresponds to a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV (neutrino beam/SPL beam energy) setting; the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve corresponds to a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting; the (\mbox {- - - -}) curve corresponds to a $260$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting and the (\mbox {------}) curve corresponds to a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting.}}{13}}
+\newlabel{fig:comp5year}{{15}{13}}
+\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon _{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:thvseps}{{10}{13}}
+\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$\nobreakspace  {}GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta _{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:sign}{{11}{13}}
+\@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{13}}
+\citation{GEANT4}
+\citation{BIGICARUS}
+\citation{DONINI}
+\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta _{CP}$ case, and for different decay tunnel length ($L_T$) and radius ($R_T$) for the $3.5$\nobreakspace  {}GeV and $4.5$\nobreakspace  {}GeV scenarios and 2 years of positive focusing plus 8 years of negative focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}). Settings are identical to those of table\nobreakspace  {}5\hbox {}.}}{14}}
+\newlabel{tab:thvsE_td}{{12}{14}}
+\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces 90\% sensitivity contours obtained with SPL beam energy of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) at $90\%$ CL. Default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{14}}
+\newlabel{fig:compDeltaTheta}{{16}{14}}
+\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces 90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$\nobreakspace  {}m and $R_T=2$\nobreakspace  {}m and different SPL beam energies ($3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV) and different horn designs ($260$\nobreakspace  {}MeV or $350$\nobreakspace  {}MeV neutrino beams): (\mbox {------}) curve for a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve for a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting, (\mbox {- - - -}) curve for a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting. Other default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}}{14}}
+\newlabel{fig:sensiDeltaTheta}{{17}{14}}
+\@writefile{toc}{\contentsline {section}{\numberline {A}Decay probability computations}{14}}
+\newlabel{sec:decayprobcomp}{{A}{14}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}Pion neutrino probability computation}{14}}
+\newlabel{sec:Ppi}{{A.1}{14}}
+\citation{donega}
+\citation{Gaisser}
+\citation{picasso}
+\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces 90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite  {CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite  {Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite  {MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite  {KOBAYASHI}. The BNL contour has been obtained from reference \cite  {BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta $ beam was analysed like a reactor experiment with 1\% systematic error \cite  {MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$\nobreakspace  {}GeV beam and a decay tunnel of $40$\nobreakspace  {}m length, and $2$\nobreakspace  {}m radius.}}{15}}
+\newlabel{fig:deltathetaFinal}{{18}{15}}
+\newlabel{probaPi}{{1}{15}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Muon neutrino probability computation}{15}}
+\newlabel{sec:Pmu}{{A.2}{15}}
+\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha $ is needed.}}{15}}
+\newlabel{fig:pionDecay}{{19}{15}}
+\@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces Flux function in the muon rest frame \cite  {Gaisser}.}}{15}}
+\newlabel{tab:Function}{{13}{15}}
+\newlabel{probaMu}{{2}{15}}
+\citation{pdg}
+\bibcite{SKNU04}{1}
+\bibcite{K2KNU04}{2}
+\bibcite{MINOS}{3}
+\bibcite{OPERA}{4}
+\bibcite{ICARUS}{5}
+\bibcite{CNGS}{6}
+\bibcite{LSND}{7}
+\bibcite{MINIBOONE}{8}
+\bibcite{PMNS}{9}
+\bibcite{CHOOZ}{10}
+\bibcite{Wpaper}{11}
+\bibcite{BETABEAM}{12}
+\bibcite{NOVA}{13}
+\bibcite{T2K}{14}
+\bibcite{BNLHS}{15}
+\bibcite{CERN}{16}
+\bibcite{DONINI}{17}
+\bibcite{DOUBLE-CHOOZ}{18}
+\@writefile{lot}{\contentsline {table}{\numberline {14}{\ignorespaces Charged and neutral kaon decay channels \cite  {pdg}.}}{16}}
+\newlabel{tab:BRKP0SL}{{14}{16}}
+\newlabel{pola}{{3}{16}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.3}The treatment of the kaons}{16}}
+\newlabel{sec:kaons}{{A.3}{16}}
+\newlabel{probaL}{{4}{16}}
+\bibcite{SPL}{19}
+\bibcite{UNO}{20}
+\bibcite{mosca}{21}
+\bibcite{Meer}{22}
+\bibcite{nuFact134}{23}
+\bibcite{MMWPSCazes}{24}
+\bibcite{JJG}{25}
+\bibcite{Mezzetto}{26}
+\bibcite{nuFact138}{27}
+\bibcite{fluka}{28}
+\bibcite{MMWPSGaroby}{29}
+\bibcite{harp}{30}
+\bibcite{minerva}{31}
+\bibcite{MARS}{32}
+\bibcite{FLUKAprivate}{33}
+\bibcite{geant}{34}
+\bibcite{SIMONE1}{35}
+\bibcite{donega}{36}
+\bibcite{MEZZETTONUFACT060}{37}
+\bibcite{DONINI-2}{38}
+\bibcite{NUANCE}{39}
+\bibcite{KAMLAND}{40}
+\bibcite{MIGLIOZZITERANOVA}{41}
+\bibcite{KOBAYASHI}{42}
+\bibcite{BNL}{43}
+\bibcite{MAOROPRIVATE}{44}
+\bibcite{GEANT4}{45}
+\bibcite{BIGICARUS}{46}
+\bibcite{Gaisser}{47}
+\bibcite{picasso}{48}
+\bibcite{pdg}{49}
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv2.blg
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv2.blg	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv2.blg	(revision 392)
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv2.log
===================================================================
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+\T1/cmr/m/sl/9 bil-ity of UNO\T1/cmr/m/n/9 , SBHEP01-3 (un-pub-lished), see als
+o
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1103--1105
+[][]\T1/cmr/m/n/9 J.E. Cam-pagne and A. Cazes, CERN-
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1103--1105
+\T1/cmr/m/n/9 NUFACT-Note-134, 2003 (un-pub-lished), see
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1107--1109
+[][]\T1/cmr/m/n/9 J.E. Cam-pagne and A. Cazes, Poster ses-sion
+ []
+
+
+Underfull \hbox (badness 7522) in paragraph at lines 1107--1109
+\T1/cmr/m/n/9 at the Physics with a Multi MegaWatt Pro-ton
+ []
+
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+Underfull \hbox (badness 4229) in paragraph at lines 1107--1109
+\T1/cmr/m/n/9 Source Work-shop at CERN 25-27 May 2004, see
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1149--1150
+[][]\T1/cmr/m/n/9 S. Gi-lar-doni, Talk at Nu-Fact03 (2003), see
+ []
+
+
+Underfull \hbox (badness 1163) in paragraph at lines 1156--1158
+[][]\T1/cmr/m/n/9 M. Mezzetto, CERN-NUFACT-Note-60, 2000 (un-pub-
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1189--1190
+[][]\T1/cmr/m/n/9 A. Ered-i-tato and A. Ru-bia, Talk at the
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1189--1190
+\T1/cmr/m/n/9 Physics with a Multi MegaWatt Pro-ton Source
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1189--1190
+\T1/cmr/m/n/9 Work-shop at CERN 25-27 May 2004, see
+ []
+
+[17] (SPLFrejusv2.aux) ) 
+Here is how much of TeX's memory you used:
+ 2436 strings out of 95897
+ 24827 string characters out of 1194805
+ 97695 words of memory out of 1079968
+ 5252 multiletter control sequences out of 35000
+ 25217 words of font info for 70 fonts, out of 500000 for 1000
+ 14 hyphenation exceptions out of 607
+ 27i,11n,28p,2088b,293s stack positions out of 1500i,500n,5000p,200000b,32768s
+
+Output written on SPLFrejusv2.dvi (17 pages, 98576 bytes).
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+%\documentclass[epj,nopacs,referee]{svjour}
+%remove referee for final version
+\documentclass[epj,nopacs]{svjour}
+%----------------------------------------------------------------------------
+%
+\usepackage[T1]{fontenc}
+\usepackage[latin1]{inputenc}
+\usepackage{graphicx}
+\usepackage{epsfig}
+\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage{latexsym}
+%
+\newcommand{\centre}[2]{\multispan{#1}{\hfill #2\hfill}}
+\newcommand{\dotted}{\protect\mbox{${\mathinner{\cdotp\cdotp\cdotp\cdotp\cdotp\cdotp}}$}}
+\newcommand{\dashed}{\protect\mbox{- - - -}}
+\newcommand{\broken}{\protect\mbox{-- -- --}}
+\newcommand{\longbroken}{\protect\mbox{--- --- ---}}
+\newcommand{\chain}{\protect\mbox{--- $\cdot$ ---}}
+\newcommand{\dashddot}{\protect\mbox{--- $\cdot$ $\cdot$ ---}}
+\newcommand{\full}{\protect\mbox{------}}
+%
+% abbreviations for IOPP journals
+%
+\newcommand{\CQG}{{\it Class. Quantum Grav.} }
+\newcommand{\CTM}{{\it Combust. Theory Modelling\/} }
+\newcommand{\DSE}{{\it Distrib. Syst. Engng\/} }
+\newcommand{\EJP}{{\it Eur. J. Phys.} } 
+\newcommand{\HPP}{{\it High Perform. Polym.} }              % added 4/5/93
+\newcommand{\IP}{{\it Inverse Problems\/} }
+\newcommand{\JHM}{{\it J. Hard Mater.} }                    % added 4/5/93
+\newcommand{\JO}{{\it J. Opt.} }
+\newcommand{\JOA}{{\it J. Opt. A: Pure Appl. Opt.} }
+\newcommand{\JOB}{{\it J. Opt. B: Quantum Semiclass. Opt.} }
+\newcommand{\JPA}{{\it J. Phys. A: Math. Gen.} }
+\newcommand{\JPB}{{\it J. Phys. B: At. Mol. Phys.} }      %1968-87
+\newcommand{\jpb}{{\it J. Phys. B: At. Mol. Opt. Phys.} } %1988 and onwards
+\newcommand{\JPC}{{\it J. Phys. C: Solid State Phys.} }   %1968--1988
+\newcommand{\JPCM}{{\it J. Phys.: Condens. Matter\/} }    %1989 and onwards
+\newcommand{\JPD}{{\it J. Phys. D: Appl. Phys.} }
+\newcommand{\JPE}{{\it J. Phys. E: Sci. Instrum.} }
+\newcommand{\JPF}{{\it J. Phys. F: Met. Phys.} }
+\newcommand{\JPG}{{\it J. Phys. G: Nucl. Phys.} }         %1975--1988
+\newcommand{\jpg}{{\it J. Phys. G: Nucl. Part. Phys.} }   %1989 and onwards
+\newcommand{\MSMSE}{{\it Modelling Simulation Mater. Sci. Eng.} }
+\newcommand{\MST}{{\it Meas. Sci. Technol.} }                 %1990 and onwards
+\newcommand{\NET}{{\it Network: Comput. Neural Syst.} }
+\newcommand{\NJP}{{\it New J. Phys.} }
+\newcommand{\NL}{{\it Nonlinearity\/} }
+\newcommand{\NT}{{\it Nanotechnology} }
+\newcommand{\PAO}{{\it Pure Appl. Optics\/} }
+\newcommand{\PM}{{\it Physiol. Meas.} }                        % added 4/5/93
+\newcommand{\PMB}{{\it Phys. Med. Biol.} }
+\newcommand{\PPCF}{{\it Plasma Phys. Control. Fusion\/} }      % added 4/5/93
+\newcommand{\PSST}{{\it Plasma Sources Sci. Technol.} }
+\newcommand{\PUS}{{\it Public Understand. Sci.} }
+\newcommand{\QO}{{\it Quantum Opt.} }
+\newcommand{\QSO}{{\em Quantum Semiclass. Opt.} }
+\newcommand{\RPP}{{\it Rep. Prog. Phys.} }
+\newcommand{\SLC}{{\it Sov. Lightwave Commun.} }               % added 4/5/93 
+\newcommand{\SST}{{\it Semicond. Sci. Technol.} }
+\newcommand{\SUST}{{\it Supercond. Sci. Technol.} }
+\newcommand{\WRM}{{\it Waves Random Media\/} }
+\newcommand{\JMM}{{\it J. Micromech. Microeng.\/} }
+%
+% Other commonly quoted journals
+%
+\newcommand{\AC}{{\it Acta Crystallogr.} }
+\newcommand{\AM}{{\it Acta Metall.} }
+\newcommand{\AP}{{\it Ann. Phys., Lpz.} }
+\newcommand{\APNY}{{\it Ann. Phys., NY\/} }
+\newcommand{\APP}{{\it Ann. Phys., Paris\/} }
+\newcommand{\CJP}{{\it Can. J. Phys.} }
+\newcommand{\JAP}{{\it J. Appl. Phys.} }
+\newcommand{\JCP}{{\it J. Chem. Phys.} }
+\newcommand{\JJAP}{{\it Japan. J. Appl. Phys.} }
+\newcommand{\JP}{{\it J. Physique\/} }
+\newcommand{\JPhCh}{{\it J. Phys. Chem.} }
+\newcommand{\JMMM}{{\it J. Magn. Magn. Mater.} }
+\newcommand{\JMP}{{\it J. Math. Phys.} }
+\newcommand{\JOSA}{{\it J. Opt. Soc. Am.} }
+\newcommand{\JPSJ}{{\it J. Phys. Soc. Japan\/} }
+\newcommand{\JQSRT}{{\it J. Quant. Spectrosc. Radiat. Transfer\/} }
+\newcommand{\NC}{{\it Nuovo Cimento\/} }
+\newcommand{\NIM}{{\it Nucl. Instrum. Methods\/} }
+\newcommand{\NP}{{\it Nucl. Phys.} }
+\newcommand{\PL}{{\it Phys. Lett.} }
+\newcommand{\PR}{{\it Phys. Rev.} }
+\newcommand{\PRL}{{\it Phys. Rev. Lett.} }
+\newcommand{\PRS}{{\it Proc. R. Soc.} }
+\newcommand{\PS}{{\it Phys. Scr.} }
+\newcommand{\PSS}{{\it Phys. Status Solidi\/} }
+\newcommand{\PTRS}{{\it Phil. Trans. R. Soc.} }
+\newcommand{\RMP}{{\it Rev. Mod. Phys.} }
+\newcommand{\RSI}{{\it Rev. Sci. Instrum.} }
+\newcommand{\SSC}{{\it Solid State Commun.} }
+\newcommand{\ZP}{{\it Z. Phys.} }
+
+\newcommand{\etal}{{et al.\/}}
+%
+%
+%----------------------------------------------------------------------------
+\begin{document}
+%
+\title{The $\theta_{13}$ and $\delta_{CP}$ sensitivities of the SPL-Fréjus project revisited}
+\author{Jean Eric Campagne, Antoine Cazes}
+\institute{ Laboratoire de l'Accélérateur Linéaire -
+Université Paris-Sud - B\^at. 200 - BP 34 -
+91898 Orsay Cedex, France}
+\mail{campagne@lal.in2p3.fr}
+\date{\today}
+%
+%
+%
+%\selectlanguage{francais}
+%
+\abstract{
+An optimization of the CERN SPL beam line has been performed guided by the sensitivities to the $\theta_{13}$ mixing angle and to the $\delta_{CP}$ Dirac CP violating phase. A UNO-like 440 ktons water \v{C}erenkov detector located at 130~km from the target in a new foreseen Fréjus laboratory has been used as a generic detector. Concerning the $\delta_{CP}$ independent $\theta_{13}$ sensitivity, a gain of about $20\%$ may be reached using a $3.5$~GeV proton beam with a 40~m long, 2~m radius decay tunnel compared to the up to now considered $2.2$~GeV beam energy and 20~m long, 1~m radius decay tunnel. This may motivate new machine developments to upgrade the nominal SPL proton beam energy.}
+%\pacs{14.60.Pq, 14.60.Lm}
+
+\maketitle
+
+
+\section{Introduction}
+The very near future of the neutrino long baseline experiments is devoted to the study of the oscillation mechanism in the range of $\Delta m^2 = \Delta m^2_{atm} \approx 2.4\times10^{-3}\mathrm{eV}^2$ \cite{SKNU04,K2KNU04}
+ using conventional $\nu_\mu$ beams. The current K2K experiment in Japan \cite{K2KNU04}, and the forthcoming MINOS in the USA \cite{MINOS} take benefit of low energy beam to measure the $\Delta m^2$ parameter using the disappearance mode $\nu_\mu\rightarrow\nu_\mu$, while OPERA/ICARUS experiments \cite{OPERA,ICARUS} using the high energy CNGS beam \cite{CNGS} will be able to detect $\nu_\tau$ appearance. If we do not consider the LSND anomaly \cite{LSND} that will be further studied soon by MiniBooNE experiment \cite{MINIBOONE}, the three flavor family scenario will be confirmed and accommodated by a $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix \cite{PMNS} with three angles ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase $\delta_{CP}$.  
+
+Beyond this medium term plan, two of the next future tasks of neutrino physics are to improve the sensitivity of the last unknown mixing angle parameter, the so-called $\theta_{13}$, and to explore the CP violation mechanism in the leptonic sector. The present upper bound on $\theta_{13}$ is $\sin^22\theta_{13}<0.14$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$~CL) \cite{CHOOZ}. This sensitivity can be improved using reactor and accelerator experiments. In reactor experiments, one uses $\bar{\nu}_e$ in disappearance mode and may reach $\sin^22\theta_{13}<0.024$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$CL) \cite{Wpaper}. In accelerator experiments, one can use $\nu_e$ and $\bar{\nu}_e$ from $\beta$ beams \cite{BETABEAM} in both  disappearance and appearance modes (\textit{i.e.} $\stackrel{\scriptscriptstyle (-)}{\nu}_e\rightarrow \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$), and also $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu$ in appearance mode (\textit{i.e.} $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu\rightarrow\stackrel{\scriptscriptstyle(-)}{\nu}_e$) with conventional beams either with sub-mega watt proton drivers \cite{NOVA,T2K} or with multi-mega watt proton drivers \cite{T2K,BNLHS,CERN}. The later neutrino beam type, called Superbeam, is foreseen to be extended to produce $\nu_\mu$ beam and $\bar{\nu}_\mu$ beam from muon decays, the so-called Neutrino Factory, in order to study the eventual leptonic CP violation. Such Neutrino Complex is under study in Japan, in USA and also in Europe at CERN and details may be found in reference \cite{CERN}. A comparison of the performances of $\beta$ beam and Superbeam may be found for instance in reference \cite{DONINI}.  The reactor experiment result on $\theta_{13}$ is straight forward as compared to Superbeam and Neutrino Factory results that are on one hand reacher but in an other hand more complex to analyse due to the interplay between the different physics factors $\theta_{13}$, $\delta_{CP}$, sign$(\Delta m^2_{23})$, sign$(\tan(2\theta_{23}))$ \cite{DONINI,DOUBLE-CHOOZ}. 
+
+This paper presents results of a new simulation of the SPL (Super Proton Linac) Superbeam that could take place at CERN \cite{SPL}, using for definitiveness a UNO-like 440kT fiducial water \v{C}erenkov detector \cite{UNO} located in a new enlarged underground laboratory under study in the Fréjus tunnel, $130$~km away from CERN \cite{mosca}. The SPL neutrino beam is created by  decays of pions, muons and kaons produced by the interactions of a $4$~MW proton beam impinging a liquid mercury jet \cite{CERN}. Pions, muons and kaons are collected using two concentric electromagnetic lenses (horns), the inner one and the outer one are hereafter called "Horn" and "Reflector" respectively \cite{Meer}. The horns are followed by a decay tunnel where most of the neutrinos are produced. A sketch of the beam line is shown on figure~\ref{fig:Sbeam}.  
+
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/cernSuperBeam_English}
+\caption{\label{fig:Sbeam}Sketch of the SPL neutrino Superbeam from CERN to the Fréjus tunnel.}	
+\end{figure}
+
+The analysis chain consists of different stages: the simulation of the interactions between the proton beam and the mercury target, the propagation of the resulting secondary particles through the magnetic field and the materials of the horns, the tracking of $\pi^\pm$, $K^{\pm,0}$ and $\mu^\pm$ until they decay, the computation of the neutrino flux at the detector site, and finally the statistical analysis. A part of the simulation chain has already been described in reference \cite{nuFact134,MMWPSCazes}. 
+
+
+Compared to recent papers on the same subject \cite{DONINI,JJG,Mezzetto}, we have reoptimized the Horn and Reflector shapes \cite{nuFact138}, and introduced the kaon background simulation which allows us to update the SPL beam energy. The organization of this document follows the simulation chain: the interaction between the proton beam and the mercury target is presented in the second section. The kaon production is detailed in the third section. The simulation of the horns is described in the forth section, while the algorithms used to compute the neutrino fluxes are explained in the fifth section. Then, the sensitivities to $\theta_{13}$ and $\delta_{CP}$ are revisited with new studies about the optimization of the proton beam energy, the pion collection and the decay tunnel geometry.
+
+\section{Target simulation}
+\label{sec:target}
+Since hadronic processes are crucial to describe the interactions of the proton beam on the target, the FLUKA simulator \cite{fluka} has been chosen for this first step of the simulation. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:targ}Liquid mercury jet parameters.}
+\begin{tabular}{ll}
+\hline\noalign{\smallskip}
+    \centre{2}{Hg target}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+      Hg jet speed & $20$~m/s \\
+      density & $13.546$ \\
+      Length, radius & $30$~cm, $7.5$~mm \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+The target used in the present study is a mercury liquid jet \cite{CERN} simulated for a sake of simplicity by a cylinder $30$~cm long (representing two hadronic lengths) and $1.5$~cm diameter (see table~\ref{tab:targ}) \cite{JJG}. Other types of target are under study \cite{CERN}. The pencil like simulated proton beam is composed with  $10^6$ mono-energetic protons, and no beam-target dynamical effects are taken into account. The beam axis is also the symmetry axis of the target and the horns and the decay tunnel. Simulations have been performed for $2.2$~GeV proton kinetic energy, the up to now nominal design \cite{SPL}, as well as for $3.5$~GeV, $4.5$~GeV, $6.5$~GeV and $8$~GeV according to possible new designs \cite{MMWPSGaroby}.
+
+Particle production yields are summarized in table~\ref{tab:nbPart}. The pion momentum spectra obtained at different energies and normalized to a 4MW SPL beam power are presented in figure~\ref{fig:compEner2}(a). At low energy, pions come from $\Delta$ decays while the high energy part is dominated with multi pion production. At very mow energy, for $P<200$~MeV/c, pions come from $\Delta$ produced by protons of the target excited by the beam interactions, while for  higher energy, pion production is due to transformation of protons of the beam into $\Delta$.
+
+The horns are designed to focus the $600$~MeV/c pions (see section~\ref{sec:horn}) and the variation of the number of such pions is rather smooth with respect to the beam energy considering a 4MW fixed beam power: $4.19\times10^{13}\pi$/s for the $2.2$~GeV beam, $4.91\times10^{13}\pi$/s for the $3.5$~GeV beam, $5.14\times10^{13}\pi$/s for the $4.5$~GeV beam, and $4.92\times10^{13}\pi$/s for the $6.5$~GeV beam. The main difference is made by the angular distribution. Figure~\ref{fig:compEner2}(b) shows this distribution for the $\pi^+$ exiting the target with a momentum between $500$~MeV/c and $700$~MeV/c. The acceptance of the horns is limited to the pion below $25^\circ$, and we see that more pions are accepted by the horns for the $3.5$~GeV and $4.5$~GeV proton beams compared to other beam energies.
+
+
+
+The secondary proton and neutron rates induce important radiation damages and power dissipation in the horns which have been addressed in reference \cite{nuFact134}, and which will require specific R\&D effort. At $2.2$~GeV, kaon yields are very low, but it has a dramatic energy dependence as further studied in section~\ref{sec:kaon}. It is worth to mention that the numbers in table~\ref{tab:nbPart} are not to be taken as face values, because the cross sections of pion and kaon productions using proton beam are still under studies as for instance by the HARP experiment \cite{harp}.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbPart}Average numbers of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA). The $\mu^+/\mu^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+$E_k$ (GeV) & p & n & $\gamma$ & $e^+$ & $e^-$ & $\pi^+$ & $\pi^-$ & $\mu^+$ & $\mu^-$ & $K^+$ & $K^0$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$2.2$ & $1.4$     &  $17$   & $5.0$  &   $0.08$  &  $0.17$    &  $0.24$   &  $0.18$ & $4$ & $1$ & $7$ & $6$ \\
+
+$3.5$ & $1.8$    &  $23$  & $7.0$   &  $0.15$  &  $0.28$    &  $0.41$   &  $0.37$ & $10$ & $3$ & $35$ & $30$ \\
+
+$4.5$ &  $2.3$  &  $25$ & $7.7$  & $0.21$  &  $0.35$    &  $0.57$ & $0.39$&  $11$ & $3.3$  &  $93$ &  $68$       \\
+
+$8$   &  $3.1$  &  $33$ & $11.0$ & $0.41$ & $0.63$    &  $1.00$  &  $0.85$ &  $30$ &  $9.5$ &  $413$ &    $340$         \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compEner2.eps}
+\caption{\label{fig:compEner2} (a) $\pi^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$~GeV/c and $0.7$~GeV/c. The different SPL beam kinetic energies presented are (\full) $2.2$~GeV, (\dashed) $3.5$~GeV, (\dotted) $4.5$~GeV and (\chain) $6.5$~GeV.}
+\end{figure*}
+%
+The cross section uncertainties are the main source of discrepancy between simulator programs. Some comparisons between FLUKA and MARS \cite{MARS} have already been presented in the same context \cite{nuFact134}. The energy distribution of the pions exiting the target, computed with the two simulator programs FLUKA and MARS, is shown on figure~\ref{fig:compFlukaMars}(a).  The discrepancy is quite large for the low energy part. However, the horns are designed to focus the high energy part of the spectrum (see section~\ref{sec:horn}), and therefore, MARS and FLUKA are in better agreement for the energy spectrum computed at the entrance of the decay tunnel, as shows figure~\ref{fig:compFlukaMars}(b). 
+%A difference of $10\%$ has been found between the  $\theta_{13}$ sensitivity computed with the two generators (see section~\ref{sec:results}), that can be taken as systematic error. 
+For a 2.2~GeV beam and a positive focusing,  $27\%$ more $\nu_\mu$ and $6\%$ more $\nu_e$ neutrinos are produced around the oscillation probability maximum with the FLUKA generator. In turn out that 
+a sensitivity $10\%$ beter for FLUKA compared to MARS has been found for the $\sin^2(2\theta_{13})$ sensitivity
+(see section~\ref{sec:results}). So, the discrepancy  at low energy between MARS and FLUKA does not matter too much for the present application, and the sensitivity difference can be taken as a systematic error. 
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compMarsFlukav2.eps}
+\caption{\label{fig:compFlukaMars}$\pi^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\dashed) and by MARS (\full).}
+\end{figure*}
+%
+\section{Kaon production}
+\label{sec:kaon}
+The possibility to increase the SPL energy in order to study the optimization of the physics program has been recently pointed out \cite{MMWPSGaroby}. Then, the kaon production should be clearly addressed because it is a source of $\nu_e$ and $\bar{\nu}_e$ background events. The kaon decay channels and branching ratios are presented in table~\ref{tab:BRKP0SL} in \ref{sec:kaons}.
+
+The target simulation described in section~\ref{sec:target} has been used with $10^6$ p.o.t with kinetic energy uniformly distributed between $2.2$~GeV and $5$~GeV. The momentum of outgoing pions and kaons are recorded when they exit the target. The number of produced $K^{o,\pm}$ at different proton beam energies are presented on figure~\ref{fig:KaonsPions} (left). In one hand the $K^o$ production rate is similar to the $K^+$ production rate, but in an other hand the $K^-$ production rate is almost forty times smaller. For comparison, the numbers of $\pi^+$ and $\pi^-$  produced in the same conditions are presented on figure~\ref{fig:KaonsPions} (right). Pion production rate is about two orders of magnitude greater than the kaon production rate.
+%
+\begin{figure*}
+\centering
+%\includegraphics[height=95mm]{../picts/KaonProd.eps}
+\includegraphics[height=95mm]{../picts/KaonPionProdFluka2003v2.eps}
+%\caption{\label{fig:KaonsPions}Kaon production (a) as a function of the incident proton beam kinetic energy ($E_k$) for $10^6$ incident protons with (\full) curve for $K^+$, (\dashed) curve for $K^-$ and (\dotted) curve for $K^0$. Pion production (b) in the same conditions with (\full) curve for $\pi^+$ and (\dashed) curve for $\pi^-$.}
+\caption{\label{fig:KaonsPions} Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).} 
+\end{figure*}
+%
+The behavior of the two pion and kaon production rates are quite different. The $\pi^+$ yield grows smoothly with the proton energy while the production of kaons seams to have two origins, which has been confirmed by FLUKA's authors \cite{FLUKAprivate}. For beam energy below approximatively $4$~GeV, the resonance production model is used, and one notices a low production rate with a maximum at about $3.4$~GeV. For beam energy above  $4$~GeV, the dual parton model is used, and the production rate experiences a threshold effect with a rapid rise. The ratio between positive kaon and pion production rates is about $0.5\%$ between $2.2$~GeV and $4$~GeV and grow up to $2.3\%$ at $5$~GeV. One notices that the transition between the two kaon production models may not be optimal.
+%
+\section{Horns simulation}
+\label{sec:horn}
+The simulation code of the electromagnetic horns is written using GEANT 3.2.1 \cite{geant} for convenience and since electromagnetic processes are dominant, FLUKA has not been considered as mandatory, but this may be revised in a future work. The geometry of the horns has been inspired by an existing CERN prototype and a Reflector design proposed in reference \cite{SIMONE1}. Depending of the current injection, only positive secondary particles or negative secondary particles are focused. The relevant parameters are detailed in table~\ref{tab:specif}.
+
+The mercury target is localized inside the Horn because of the low energy and the large emittance of the secondary pions produced: $$<P_{\pi T}>/<P_\pi> \approx 240~\mathrm{MeV}/400~\mathrm{MeV}$$ ($2.2$~GeV proton beam energy). This explains the Horn design (figure~\ref{fig:plan}), with a cylindrical part around the target, called the neck, which is larger than the transversal size of the target to simulate the room for target handling, and a conic part designed such that the relevant pions are focused as much as possible to exit the magnetic field parallel to the beam axis.
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/corne350.eps}
+\caption{\label{fig:plan}Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350~MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}
+\end{figure}
+
+\begin{table}
+\centering
+\caption{\label{tab:specif}Relevant parameters of the horns in case of the generation of a $260$~MeV neutrino beam (or $350$~MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$~MeV/c (or $800$~MeV/c) pion momentum.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+ & Horn & Reflector \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+  neck inner radius & $3.7$~cm &  $20.3$~cm \\
+  neck length & $40$~cm        &  $120 (140)$~cm \\ 
+  end cone inner radius & $16$~cm        &  $35.7$~cm \\
+  outer radius & $20.3$~cm      & $40$~cm \\ 
+  total length & $120 (140)$~cm       & $190 (220)$~cm \\  
+  Alu thickness  & $3$~mm       & $3$~mm \\            
+  Peak current & $300$~kA       & $600$~kA \\
+  Frequency & $50$~Hz            & $50$~Hz \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The shape of the horn conductors is a crucial point since it determines the energy spectrum of the neutrino at the detector site. The details of the conductor shape optimization for the present context may be found in reference \cite{nuFact138}. We just recall here some ingredients. For a $\theta_{13}$ driven $\nu_\mu \rightarrow \nu_e$ oscillation, a $\Delta m^2_{23}$ parameter value of $2.4\times10^{-3}\mathrm{eV}^2$, and a baseline distance of $130$~km, the first oscillation maximum occurs for a neutrino energy of $260$~MeV. The   optimization of the physics potential depends at first approximation on the pion neutrino characteristics, which energy is fully determined by the pion 2-body decay and boost. To reach an energy of $260$~MeV, the pion needs a $\beta=0.97$, which in turn induces a pion momentum of $600$~MeV/c. Then, the shape of the conic part of the horns is determined such that these $600$~MeV/c pions exit parallel to the beam axis. 
+
+An other shape of the horn conductors has been used to produce a $350$~MeV neutrino beam to compare the sensitivity potential (see section \ref{sec:results}). In that case, keeping the current intensity unchanged ($300/600$~kA), the lengths of the Horn and the Reflector should be increased by $16$\% and $18.5$\%, respectively (see table~\ref{tab:specif}).
+
+Before closing this section, it is worth to quote that the Horn/Reflector conductor shapes optimized in the present study to focus a given pion momentum value, is not affected at first order by a proton beam energy change. What is affected is the production rate of the relevant pions. This Horn/Reflector design consideration would be different if one wishes to focus as much as possible all the pions produced for which the mean energy is of course affected by a proton beam energy change.    
+%
+\section{Particle decay treatment and flux calculation}
+%
+The decay tunnel representation is a simple cylinder with variable length ($L_T$) and radius ($R_T$) filled with "vacuum" and located right after the horns. The default design is a $20$~m long and $1$~m radius cylinder, but simulations have also been conducted with lengths of $10$~m, $40$~m and $60$~m, and radius of $1.5$~m and $2$~m in the spirit of reference \cite{donega}. In the GEANT simulation, to gain in CPU time, only pions, muons and kaons are tracked in the volume of the tunnel, and all particles exiting this volume are discarded. 
+
+Beyond the $1/L^2$ solid angle factor due to the source-detector distance ($L$) which decreases dramatically the fluxes, the neutrino beam focusing is very limited due to the small pion boost factor ($\approx 4$). Therefore, computational algorithms have been used to avoid a too prohibitive CPU time resulting from the simulation of each secondary particle decay. Otherwise, about $10^{15}$ p.o.t would have been necessary to obtain reliable statistics for the estimation of the $\bar{\nu}_e$ flux for instance.
+
+It is worth to mention that the particle decays occurring before the entrance of the decay tunnel are also taken into account and treated in the same manner, which is not the case in reference \cite{donega}. 
+%
+\subsection{Algorithm description}
+\label{sec:algo}
+The decay code has been included in the GEANT code. The basic idea of this algorithm is to compute the neutrino fluxes using the probability of reaching the detector for each neutrino produced by a $\pi$ or a $K$ or a $\mu$ particle (on-axis neutrino beam). This method has already been used in reference \cite{donega} and has been modified and extended to the kaon decay chain for the present study. 
+
+Muon neutrino comes mostly from pion decay. In a first stage, each pion is tracked by GEANT until it decays. Then, the probability for the produced muon neutrino to reach the detector is computed. The flux is obtained applying the probability as a weight for each neutrino. All the pions produced in the simulation are therefore useful to compute the flux, and this allows to reduce the number of events in the simulation to $10^6$ p.o.t. In this computation, the decay region (horns and tunnel) is considered as point like compared to the source-detector distance. 
+
+The same method is applied for neutrino coming from muons and kaons with some modifications  because most of the muons do not decay, and there are very few kaons produced (see table~\ref{tab:nbPart}).
+The probability computation is presented in appendix~\ref{sec:decayprobcomp}. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:proton}Number of protons on target for different beam energy at 4~MW constant power. One year is defined as $10^7$~s.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			Beam energy  & Number of proton \\
+			  (GeV)      & per year ($10^{23}$ p.o.t/y) \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			2.2 & 1.10 \\
+			3.5 & 0.70 \\
+			4.5 & 0.56 \\
+			6.5 & 0.40 \\
+			8.0 & 0.30 \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table*}
+\centering
+\caption{\label{tab:speciesfluxes}Integral of the total flux of the different species with different settings. The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are expressed in $10^{13}/100\mathrm{m}^2/y$ unit while the $\nu_e$ and $\bar{\nu}_e$ fluxes are expressed in $10^{11}/100\mathrm{m}^2/y$ unit. The positive focusing  and negative focusing  are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. %Setting (1) means $L_T = 10$~m and $R_T = 1$~m. Setting (2) is the default option and means $L_T = 20$~m and $R_T = 1$~m. Setting (3) means $L_T = 20$~m and $R_T = 1.5$~m. Setting (4) means $L_T = 30$~m and $R_T = 1$~m. Setting (5) means $L_T = 40$~m and $R_T = 1$~m. Setting (6) means $L_T = 40$~m and $R_T = 1.5$~m. Setting (7) means $L_T = 40$~m and $R_T = 2$~m.  Setting (8) means $L_T = 60$~m and $R_T = 1$~m, and finally, setting (9) means $L_T = 60$~m and $R_T = 1.5$~m.
+}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+
+			\centre{3}{Settings}  & \centre{2}{$\nu_\mu$} & \centre{2}{$\nu_e$} 
+								&	\centre{2}{$\bar{\nu}_\mu$} & \centre{2}{$\bar{\nu}_e$} \\
+								$E_p$ & $L_T$ & $R_T$ & $+$ & $-$ & $+$ & $-$ & $+$ & $-$ 
+								& $+$ & $-$ \\ 
+\noalign{\smallskip}\hline\noalign{\smallskip}
+
+$2.2$~GeV & $10$~m &  $1$~m 
+	& $5.5$          & $0.4$ 
+	& $1.7$          & $0.2$
+	& $0.3$          & $4.3$  
+	& $0.1$ 	 & $0.8$ \\		
+
+$3.5$~GeV  & $10$~m &  $1$~m  
+	& $7.7$          & $0.7$ 
+	& $2.6$          & $0.6$
+	& $0.6$          & $6.6$  
+	& $0.3$ 	 & $1.3$ \\		
+	
+$4.5$~GeV  & $10$~m &  $1$~m  
+	& $7.1$          & $1.0$ 
+	& $2.8$          & $0.9$
+	& $0.5$          & $5.2$  
+	& $0.3$ 	 & $1.1$ \\		  
+
+$6.5$~GeV  & $10$~m &  $1$~m  
+	& $8.3$          & $1.2$ 
+	& $4.7$          & $1.9$
+	& $0.8$          & $5.6$  
+	& $0.9$          & $1.8$ \\
+
+$8.0$~GeV  & $10$~m &  $1$~m  
+	& $7.7$          & $1.2$ 
+	& $5.1$          & $2.2$
+	& $0.9$          & $5.6$  
+	& $1.1$ 	 & $2.1$ \\
+
+$2.2$~GeV & $20$~m &  $1$~m   
+	& $7.6$         & $0.4$ 
+	& $3.2$ 	& $0.2$
+	& $0.3$ 	& $5.8$  
+	& $0.1$ 	& $1.6$ \\		  
+
+$3.5$~GeV & $20$~m &  $1$~m    
+	& $10.0$          & $0.9$ 
+	& $4.4$           & $0.6$
+	& $0.7$ 	  & $8.5$  
+	& $0.3$ 	  & $2.2$ \\		  
+
+$4.5$~GeV & $20$~m &  $1$~m    
+	& $10.9$          & $1.1$ 
+	& $5.1$           & $1.0$
+	& $0.7$ 	  & $6.7$  
+	& $0.4$ 	  & $1.8$ \\		  
+
+$6.5$~GeV & $20$~m &  $1$~m    
+	& $10.4$          & $1.4$ 
+	& $6.4$           & $2.0$
+	& $1.0$           & $7.1$  
+	& $0.9$ 	  & $2.5$ \\	
+
+$8.0$~GeV & $20$~m &  $1$~m    
+	& $9.7$           & $1.5$ 
+	& $6.7$           & $2.3$
+	& $1.2$           & $7.1$  
+	& $1.1$ 	  & $2.8$ \\
+
+$2.2$~GeV & $20$~m &  $1.5$~m    
+	& $9.0$           & $0.6$ 
+	& $4.4$           & $0.4$
+	& $0.4$           & $6.7$  
+	& $0.2$  	  & $2.2$ \\
+
+$4.5$~GeV & $20$~m &  $1.5$~m    
+	& $13.2$          & $1.5$ 
+	& $6.9$           & $1.4$
+	& $0.9$           & $8.1$  
+	& $0.6$  	  & $2.7$ \\
+
+$3.5$~GeV & $30$~m &  $1$~m    
+	& $10.9$          & $0.9$ 
+	& $5.7$           & $0.7$
+	& $0.7$           & $9.4$  
+	& $0.3$  	  & $2.9$ \\
+
+$4.5$~GeV & $30$~m &  $1$~m   
+	& $11.6$          & $1.2$ 
+	& $6.3$           & $1.0$
+	& $0.7$           & $7.1$  
+	& $0.4$    	  & $2.3$ \\
+
+$2.2$~GeV & $40$~m &  $1$~m    
+	& $8.9$           & $0.5$ 
+	& $5.1$           & $0.3$
+	& $0.5$           & $6.7$  
+	& $0.1$   	  & $2.4$ \\	
+
+$3.5$~GeV & $40$~m &  $1$~m  
+	& $11.3$          & $0.9$ 
+	& $6.5$           & $0.6$
+	& $0.8$           & $9.7$  
+	& $0.3$ 	  & $3.3$ \\	
+
+$4.5$~GeV & $40$~m &  $1$~m  
+	& $12.3$          & $1.2$ 
+	& $7.2$           & $1.0$
+	& $0.8$           & $7.5$  
+	& $0.4$   	  & $2.6$ \\	
+
+$6.5$~GeV & $40$~m &  $1$~m  
+	& $11.7$          & $1.6$ 
+	& $8.3$           & $2.2$
+	& $1.1$           & $8.0$  
+	& $0.9$   	  & $3.3$ \\	
+
+$8.0$~GeV & $40$~m &  $1$~m  
+	& $10.9$          & $1.7$ 
+	& $8.5$           & $2.4$
+	& $1.3$           & $8.0$  
+	& $1.2$    	  & $3.6$ \\	
+
+$3.5$~GeV & $40$~m &  $1.5$~m  
+	& $14.5$          & $1.3$ 
+	& $10.0$          & $1.0$
+	& $1.0$           & $12.3$  
+	& $0.5$  	  & $5.3$ \\
+	
+$4.5$~GeV & $40$~m &  $1.5$~m 
+	& $15.5$          & $1.7$ 
+	& $10.8$          & $1.5$
+	& $1.0$           & $9.5$  
+	& $0.6$  	  & $4.2$ \\
+		
+$3.5$~GeV & $40$~m &  $2$~m 
+	& $16.6$          & $1.5$ 
+	& $12.9$          & $1.3$
+	& $1.3$           & $13.9$  
+	& $0.7$  	  & $6.9$ \\
+	
+$4.5$~GeV & $40$~m &  $2$~m 
+	& $18.2$          & $2.1$ 
+	& $14.3$          & $1.9$
+	& $1.3$           & $11.1$  
+	& $0.8$  	  & $5.6$ \\
+	
+$3.5$~GeV & $60$~m &  $1$~m 
+	& $11.7$          & $0.9$ 
+	& $7.6$           & $0.7$
+	& $0.7$           & $10.1$  
+	& $0.3$      	  & $3.7$ \\
+	
+$4.5$~GeV & $60$~m &  $1$~m 
+	& $12.5$          & $1.3$ 
+	& $8.1$           & $1.1$
+	& $0.7$           & $7.7$  
+	& $0.4$ 	  & $2.9$ \\
+	
+$3.5$~GeV & $60$~m &  $1.5$~m 
+	& $15.1$          & $1.3$ 
+	& $12.2$          & $1.0$
+	& $1.0$           & $12.8$  
+	& $0.5$  	  & $6.3$ \\
+	
+$4.5$~GeV & $60$~m &  $1.5$~m 
+	& $16.2$          & $1.8$ 
+	& $13.1$          & $1.6$
+	& $1.0$           & $9.9$  
+	& $0.6$ 	  & $4.9$ \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\subsection{Validation of the algorithm}
+The validity of the method presented in the previous section have been tested against a straight forward  algorithm consisting of decaying each pion $N$ times ($N \approx 10^6$) in a full GEANT simulation of the event (decays included). Such method presents the advantage to keep all the information of the neutrino available for further studies. It can be a good approach to compute the muon neutrino flux coming from pion decays. It can also provide the beam profile, but it shows its limits for the muon induced fluxes, especially the $\bar{\nu}_e$ flux. Indeed, this means that each muon is duplicated $N$ times and when a muon decays, it must decay $N$ times again. For $N\approx 10^6$, this is a prohibitive CPU time consuming.
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compGeantDonega.eps}
+\caption{\label{fig:compGeantDonega}Comparison between the probability method, (\full) curve, and the full GEANT simulation method, (\dashed) curve, for the $\nu_\mu$ from $\pi^+$ flux (a) and the $\bar{\nu}_\mu$ from $\pi^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu_e$ and $\bar{\nu}_e$ fluxes contrary to the former simulation.}
+\end{figure*}
+%
+The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are displayed on figure~\ref{fig:compGeantDonega} for both methods. The two spectra shows a clear agreement, and this makes confidence on the probability method.
+%
+\subsection{Simulated fluxes}
+The fluxes are computed at a distance of $100$~km from the source by convention and can be rescaled at any desired distance. They provide the number of the four neutrino species ($\nu_\mu$, $\bar{\nu}_\mu$, $\nu_e$, $\bar{\nu}_e$) passing through a $100$~m$^2$ fiducial area during $1$~year.
+
+In practice, the fluxes are given as a function of the neutrino energy via histograms composed of $20$~MeV bin width.  These histograms are filled with the energy of each neutrino weighted by the probability to reach the detector (section~\ref{sec:algo}). To obtain the fluxes, the histograms are rescaled to the number of p.o.t per year depending on the beam energy. Table~\ref{tab:proton} reports on the number of p.o.t per year for the different energies studied using the definition of one year being $10^7$~s and keeping the beam power constant (\textit{i.e.} $4$~MW).
+
+Three origins are identified in the composition of each neutrino flux:
+\begin{description}
+	\item[-] neutrinos from pions, which includes neutrinos created by primary pion decays and neutrinos coming from the muons produced by pion decays or muons directly exiting the target. This is the component studied in reference \cite{donega} but with different settings and event generator;
+	\item[-] neutrinos emitted during the decay chain of the charged kaons, either by direct production, or produced by the daughter pions and muons;
+	\item[-] neutrinos coming from the decay chain of the neutral kaons.
+\end{description}
+
+The three components of the fluxes for the four neutrino species are presented on figure~\ref{fig:flux22p} for positive particle focusing and a proton beam kinetic energy of $2.2$~GeV. The $\nu_\mu$ flux is dominated by the neutrinos of pion decays, but a tail above $500$~MeV (insert on the top left part) is created by the $K^+\rightarrow \mu^+\nu_\mu$ channel, which is anyway at least three order of magnitude below the flux maximum. The $\bar{\nu}_\mu$ flux is mostly due to the decays of $\pi^-$ that are not unfocused by the horns, but the higher energy part comes from $\mu^+$ decays. It is noticable that the $\nu_e$ and $\bar{\nu}_e$ fluxes are respectively more than $200$ and more than $7000$ times smaller than the $\nu_\mu$ flux. The $\bar{\nu}_e$ are produced in a large part by the $K^0_L\rightarrow\pi^+e^-\bar{\nu}_e$ decay channel and by $\mu^-$ decays, while the  $\nu_e$ flux is dominated by the $\mu^+$ decays.
+
+On figure~\ref{fig:flux22m}, the horns are set to focus negative particles keeping other parameters identical. By comparison with positive focusing, one can at first approximation translate the results by exchanging particles and anti-particles, except that the $K^+/K^-$ ratio is about 50 in the beam-target interactions (see table~\ref{tab:nbPart}).
+
+On figures~\ref{fig:flux45p} and \ref{fig:flux8p}, one observes the evolution of figure~\ref{fig:flux22p} when the proton beam kinetic energy increases to $3.5$~GeV and $8$~GeV, respectively. Correspondingly, the results for negative particle focusing are presented on figures~\ref{fig:flux45m} and \ref{fig:flux8m}. One clearly notices the increase of the kaon induced neutrino contents as the beam energy grows.
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22p.eps}
+\caption{	\label{fig:flux22p}Neutrino fluxes, $100$~km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$~GeV (4~MW), a decay tunnel with a length of $20$~m and a radius of $1$~m. The top left panel contains the $\nu_\mu$ fluxes, and the top right panel shows the $\bar{\nu}_\mu$ fluxes. The bottom left panel presents the $\nu_e$ fluxes while the bottom right panel displays the $\bar{\nu}_e$ fluxes. The (\full) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\dashed) curve is the contribution from the charged kaon decay chain, and the (\dotted) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22m.eps}
+\caption{\label{fig:flux22m}Same legend as for figure~\ref{fig:flux22p} but the horns are focusing negative particles.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35p.eps}
+\caption{\label{fig:flux45p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35m.eps}
+\caption{\label{fig:flux45m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8p.eps}
+\caption{\label{fig:flux8p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8m.eps}
+\caption{\label{fig:flux8m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+On table~\ref{tab:speciesfluxes} are reported the integral of the fluxes when one modifies the decay tunnel length and radius, as well as the beam kinetic energy. Changing the length from $10$~m to $40$~m will increase the $\nu_\mu$ flux by $50\%$ to $70\%$ and in the same time, the number of $\nu_e$ will be multiply by a factor $1.5$ to $2$. One can notice that going from $40$~m to $60$~m does not increase the signal-like events but increase the background-like events. For a $40$~m length of the decay tunnel, the increase of the radius improve the number of signal-like events by $50\%$, and the backgroud increase by $70\%$ to $100\%$. Notice that the $\nu_\mu/\bar{\nu}_\mu$ flux ratio is rather insensitive to the decay tunnel length. The feeling that $L_T = 40$~m and $R_T = 2$~m is a good signal over background compromise is confirmed by sensitivity quantitative studies reported in section~\ref{sec:results}.
+
+Looking at the evolution of $\nu_\mu$ flux with respect to the beam energy, one notices that a maximum is reached around $4.5$~GeV. This is due to the competition between the cross section rise with respect to the energy and the decrease of the number of p.o.t due to the constant SPL power ($4$~MW).
+%
+\section{Sensitivity computation ingredients}
+%
+The sensitivity to $\theta_{13}$ and $\delta_{CP}$ is computed for a $\nu_\mu\rightarrow\nu_e$ appearance experiment. The detector considered for definitiveness is similar to the UNO detector, \textit{i.e.} a $440$~kt fiducial water \v{C}erenkov detector \cite{UNO}. The detector simulation has been presented in reference \cite{JJG} and the analysis program described in reference \cite{MEZZETTONUFACT060} has been used for sensitivity computation following previous work of reference \cite{Mezzetto}. See table~\ref{tab:param} for the default user parameter values used in this paper. We just remind here some key points of the sensitivity analysis program. 
+
+It is included a full 3-flavors oscillation probability computation with matter effects, but no ambiguities are taken into account. This latest point may be revisited in a future work using reference \cite{DONINI-2}. Concerning the background events, the $\nu_e/\bar{\nu}_e$ from the beam, the $\nu_\mu e^-$ elastic scattering process, the $\pi^o$ production as well as the $\mu/e$ misidentification are taken into account. The cross-sections from the NUANCE program are used \cite{NUANCE}. The systematics error on the total $\nu_e$ and $\bar{\nu}_e$ fluxes determination is a user parameter and we have used the $2\%$ value considered as a final goal, but also $5\%$ and $10\%$ \cite{MEZZETTONUFACT060}. The detector is located at $L = 130$~km from CERN, in the foreseen new Fréjus laboratory \cite{mosca}. It is worth to mention that if one wants to evaluate the influence of $L$ on the sensitivity, it would mean a re-optimization of the horns for each $L$ envisaged (see section~\ref{sec:horn}).  
+%
+\begin{table}
+\centering
+\caption{\label{tab:param}Default parameters used to compute the sensitivity curves \cite{MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite{KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite{JJG}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			$\Delta m^2_{12} = 8.2 (0.5)\times 10^{-5}~\mathrm{eV}^2$ & $\sin^22\theta_{12} = 0.82 (9\%)$ \\
+			$\Delta m^2_{23} = 2.5 (0.1)\times 10^{-3}~\mathrm{eV}^2$ & $\sin^22\theta_{23} = 1.0 (1\%)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		  $L_T = 20$~m & $R_T = 1$~m \\ 
+		  $M=440$~kT   & $\epsilon_{syst}=2\%$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+\centre{2}{Horn/Reflector shapes to produce a $260$~MeV neutrino beam} \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The running time scenario has been fixed either by focusing positive particles during 5 years, either  by focusing positive particles during 1 (or 2) year(s) followed by focusing negative particles during 4 (or 8) years.
+%
+\section{Results}
+\label{sec:results}
+\subsection{The positive only focusing scenario}
+The $\theta_{13}$ and $\delta_{CP}$ sensitivities are computed with $\theta_{13} = 0^\circ$ and $\delta_{CP} = 0^\circ$ if not explicitly mentioned. It is worth to stress that the default parameters of table~\ref{tab:param} are used if not contrary mentioned, in particular, the decay tunnel geometry parameters ($L_T=20$~m and $R_T=1$~m), and the horn design to generate a $260$~MeV neutrino beam. 
+
+Table~\ref{tab:nbvsE} presents the number of signal and background events for a $5$ years positive focusing experiment, but with different beam energy settings. 
+%The quality factor ($S$) is defined in reference \cite{MEZZETTONUFACT060} as\footnote{Contrary to the definition of the significance of reference \cite{MEZZETTONUFACT060}, the systematical factor is applied to the total $\nu_e$ flux in agreement with the sensitivity contour computation.}:
+%\begin{equation}
+%\begin{aligned}
+%\mathcal{S} &= \frac{N^{osc}_{\nu_e}}{\sqrt{ N^{tot}_{\nu_e} + \left(N^{tot}_{\nu_e}\times\epsilon_{syst}\right)^2}}\\
+%\mathrm{with}\quad N^{tot}_{\nu_e} &= N^{osc}_{\nu_e} + N^{beam}_{\nu_e} + N^{oth. bkg}
+%\label{eq:significance}
+%\end{aligned}
+%\end{equation}
+%and $N^{osc}_{\nu_e}$ the number of $\nu_e$ events due to $\nu_\mu$ oscillations, $N^{beam}_{\nu_e}$ the number of background events coming from the $\nu_e+\bar{\nu}_e$ contamination of the beam, $N^{oth. bkg}$ the other kinds of background events and $\epsilon_{syst}$ the systematical factor.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbvsE}Number of events for 5 years positive focusing scenario with default parameters of table~\ref{tab:param}. Other backgrounds are $\pi^0$, $\nu_\mu$-elast., $\mu/e$-missId. 
+%The $S$ factor is defined by equation~\ref{eq:significance}.
+}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		 & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			non oscillated $\nu_\mu$       & $36917$  & $60969$  & $73202$  & $78024$ & $76068$ \\ 
+			oscillated $\nu_e$             & $43$     & $60$     & $64$     & $61$    & $56$ \\
+			beam $\nu_e$                   & $165$    & $222$    & $242$    & $288$   & $299$ \\
+			other background               & $70$     & $105$    & $127$    & $148$   & $152$ \\
+%			S factor                       & $1.88$   & $2.16$   & $2.17$   & $1.87$  & $1.69$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+The contours at $90\%$, $95\%$ and $99\%$~CL of the $\theta_{13}$ sensitivity are presented in the ($\sin^22\theta_{13}$, $\Delta m^2_{23}$) plane on figure~\ref{fig:sensi45} for $3.5$~GeV proton beam kinetic energy. 
+The comparison between the contours at $90\%$~CL with $2.2$~GeV, $3.5$~GeV, $4.5$~GeV and $8$~GeV beam energies is shown on figure~\ref{fig:compSensi}. One notices in this scenario a better perfomence reached with a $4.5$~GeV energy beam. 
+%as a confirmation of significance parameter value. 
+But, in fact there is not much visual difference between a sensitivity obtained with $3.5$~GeV and $4.5$~GeV, even if one should keep in mind that kaon production models are different at these two energies (see section~\ref{sec:kaon}). These two energy settings have been studied with different decay tunnel geometry and  results are reported on table~\ref{tab:thvsE_3545}. One notice that similar results can be reached with a $3.5$~GeV beam, compared to a $4.5$~GeV beam.
+
+Quantitative studies of the minimum $\sin^22\theta_{13}$ with respect to the kinetic beam energy $E_k(proton)$, and the decay length $L_T$, and the systematics $\epsilon_{syst}$ are presented in tables~\ref{tab:thvsE} and \ref{tab:thvseps}. One notices that for $\epsilon_{syst} = 5\%$ there is no difference between a $3.5$~GeV and a $4.5$~GeV beam.
+\begin{table}
+\centering
+\caption{\label{tab:thvsE}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		        & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV  \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$10$~m & $1.10$ & $0.92$ & $1.04$ & $1.07$ & $1.16$ \\
+			$20$~m & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$40$~m & $1.23$ & $1.00$ & $0.99$ & $1.08$ & $1.19$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table*}
+\centering
+\caption{\label{tab:thvsE_3545}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) at and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings in parenthesis are identical to those of table~\ref{tab:speciesfluxes}, except that the setting (7b) corresponds to the tunnel geometry of setting (7) but the horn geometry producing a $350$~MeV neutrino beam is used. We remind that the setting (2) is the default one, and the settings (7) and (7b) corresponds to $L_T = 40$~m and $R_T = 2$~m.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+setting & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (7b) & (8) & (9)\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$3.5$~GeV   & $0.92$ & $0.92$ & $0.83$ & $0.98$ & $1.00$ & $0.93$ & $0.91$ & $0.76$ & $1.05$ & $1.01$ \\
+$4.5$~GeV   & $1.04$ & $0.89$ & $0.82$ & $0.94$ & $0.99$ & $0.92$ & $0.87$ & $0.71$ & $1.03$ & $1.00$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensi35.eps}
+\caption{\label{fig:sensi45}Sensitivity contours obtained with a SPL energy of $3.5$~GeV and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m. (\full), (\dashed) and (\dotted) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compSensi.eps}
+\caption{\label{fig:compSensi}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+We have also considered the $3.5$~GeV and $4.5$~GeV beam energies with the tunnel geometry parameters $L_T=40$~m and $R_T=2$~m, and the horn design producing a $350$~MeV neutrino beam (see section~\ref{sec:horn}). In table~\ref{tab:thvsE_3545} are reported numerical values, and on figure~\ref{fig:comp5year} are shown the $90$\% CL sensitivity contours. With the $350$~MeV neutrino beam, one can expect a $16$\% improvment with respect to the $260$~MeV neutrino beam. One notices also that there is marginal gain to increase the beam energy from $3.5$~GeV to $4.5$~GeV, as already mentioned. 
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comp5year.eps}
+\caption{\label{fig:comp5year}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$~GeV or $4.5$~GeV, and either a $260$~MeV (default) neutrino beam or a $350$~MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$~m and $R_T = 2$~m. The (\chain) curve corresponds to a $350$~MeV/$4.5$~GeV (neutrino beam/SPL beam energy) setting; the (\dotted) curve corresponds to a $350$~MeV/$3.5$~GeV setting; the (\dashed) curve corresponds to a $260$~MeV/$4.5$~GeV setting and the (\full) curve corresponds to a  $260$~MeV/$3.5$~GeV setting.}
+\end{figure}
+%
+
+There are also variations on the minimum $\sin^22\theta_{13}$ value that may be reached in a $\nu_\mu \rightarrow \nu_e$ experiment which are due to the $\mathrm{sign}(\Delta m^2_{23})$ ambiguity and the $\delta_{CP}$ value. On table~\ref{tab:sign} are presented these kind of variations. Other ambiguities coming from the sign$(\tan(2\theta_{23}))$ ignorance also take place as studied in reference \cite{DONINI}. From figure~9 of this reference, we estimate a 30\% effect on $\sin^2(2\theta_{13})$ sensivity due to these ambiguities.
+%
+\subsection{Mixed positive/negative focusing scenario}
+%
+The combined $\sin^22\theta_{13}$ and $\delta_{CP}$ sensitivity for the 5 years positive focusing scenario and the default parameters of table~\ref{tab:param} is presented on figure~\ref{fig:compDeltaTheta}(a). The results obtained with a $3.5$~GeV and $4.5$~GeV SPL beam are similar and better than with the other energy settings. On figure~\ref{fig:sensiDeltaTheta}(a) the results obtained with a $260$~MeV neutrino beam and a $350$~MeV neutrino beam are presented with a $40$~m long, $2$~m radius decay tunnel. With the $350$~MeV neutrino beam, one can reached better sensitivity results in the range $|\delta_{CP}| < 120^o$, and comparatively the gain obtained when switching from a $3.5$~GeV proton beam to a $4.5$~GeV proton beam is marginal. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:thvseps}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon_{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			      & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$2\%$ & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$5\%$ & $1.48$ & $1.25$ & $1.25$ & $1.48$ & $1.64$ \\
+			$10\%$ & $2.40$ & $2.14$ & $2.21$ & $2.72$ & $3.09$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table}
+\centering
+\caption{\label{tab:sign}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$~GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta_{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			    & $-180^\circ$ & $-90^\circ$ & $0^\circ$ & $90^\circ$ & $180^\circ$\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$+$ & $1.40$ & $0.43$ & $1.16$ & $11.48$ & $1.40$\\
+			$-$ & $1.45$ & $11.75$& $1.11$ & $0.43$  & $1.45$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+To improve the $\delta_{CP}$-independent limit on $\sin^22\theta_{13}$, especially around $\delta_{CP}=90^\circ$, one may envisaged a combination of 2 years with positive focusing and 8 years negative focusing as in references \cite{DONINI,JJG,Mezzetto}. The comparison of the results obtained with different SPL beam energies on the combined sensitivity contours are presented in figure~\ref{fig:compDeltaTheta}(b). Quantitative results with this kind of mixed focusing scenario are reported table \ref{tab:thvsE_td}. One generally gets $10\%$ to $20\%$ better limit on $\sin^22\theta_{13}$ independently of $\delta_{CP}$ with a $3.5$~GeV kinetic energy beam compare to a $2.2$~GeV beam. Doubling the length and the radius of the decay tunnel allows to reach a $10\%$ better limit.
+
+On figure~\ref{fig:sensiDeltaTheta}(b) are presented the results considering the effects of a $350$~MeV neutrino beam obtained either with a $3.5$~GeV proton beam or a $4.5$~GeV proton beam compared to a $260$~MeV neutrino beam obtained with a $4.5$~GeV proton beam. The tunnel geometry parameters are $L_T=40$~m and $R_T=2$~m (other tunnel geometry have been studied but the results are worse and so are not reported). Except in the region $|\delta_{CP}|>150^o$, the results obtained with the $350$~MeV neutrino beam ($3.5$~GeV proton beam) are somewhat better, even if a $11\%$ improvement of the $\delta_{CP}$-independent $\sin^22\theta_{13}$ limit can be reached with the $260$~MeV neutrino beam obtained with the $3.5$~GeV proton beam.
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compDeltaTheta.eps}
+\caption{\label{fig:compDeltaTheta}90\% sensitivity contours obtained with SPL beam energy of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) at $90\%$ CL. Default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensiDeltaTheta.eps}
+\caption{\label{fig:sensiDeltaTheta}90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$~m and $R_T=2$~m and different SPL beam energies ($3.5$~GeV or $4.5$~GeV) and different horn designs ($260$~MeV or $350$~MeV neutrino beams): (\full) curve for a $350$~MeV/$4.5$~GeV setting, (\dotted) curve for a $350$~MeV/$3.5$~GeV setting, (\dashed) curve for a $260$~MeV/$3.5$~GeV setting. Other default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comparaisonFinale.eps}
+\caption{\label{fig:deltathetaFinal}90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite{CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite{Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite{MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite{KOBAYASHI}. The BNL contour has been obtained from reference \cite{BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu_e$ and $\bar{\nu}_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta$ beam was analysed like a reactor experiment with 1\% systematic error \cite{MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$~GeV beam and a decay tunnel of $40$~m length, and $2$~m radius.}
+\end{figure}
+%
+\section{Summary and outlook}
+A complete chain of simulation has been set up for the SPL-Fréjus project. The neutrino production has been extended to the kaon decay contribution, which is important to test SPL energy scenario above $2.2$~GeV.
+
+The beam line optimization has been performed using the sensitivity to $\sin^22\theta_{13}$ and $\delta_{CP}$. The shape of the focusing system has been updated to obtain a neutrino beam energy around $260$~MeV or $350$~MeV.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:thvsE_td}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta_{CP}$ case, and for different decay tunnel length ($L_T$) and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 2 years of positive focusing plus 8 years of negative focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings are identical to those of table~\ref{tab:speciesfluxes}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+setting & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (7b) & (8) & (9)\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$2.2$~GeV &        & $2.52$ &        &        & $2.58$ &        & $2.30$ &        &         &       \\
+$3.5$~GeV & $2.34$ & $2.22$ & $2.10$ & $2.13$ & $2.09$ & $2.08$ & $2.02$ & $2.28$ &  $2.16$ & $2.09$\\
+$4.5$~GeV & $2.91$ & $2.60$ & $2.43$ & $2.48$ & $2.52$ & $2.39$ & $2.34$ & $2.55$ &  $2.53$ & $2.47$\\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+
+In a positive only focusing scenario, the best limit on $\sin^22\theta_{13}$ is $0.82\times10^{-3}$
+ ($90\%$ CL, $\delta_{CP}=0$), with a $4.5$~GeV beam energy and a $20$~m long, $1.5$~m radius decay tunnel. However, the $3.5$~GeV beam may also obtain rather similar limit with $0.83\times10^{-3}$ ($90\%$ CL) with the same tunnel parameters. The $\delta_{CP}$ independant $\sin^22\theta_{13}$ sensitivity is limited to $\approx 10^{-2}$ due to the $\delta_{CP} \approx 90^o$ region.
+ 
+In a mixed focusing scenario, the best limit on $\sin^22\theta_{13}$ independent of $\delta_{CP}$ is $2.02\times10^{-3}$ ($90\%$ CL) obtained with a $3.5$~GeV beam energy and a $40$~m long, $2$~m radius decay tunnel.
+
+The comparison of the optimization presented in this paper with the results obtained by other projects is displayed on figure \ref{fig:deltathetaFinal}. It is presented the 5 years positive focusing scenario, and two versions of a mixed scenario using positive and negative focusing: one scenario duration is 5 years in total and the other one is 10 years running in total and has been used in the previous section. It shows the complementarity of the SPL-Fr\'ejus project with the beta beam-Fr\'ejus project. Especially when considering the sensitivity to $\sin^22\theta_{13}$ for $\delta_{CP}<0$. 
+
+The authors think that the present study may be extended in many respects. The beam line simulation part may be performed with a single simulator as FLUKA (or GEANT4 \cite{GEANT4} for comparison). Other targets may be envisaged (tantalum, carbon) as well as other detector types as a Large Liquid Argon detector \cite{BIGICARUS}. The baseline length may also be revisited as well as the off axis option. The sensitivity analysis may be deeper investigated using the complete set of possible ambiguities as in reference \cite{DONINI}, and the $\theta_{13}$ or $\delta_{CP}$ measurement accuracy with new beam energy scenario may be investigated too.     
+%
+\begin{acknowledgement}
+The authors would like to thank M.~Mezzetto to have expressed his interest since the early stage of this work and to have provided us with his sensitivity computation program. Also the authors thank S.~Gilardoni for fruitful discussions.
+\end{acknowledgement}
+%
+\appendix
+\setcounter{section}{0}
+\section{Decay probability computations}
+\label{sec:decayprobcomp}
+This appendix contains the probability formulas and the algorithms used in the flux computation (see section~\ref{sec:algo}).
+
+\subsection{Pion neutrino probability computation}
+\label{sec:Ppi}
+Pions decay only as $\pi^+\rightarrow \mu^+ + \nu_\mu$ or $\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$ and the neutrinos are emitted isotropically in the pion rest frame, with an energy of about $30$~MeV given by the 2-body decay kinematics. Applying a Lorentz boost knowing the pion momentum and direction, it is possible to compute the probability to reach the detector for the neutrinos. Only neutrino parallel to the beam axis are supposed to pass through the detector fiducial area, and therefore, the neutrino must be emitted by the pion with an angle opposite to the angle between the pion and the beam axis (see figure~\ref{fig:pionDecay}). This gives:
+\begin{equation}
+\mathcal{P}_\pi = \frac{1}{4\pi}\frac{A}{L^2}\frac{1-\beta^2}{(\beta\cos\alpha-1)^2}
+\label{probaPi}
+\end{equation}
+where $\beta$ is the velocity of the pion in the tunnel frame, $A$ is the fiducial detector surface, $L$ the distance between the neutrino source and the detector, and $\alpha$ the angle between the pion direction and the beam axis in the laboratory frame.
+
+\begin{figure}
+\centering
+\includegraphics{../picts/pionDecay.eps}
+\caption{\label{fig:pionDecay}Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha$ is needed.}
+\end{figure}
+
+\subsection{Muon neutrino probability computation}
+\label{sec:Pmu}
+Muons decay only as $\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_\mu$ or $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$, and will produce background events. The mean decay length of the muons is $2$~km, therefore, most of them do not decay in the tunnel. This induces a lack of statistics to estimate the corresponding level of background. This problem has been solved using each muon appearing in the simulation in the following steps:
+\begin{enumerate}
+	\item the probability for the muon to decay into the tunnel has been computed using a straight line propagation;
+	\item the available energy for the neutrino in the tunnel frame has been divided in $20$~MeV energy bins; 
+	% (the number of bin depending of the muon energy).
+	\item one $\nu_e$ and one $\nu_\mu$ have been simulated in each of the energy bins (step 2). Then, the probability to reach the detector has been computed, and multiplied by the probability computed at step (1).%the neutrino energy is stored in an histogram, weighted with this probability and 
+\end{enumerate}
+After the probability computation, the non useful muon is discarded by GEANT to gain in CPU time. 
+
+The probability for the muon neutrino and the electron neutrino to be emitted parallel to the beam axis is \cite{donega}:
+\begin{multline}
+\frac{d\mathcal{P}_\mu}{dE_\nu} = \frac{1}{4\pi}\frac{A}{L^2}\frac{2}{m_\mu}\frac{1}{\gamma_\mu(1+\beta_\mu\cos\theta^*)}\\ \times \frac{1-\beta_\mu^2}{(\beta_\mu\cos\rho-1)^2}\left[f_0(x)\mp \Pi_\mu^L f_1(x)\cos\theta^*\right]
+\label{probaMu}
+\end{multline}
+where $\beta_\mu$ and $\gamma_\mu$ are the velocity and the Lorentz boost of the muon in the tunnel frame, $\theta^*$ is the angle with respect to the beam axis of the muon in the muon rest frame, $\rho$ is the corresponding angle in the tunnel frame. Like in the pion case, this angle appears because the neutrino must be parallel to the beam axis. $\Pi_\mu^L$ is the muon longitudinal polarization, the parameter $x$ is defined as $x=2E_\nu^*/m_\mu$ where $E_\nu^*$ is the neutrino energy in the muon rest frame, and the function $f_0(x)$ and $f_1(x)$ coming from the matrix element of the muon decay are given in table~\ref{tab:Function}. The sign in front of $\Pi_\mu^L$ in equation~\ref{probaMu} is $(-)$ for the $\mu^+$ decays and $(+)$ for the $\mu^-$ decays, respectively.
+
+%\Table{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%\br
+%		      &  $f_0(x)$ & $f_1(x)$ \\
+%\mr
+%		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+%		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		      &  $f_0(x)$ & $f_1(x)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+Muon polarization is computed using the conservation of the transverse component of the velocity four-vector $\gamma(1,\beta)$ between the muon rest frame (where the polarization is computed) and the pion rest frame, where the muon helicity is $-1$, due to the parity non conservation. It yields \cite{picasso}:
+\begin{equation}
+\Pi_\mu^T = \frac{\gamma_\pi\beta_\pi}{\gamma_\mu\beta_\mu}\sin\theta^*
+\mbox{ and }\Pi_\mu^L = \sqrt{1-\Pi_\mu^{T2}}
+\label{pola}
+\end{equation}
+where $\gamma_\pi$, $\beta_\pi$, $\gamma_\mu$, and $\beta_\mu$ are the Lorentz boost and velocity of the pion and of the muon in the tunnel frame, and $\theta^*$ the angle with respect to the beam axis of the muon in the pion rest frame.
+
+\subsection{The treatment of the kaons}
+\label{sec:kaons}
+Contrary to pions and muons, kaons have many decay channels. They are summarized in table~\ref{tab:BRKP0SL}.
+
+%\Table{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%\br
+%\centre{2}{$K^\pm$}                                               & \centre{2}{$K^0_L$}     &          \centre{2}{$K^0_S$}\\
+%\mr
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu$   & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+%$\pi^\pm\pi^0$ & $21.17\%$                                        & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+%$\pi^\pm\pi^+\pi^-$ & $5.59\%$                                    & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+%$e^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+%$\pi^\pm\pi^0\pi^0$ & $1.73\%$                                    & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+\centre{2}{$K^\pm$}         & \centre{2}{$K^0_L$}     & \centre{2}{$K^0_S$}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$\mu^\pm\nu_\mu$ & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+$\pi^\pm\pi^0$ & $21.17\%$   & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+$\pi^\pm\pi^+\pi^-$ & $5.59\%$ & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+$e^\pm\nu_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+$\mu^\pm\nu_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+$\pi^\pm\pi^0\pi^0$ & $1.73\%$ & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+There is a very small amount of kaons produced (section~\ref{sec:kaon}), and this number has been artificially increased in order to obtain statistically significant results.  The multiplicity of decay channels makes impossible the method used for the muon case (\ref{sec:Pmu}). The method chosen for the good compromise between the gain in CPU and the statistical uncertainty of the results, is to duplicate many times each kaon exiting the target. The number of duplication varies between 10 and 300. It depends on the initial kaon rate and therefore on the beam energy.
+
+All the kaons daughter particles are tracked by GEANT until they decay. Three different types of daughter particles are identified in the kaon decays. The first type corresponds to primary neutrinos, the second type concerns charged pions and muons, and the neutral pions are left for the last type.
+
+In the $K^\pm\rightarrow\mu^\pm \nu_\mu(\bar{\nu}_\mu)$ decay modes, the computation of the probability for a neutrino to reach the detector is the same than the 2-body decay formula used to in the pion decay (equation~\ref{probaPi}), where $\beta$ is now the kaon velocity, and $\alpha$ the angle of the kaon with respect to the beam axis. 
+
+When a neutrino is produced by a kaon 3-body decay, the probability to reach the detector is computed using a pure phase space formula. It yields:
+\begin{multline}
+\mathcal{P}_K = \frac{1}{4\pi}\frac{A}{L^2}\frac{1}{m_K-m_\pi-m_l} \\ \times \frac{1}{\gamma_K(1+\beta_K\cos\theta^*)}
+\frac{1-\beta_K^2}{(\beta_K\cos\delta-1)^2}
+\label{probaL}
+\end{multline}
+where $m_K$ is the kaon mass (charged or neutral), $m_\pi$ is the pion mass ($\pi^0$ mass in $K^\pm$ decays and $\pi^\pm$ mass in $K_L^0$ decays), and $m_l$ is the mass of the lepton associated with the neutrino. The $\beta_K$ and $\gamma_K$ are the velocity and the Lorentz boost of the kaon, $\theta^*$ is the angle between the neutrino direction and the kaon direction, in the kaon rest frame. Finally, $\delta$ is the angle between the kaon direction and the beam axis in the tunnel frame.
+
+When a $\pi^\pm$ is produced in the kaon decay chain, it is tracked by GEANT until it decays, and the probability of equation~\ref{probaPi} is applied to the produced neutrino. In case of a muon, it is treated as explained in \ref{sec:Pmu}. The muon polarization is computed this time using the kaon decay informations. Finally, when a $\pi^0$ is produced, as it cannot create neutrinos, it is simply discarded.
+
+%
+%\section*{References}
+\begin{thebibliography}{99}
+%
+%\bibitem{SKNU04}
+%Kearns E [SuperKamiokande Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%
+%\bibitem{K2KNU04}
+%Nakaya T [K2K Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%
+%\bibitem{MINOS}
+%Thomson T [MINOS Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%\nonum Adamson P \etal NuMi-L-337
+%
+%\bibitem{OPERA}
+%Autiero D [OPERA Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)\\
+%Guler M \etal \textit{ Experiment proposal} CERN/SPSC 2000-028 SPSC/P318 LNGS P25/2000 
+%
+%\bibitem{ICARUS}
+%Guler M \etal [ICARUS Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%\nonum Aprili P \etal CERN-SPSC-2002-027
+%
+%\bibitem{CNGS}
+%Acquistapace G \etal CERN-98-02
+%
+%\bibitem{LSND}
+%Athanassopoulos A \etal [LSND Collaboration] 1998 \PRL {\bf 81} 1774
+%\nonum Aguilar A \etal [LSND Collaboration] 2001 \PR D {\bf 64} 112007
+%
+%\bibitem{MINIBOONE}
+%Stancu I \etal [MiniBooNE Collaboration] FERMILAB-TM-2207
+%
+%\bibitem{PMNS}
+%Pontecorvo B  1957 \textit{Sov. Phys.--JETP} {\bf 6} 429 [1957 \textit{Zh. Eksp. Teor. Fiz.} \textbf{33} 549]
+%\nonum Maki Z, Nakagawa M and Sakata S 1962 \textit{Prog. Theor. Phys.} \textbf{28} 870\\
+%Pontecorvo B 1968 \textit{Sov. Phys.--JETP} \textbf{26}  984 [1967 \textit{Zh. Eksp. Teor. Fiz.} \textbf{53} 1717]
+%\nonum Gribov V N and Pontecorvo B 1969 \PL B \textbf{28} 493
+%
+%\bibitem{CHOOZ}
+%Apollonio M \etal  [CHOOZ Collaboration] 1999 \PL B {\bf 466} 415
+%\nonum Apollonio M \etal  [CHOOZ Collaboration] 2003 \EJP C {\bf 27}  331
+%
+%\bibitem{Wpaper}
+%Anderson K \etal 2004 \textit{White paper report on using nuclear reactors to search for a value of $\theta_{13}$} http://www.hep.anl.gov/minos/reactor13/reactor13.pdf
+%
+%\bibitem{BETABEAM}
+%Zucchelli P 2002 \PL B \textbf{532} 166
+%
+%\bibitem{NOVA}
+%Ambats I \etal 2004 NO$\nu$A proposal FNAL P929
+%
+%\bibitem{T2K}
+%Itow Y 2001 KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05 \\
+%see also arXiv:hep-ex/0106019
+%
+%\bibitem{BNLHS}
+%Diwan M V 2003 \PR D {\bf 68} 012002
+%
+%\bibitem{CERN}
+%Blondel A \etal CERN-2004-002
+%
+%\bibitem{DONINI}
+%Donini A \etal 2004 IFT-UAM/CSIC-04-30\\
+%see also arXiv:hep-ph/0406132.
+%
+%\bibitem{DOUBLE-CHOOZ}
+%Dalnoki-Veress F for the Double-CHOOZ project arXiv:hep-ex/0406070
+%
+%\bibitem{SPL}
+%Autin B \etal CERN-2000-12
+%
+%\bibitem{UNO} 
+%The UNO whitepaper \textit{Physics Potential and Feasibility of UNO} (preprint SBHEP01-3) (see also http://ale.physics.sunysb.edu/uno/)
+%
+%\bibitem{mosca}
+%Mosca L 2004 Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+%
+%\bibitem{Meer}
+%van der Meer S 1961 CERN-Report No 61-7
+%
+%\bibitem{nuFact134} 
+%Campagne J E and Cazes A 2003 CERN-NUFACT-Note-134\\ http://slac.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{MMWPSCazes} 
+%Campagne J E and Cazes A 2004 Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 \\
+%http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+%
+%\bibitem{JJG}
+%G\'omez Gadenas J J \etal 2001 IFIC/01-31 \\
+%see also arXiv:hep-ph/0105297
+%
+%\bibitem{Mezzetto}
+%Mezzetto M 2003 \jpg {\bf 29} 1781-1784\\
+%see also arXiv:hep-ex/0302005
+%
+%
+%\bibitem{nuFact138} 
+%Campagne J E 2004 CERN-NUFACT-Note-138\\
+% http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{fluka}
+%Fasso A \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, Kling A \etal - eds., Springer-Verlag Berlin, p159-164 (2001);
+%\nonum Fasso A \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, Kling A \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+%
+%\bibitem{MMWPSGaroby} 
+%Garoby R 2004 Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+%
+%\bibitem{harp}
+%Catanesi C \etal [HARP Collaboration] CERN-SPSC 2002/019
+%
+%\bibitem{MARS}
+%Mokhov N V \etal 1995 The MARS Code System User Guide, Version 13(95), Fermilab-FN-628
+%\nonum Mokhov N V \etal 1998 MARS oed Develepments; LANL Report LA-UR-98-5716, nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+%
+%\bibitem{FLUKAprivate}
+%Battistoni G and Ferrari A \textit{private communication}
+%
+%\bibitem{geant}
+%Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+%
+%\bibitem{SIMONE1}
+%Gilardoni S 2003 Talk at NuFact03 http://www.cap.bnl.gov/nufact03/
+%
+%\bibitem{donega}
+%Blondel A \etal 2001 CERN-NUFACT-Note-78\\
+% http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{MEZZETTONUFACT060}
+%Mezzetto M 2000 CERN-NUFACT-Note-60\\
+% http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{DONINI-2}
+%Donini A, Meloni D and Rigolin S 2004 J. High Energy Phys. \textbf{0406} 011\\
+%see also arXiv:hep-ph/0312072
+%
+%\bibitem{NUANCE}
+%Casper D  2002\textit{ Nucl. Phys. Proc. Suppl.} \textbf{112} 161-170\\
+%see also arXiv:hep-ph/0208030
+%
+%
+%\bibitem{KAMLAND}
+%Gratta G [KamLAND Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%
+%\bibitem{GEANT4}
+%Agostinelli A \etal [GEANT4 Collaboration] 2003 \NIM A \textbf{506} 250-503
+%
+%\bibitem{Gaisser}
+%Gaisser T K 1990 \textit{Cosmic Rays and Particle Physics} Cambridge University Press 
+%
+%\bibitem{picasso}
+%Combley F and Picasso E 1974 \textit{Phys. Rept.} {\bf 14} 1
+%
+%\bibitem{pdg}
+%Hagiwara K \etal 2002 \PR D {\bf 66}  010001
+%
+\bibitem{SKNU04}
+E. Kearns [SuperKamiokande Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{K2KNU04}
+T. Nakaya [K2K Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{MINOS}
+T. Thomson [MINOS Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement);
+P. Adamson \etal, NuMi-L-337 (unpublished)
+
+\bibitem{OPERA}
+D. Autiero [OPERA Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement);
+M. Guler  \etal, \textsl{Experiment proposal} CERN/SPSC 2000-028 SPSC/P318 LNGS P25/2000 (unpublished) 
+
+\bibitem{ICARUS}
+M. Guler  [ICARUS Collaboration], in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement);
+P. Aprili \etal, CERN-SPSC-2002-027 (unpublished)
+
+\bibitem{CNGS}
+G. Acquistapace  \etal, CERN-98-02 (unpublished)
+
+\bibitem{LSND}
+A. Athanassopoulos \etal, \PRL {\bf 81}, 1774  (1998);
+A. Aguilar \etal, \PR D {\bf 64}, 112007 (2001) 
+
+\bibitem{MINIBOONE}
+I. Stancu \etal, FERMILAB-TM-2207 (unpublished)
+
+\bibitem{PMNS}
+B. Pontecorvo \textsl{Sov. Phys.--JETP} {\bf 6}, 429 (1957) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{33}, 549 (1957)];
+Z. Maki, M. Nakagawa and S. Sakata \textsl{Prog. Theor. Phys.} \textbf{28}, 870 (1962);
+Pontecorvo B \textsl{Sov. Phys.--JETP} \textbf{26},  984 (1968) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{53}, 1717 (1967)];
+V. N. Gribov and B. Pontecorvo \PL B \textbf{28}, 493 (1969) 
+
+\bibitem{CHOOZ}
+M. Apollonio \etal, \PL B {\bf 466}, 415 (1999);
+M. Apollonio \etal, \EJP C {\bf 27},  331 (2003)
+
+\bibitem{Wpaper}
+K. Anderson \etal, \textsl{White paper report on using nuclear reactors to search for a value of $\theta_{13}$} (2004), http://www.hep.anl.gov/minos/reactor13/reactor13.pdf (unpublished); 
+F.~Arbelier \etal, \textsl{Letter of Intend for Double-CHOOZ}, arXiv:hep-ex/0405032 (unpublished)
+
+\bibitem{BETABEAM}
+P. Zucchelli, \PL B \textbf{532}, 166 (2002) 
+
+\bibitem{NOVA}
+I. Ambats \etal,  NO$\nu$A proposal FNAL P929, 2004 (unpublished)
+
+\bibitem{T2K}
+Y. Itow, KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05 (unpublished),
+see also arXiv:hep-ex/0106019
+
+\bibitem{BNLHS}
+M. V. Diwan, \PR D {\bf 68}, 012002 (2003)
+
+\bibitem{CERN}
+A. Blondel \etal, CERN-2004-002 (unpublished)
+
+\bibitem{DONINI}
+A. Donini \etal, IFT-UAM/CSIC-04-30, 2004 (unpublished);
+see also arXiv:hep-ph/0406132
+
+\bibitem{DOUBLE-CHOOZ}
+F. Dalnoki-Veress, the Double-CHOOZ project arXiv:hep-ex/0406070 (unpublished)
+
+\bibitem{SPL}
+B. Autin \etal, CERN-2000-12 (unpublished)
+
+\bibitem{UNO} 
+The UNO whitepaper, \textsl{Physics Potential and Feasibility of UNO}, SBHEP01-3 (unpublished), see also http://ale.physics.sunysb.edu/uno/
+
+\bibitem{mosca}
+L. Mosca, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Meer}
+S. van der Meer, CERN-Report No 61-7, 1961 (unpublished)
+
+\bibitem{nuFact134} 
+J.E. Campagne and A. Cazes, CERN-NUFACT-Note-134, 2003 (unpublished), see http://slac.web.cern.ch/slap/NuFact/NuFact/\\
+NFNotes.html
+
+\bibitem{MMWPSCazes} 
+J.E. Campagne and A. Cazes, Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004,
+see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{JJG}
+J.J. G\'omez Gadenas \etal,  IFIC/01-31, Proceedings of Venice 2001, Neutrino telescopes, vol. 2, p463-481;
+see also arXiv:hep-ph/0105297; A. Blondel \etal, \NIM A {\bf 503} 173 (2001);
+A. Blondel \etal, CERN-2004-002
+
+\bibitem{Mezzetto}
+M. Mezzetto,  \jpg {\bf 29}, 1781-1784 (2003),
+see also arXiv:hep-ex/0302005
+
+
+\bibitem{nuFact138} 
+J.E. Campagne, CERN-NUFACT-Note-138, 2004 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{fluka}
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p159-164 (2001);
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+
+\bibitem{MMWPSGaroby} 
+R. Garoby, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{harp}
+C. Catanesi \etal, CERN-SPSC 2002/019 (unpublished)
+
+\bibitem{minerva} 
+D. Drakoulakos \etal, Fermilab P-938 (unpublished),
+see also arXiv:hep-ex/405002
+
+\bibitem{MARS}
+N.V. Mokhov \etal, The MARS Code System User Guide, Version 13(95), Fermilab-FN-628 (1995);
+N.V. Mokhov  \etal, MARS oed Develepments, LANL Report LA-UR-98-5716 (1998), nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+
+\bibitem{FLUKAprivate}
+G. Battistoni and A. Ferrari, \textsl{private communication}
+
+\bibitem{geant}
+Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+
+\bibitem{SIMONE1}
+S. Gilardoni, Talk at NuFact03 (2003), see http://www.cap.bnl.gov/nufact03/
+
+\bibitem{donega}
+A. Blondel \etal, CERN-NUFACT-Note-78, 2001 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{MEZZETTONUFACT060}
+M. Mezzetto, CERN-NUFACT-Note-60, 2000 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+
+\bibitem{DONINI-2}
+A. Donini, D. Meloni and S. Rigolin, J. High Energy Phys. \textbf{0406}, 011 (2004),
+see also arXiv:hep-ph/0312072
+
+\bibitem{NUANCE}
+D. Casper, \textsl{ Nucl. Phys. Proc. Suppl.} \textbf{112}, 161-170 (2002),
+see also arXiv:hep-ph/0208030
+
+
+\bibitem{KAMLAND}
+G. Gratta, in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{MIGLIOZZITERANOVA}
+M. Komatsu, P Migliozzi and F. Terranova,  \jpg {\bf 29}, 443 (2003); see also arXiv:hep-ph/0210043
+
+\bibitem{KOBAYASHI}
+T. Kobayashi, in \textit{Proceedings of the International Conference NEUTRINO 2004},  to be published in \NP B (Proceedings Supplement)
+
+\bibitem{BNL}
+ M.V. Diwan \etal, \PR D \textbf{68}, 012002 (2003); see also figure~8 of 
+arXiv:hep-ph/0303081
+
+\bibitem{MAOROPRIVATE}
+M. Mezzetto, \textsl{private communication}: the corresponding $\theta_{13}$ limit is $3.4^o$.
+
+\bibitem{GEANT4}
+A. Agostinelli \etal, \NIM A \textbf{506}, 250-503 (2003) 
+
+\bibitem{BIGICARUS}
+A. Ereditato and A. Rubia, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Gaisser}
+T.K. Gaisser, \textsl{Cosmic Rays and Particle Physics} (Cambridge University Press, 1990)  
+
+\bibitem{picasso}
+F. Combley and E. Picasso, \textsl{Phys. Rept.} {\bf 14}, 1 (1974) 
+
+\bibitem{pdg}
+K. Hagiwara \etal,  \PR D {\bf 66},  010001 (2002)
+
+
+%
+\end{thebibliography}
+%
+\end{document}
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3.aux
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3.aux	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3.aux	(revision 392)
@@ -0,0 +1,224 @@
+\relax 
+\citation{SKNU04,K2KNU04}
+\citation{K2KNU04}
+\citation{MINOS}
+\citation{OPERA,ICARUS}
+\citation{CNGS}
+\citation{LSND}
+\citation{MINIBOONE}
+\citation{PMNS}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{BETABEAM}
+\citation{NOVA,T2K}
+\citation{T2K,BNLHS,CERN}
+\citation{CERN}
+\citation{DONINI}
+\citation{DONINI,DOUBLE-CHOOZ}
+\citation{SPL}
+\citation{UNO}
+\citation{mosca}
+\citation{CERN}
+\citation{Meer}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Sketch of the SPL neutrino Superbeam from CERN to the Fr\'ejus tunnel.}}{1}}
+\newlabel{fig:Sbeam}{{1}{1}}
+\citation{nuFact134,MMWPSCazes}
+\citation{DONINI,JJG,Mezzetto}
+\citation{nuFact138}
+\citation{fluka}
+\citation{CERN}
+\citation{JJG}
+\citation{CERN}
+\citation{SPL}
+\citation{MMWPSGaroby}
+\citation{nuFact134}
+\citation{harp}
+\citation{MARS}
+\citation{nuFact134}
+\citation{MMWPSGaroby}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Liquid mercury jet parameters.}}{2}}
+\newlabel{tab:targ}{{1}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Target simulation}{2}}
+\newlabel{sec:target}{{2}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Kaon production}{2}}
+\newlabel{sec:kaon}{{3}{2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  (a) $\pi ^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi ^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$\nobreakspace  {}GeV/c and $0.7$\nobreakspace  {}GeV/c. The different SPL beam kinetic energies presented are (\mbox {------}) $2.2$\nobreakspace  {}GeV, (\mbox {- - - -}) $3.5$\nobreakspace  {}GeV, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) $4.5$\nobreakspace  {}GeV and (\mbox {--- $\cdot $ ---}) $6.5$\nobreakspace  {}GeV.}}{3}}
+\newlabel{fig:compEner2}{{2}{3}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces $\pi ^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\mbox {- - - -}) and by MARS (\mbox {------}).}}{3}}
+\newlabel{fig:compFlukaMars}{{3}{3}}
+\citation{FLUKAprivate}
+\citation{geant}
+\citation{SIMONE1}
+\citation{nuFact138}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Average numbers of the most relevant secondary particles exiting the $30$\nobreakspace  {}cm long, $1.5$\nobreakspace  {}cm diameter mercury target per incident proton (FLUKA). The $\mu ^+/\mu ^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}}{4}}
+\newlabel{tab:nbPart}{{2}{4}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Horns simulation}{4}}
+\newlabel{sec:horn}{{4}{4}}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Relevant parameters of the horns in case of the generation of a $260$\nobreakspace  {}MeV neutrino beam (or $350$\nobreakspace  {}MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$\nobreakspace  {}MeV/c (or $800$\nobreakspace  {}MeV/c) pion momentum.}}{4}}
+\newlabel{tab:specif}{{3}{4}}
+\citation{donega}
+\citation{donega}
+\citation{donega}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).}}{5}}
+\newlabel{fig:KaonsPions}{{4}{5}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350\nobreakspace  {}MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}}{5}}
+\newlabel{fig:plan}{{5}{5}}
+\@writefile{toc}{\contentsline {section}{\numberline {5}Particle decay treatment and flux calculation}{5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Algorithm description}{5}}
+\newlabel{sec:algo}{{5.1}{5}}
+\citation{donega}
+\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Number of protons on target for different beam energy at 4\nobreakspace  {}MW constant power. One year is defined as $10^7$\nobreakspace  {}s.}}{6}}
+\newlabel{tab:proton}{{4}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Validation of the algorithm}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Simulated fluxes}{6}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  Neutrino fluxes, $100$\nobreakspace  {}km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$\nobreakspace  {}GeV (4\nobreakspace  {}MW), a decay tunnel with a length of $20$\nobreakspace  {}m and a radius of $1$\nobreakspace  {}m. The top left panel contains the $\nu _\mu $ fluxes, and the top right panel shows the $\mathaccentV {bar}016{\nu }_\mu $ fluxes. The bottom left panel presents the $\nu _e$ fluxes while the bottom right panel displays the $\mathaccentV {bar}016{\nu }_e$ fluxes. The (\mbox {------}) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\mbox {- - - -}) curve is the contribution from the charged kaon decay chain, and the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}}{7}}
+\newlabel{fig:flux22p}{{6}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but the horns are focusing negative particles.}}{7}}
+\newlabel{fig:flux22m}{{7}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{8}}
+\newlabel{fig:flux45p}{{8}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{8}}
+\newlabel{fig:flux45m}{{9}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{9}}
+\newlabel{fig:flux8p}{{10}{9}}
+\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{9}}
+\newlabel{fig:flux8m}{{11}{9}}
+\citation{UNO}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{Mezzetto}
+\citation{DONINI-2}
+\citation{NUANCE}
+\citation{MEZZETTONUFACT060}
+\citation{mosca}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Integral of the total flux of the different species with different settings. The $\nu _\mu $ and $\mathaccentV {bar}016{\nu }_\mu $ fluxes are expressed in $10^{13}/100\@mathrm {m}^2/y$ unit while the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes are expressed in $10^{11}/100\@mathrm {m}^2/y$ unit. The positive focusing and negative focusing are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. }}{10}}
+\newlabel{tab:speciesfluxes}{{5}{10}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Sensitivity computation ingredients}{10}}
+\@writefile{toc}{\contentsline {section}{\numberline {7}Results}{10}}
+\newlabel{sec:results}{{7}{10}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}The positive only focusing scenario}{10}}
+\citation{DONINI}
+\citation{DONINI,JJG,Mezzetto}
+\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Comparison between the probability method, (\mbox {------}) curve, and the full GEANT simulation method, (\mbox {- - - -}) curve, for the $\nu _\mu $ from $\pi ^+$ flux (a) and the $\mathaccentV {bar}016{\nu }_\mu $ from $\pi ^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes contrary to the former simulation.}}{11}}
+\newlabel{fig:compGeantDonega}{{12}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Default parameters used to compute the sensitivity curves \cite  {MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite  {KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite  {JJG}.}}{11}}
+\newlabel{tab:param}{{6}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Number of events for 5 years positive focusing scenario with default parameters of table\nobreakspace  {}6\hbox {}. Other backgrounds are $\pi ^0$, $\nu _\mu $-elast., $\mu /e$-missId. }}{12}}
+\newlabel{tab:nbvsE}{{7}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Sensitivity contours obtained with a SPL energy of $3.5$\nobreakspace  {}GeV and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m. (\mbox {------}), (\mbox {- - - -}) and (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}}{12}}
+\newlabel{fig:sensi45}{{13}{12}}
+\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{12}}
+\newlabel{tab:thvsE}{{8}{12}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Mixed positive/negative focusing scenario}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{12}}
+\newlabel{fig:compSensi}{{14}{12}}
+\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) at and radius ($R_T$) for the $3.5$\nobreakspace  {}GeV and $4.5$\nobreakspace  {}GeV scenarios and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}). Settings in parenthesis are identical to those of table\nobreakspace  {}5\hbox {}, except that the setting (7b) corresponds to the tunnel geometry of setting (7) but the horn geometry producing a $350$\nobreakspace  {}MeV neutrino beam is used. We remind that the setting (2) is the default one, and the settings (7) and (7b) corresponds to $L_T = 40$\nobreakspace  {}m and $R_T = 2$\nobreakspace  {}m.}}{13}}
+\newlabel{tab:thvsE_3545}{{9}{13}}
+\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta _{CP}$ case, and for different decay tunnel length ($L_T$) and radius ($R_T$) for the $3.5$\nobreakspace  {}GeV and $4.5$\nobreakspace  {}GeV scenarios and 2 years of positive focusing plus 8 years of negative focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}). Settings are identical to those of table\nobreakspace  {}5\hbox {}.}}{13}}
+\newlabel{tab:thvsE_td}{{12}{13}}
+\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV, and either a $260$\nobreakspace  {}MeV (default) neutrino beam or a $350$\nobreakspace  {}MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$\nobreakspace  {}m and $R_T = 2$\nobreakspace  {}m. The (\mbox {--- $\cdot $ ---}) curve corresponds to a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV (neutrino beam/SPL beam energy) setting; the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve corresponds to a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting; the (\mbox {- - - -}) curve corresponds to a $260$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting and the (\mbox {------}) curve corresponds to a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting.}}{13}}
+\newlabel{fig:comp5year}{{15}{13}}
+\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon _{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:thvseps}{{10}{13}}
+\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$\nobreakspace  {}GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta _{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:sign}{{11}{13}}
+\@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{13}}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\citation{GEANT4}
+\citation{BIGICARUS}
+\citation{DONINI}
+\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces 90\% sensitivity contours obtained with SPL beam energy of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) at $90\%$ CL. Default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{14}}
+\newlabel{fig:compDeltaTheta}{{16}{14}}
+\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces 90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$\nobreakspace  {}m and $R_T=2$\nobreakspace  {}m and different SPL beam energies ($3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV) and different horn designs ($260$\nobreakspace  {}MeV or $350$\nobreakspace  {}MeV neutrino beams): (\mbox {------}) curve for a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve for a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting, (\mbox {- - - -}) curve for a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting. Other default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}}{14}}
+\newlabel{fig:sensiDeltaTheta}{{17}{14}}
+\@writefile{toc}{\contentsline {section}{\numberline {A}Decay probability computations}{14}}
+\newlabel{sec:decayprobcomp}{{A}{14}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}Pion neutrino probability computation}{14}}
+\newlabel{sec:Ppi}{{A.1}{14}}
+\citation{donega}
+\citation{Gaisser}
+\citation{picasso}
+\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces 90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite  {CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite  {Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite  {MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite  {KOBAYASHI}. The BNL contour has been obtained from reference \cite  {BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta $ beam was analysed like a reactor experiment with 1\% systematic error \cite  {MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$\nobreakspace  {}GeV beam and a decay tunnel of $40$\nobreakspace  {}m length, and $2$\nobreakspace  {}m radius.}}{15}}
+\newlabel{fig:deltathetaFinal}{{18}{15}}
+\newlabel{probaPi}{{1}{15}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Muon neutrino probability computation}{15}}
+\newlabel{sec:Pmu}{{A.2}{15}}
+\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha $ is needed.}}{15}}
+\newlabel{fig:pionDecay}{{19}{15}}
+\@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces Flux function in the muon rest frame \cite  {Gaisser}.}}{15}}
+\newlabel{tab:Function}{{13}{15}}
+\newlabel{probaMu}{{2}{15}}
+\citation{pdg}
+\bibcite{SKNU04}{1}
+\bibcite{K2KNU04}{2}
+\bibcite{MINOS}{3}
+\bibcite{OPERA}{4}
+\bibcite{ICARUS}{5}
+\bibcite{CNGS}{6}
+\bibcite{LSND}{7}
+\bibcite{MINIBOONE}{8}
+\bibcite{PMNS}{9}
+\bibcite{CHOOZ}{10}
+\bibcite{Wpaper}{11}
+\bibcite{BETABEAM}{12}
+\bibcite{NOVA}{13}
+\bibcite{T2K}{14}
+\bibcite{BNLHS}{15}
+\bibcite{CERN}{16}
+\bibcite{DONINI}{17}
+\bibcite{DOUBLE-CHOOZ}{18}
+\bibcite{SPL}{19}
+\bibcite{UNO}{20}
+\@writefile{lot}{\contentsline {table}{\numberline {14}{\ignorespaces Charged and neutral kaon decay channels \cite  {pdg}.}}{16}}
+\newlabel{tab:BRKP0SL}{{14}{16}}
+\newlabel{pola}{{3}{16}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.3}The treatment of the kaons}{16}}
+\newlabel{sec:kaons}{{A.3}{16}}
+\newlabel{probaL}{{4}{16}}
+\bibcite{mosca}{21}
+\bibcite{Meer}{22}
+\bibcite{nuFact134}{23}
+\bibcite{MMWPSCazes}{24}
+\bibcite{JJG}{25}
+\bibcite{Mezzetto}{26}
+\bibcite{nuFact138}{27}
+\bibcite{fluka}{28}
+\bibcite{MMWPSGaroby}{29}
+\bibcite{harp}{30}
+\bibcite{minerva}{31}
+\bibcite{MARS}{32}
+\bibcite{FLUKAprivate}{33}
+\bibcite{geant}{34}
+\bibcite{SIMONE1}{35}
+\bibcite{donega}{36}
+\bibcite{MEZZETTONUFACT060}{37}
+\bibcite{DONINI-2}{38}
+\bibcite{NUANCE}{39}
+\bibcite{KAMLAND}{40}
+\bibcite{MIGLIOZZITERANOVA}{41}
+\bibcite{KOBAYASHI}{42}
+\bibcite{BNL}{43}
+\bibcite{MAOROPRIVATE}{44}
+\bibcite{GEANT4}{45}
+\bibcite{BIGICARUS}{46}
+\bibcite{Gaisser}{47}
+\bibcite{picasso}{48}
+\bibcite{pdg}{49}
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3.blg
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3.blg	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3.blg	(revision 392)
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+(There were 2 error messages)
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3.log
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3.log	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3.log	(revision 392)
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@@ -0,0 +1,1205 @@
+%\documentclass[epj,nopacs,referee]{svjour}
+%remove referee for final version
+\documentclass[epj,nopacs]{svjour}
+%----------------------------------------------------------------------------
+%
+\usepackage[T1]{fontenc}
+\usepackage[latin1]{inputenc}
+\usepackage{graphicx}
+\usepackage{epsfig}
+\usepackage{amssymb}
+\usepackage{amsmath}
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+%
+% abbreviations for IOPP journals
+%
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+\newcommand{\DSE}{{\it Distrib. Syst. Engng\/} }
+\newcommand{\EJP}{{\it Eur. J. Phys.} } 
+\newcommand{\HPP}{{\it High Perform. Polym.} }              % added 4/5/93
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+\newcommand{\JOB}{{\it J. Opt. B: Quantum Semiclass. Opt.} }
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+\newcommand{\JPC}{{\it J. Phys. C: Solid State Phys.} }   %1968--1988
+\newcommand{\JPCM}{{\it J. Phys.: Condens. Matter\/} }    %1989 and onwards
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+\newcommand{\JPE}{{\it J. Phys. E: Sci. Instrum.} }
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+\newcommand{\jpg}{{\it J. Phys. G: Nucl. Part. Phys.} }   %1989 and onwards
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+\newcommand{\MST}{{\it Meas. Sci. Technol.} }                 %1990 and onwards
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+\newcommand{\NJP}{{\it New J. Phys.} }
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+\newcommand{\NT}{{\it Nanotechnology} }
+\newcommand{\PAO}{{\it Pure Appl. Optics\/} }
+\newcommand{\PM}{{\it Physiol. Meas.} }                        % added 4/5/93
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+\newcommand{\PPCF}{{\it Plasma Phys. Control. Fusion\/} }      % added 4/5/93
+\newcommand{\PSST}{{\it Plasma Sources Sci. Technol.} }
+\newcommand{\PUS}{{\it Public Understand. Sci.} }
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+\newcommand{\QSO}{{\em Quantum Semiclass. Opt.} }
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+\newcommand{\SLC}{{\it Sov. Lightwave Commun.} }               % added 4/5/93 
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+\newcommand{\WRM}{{\it Waves Random Media\/} }
+\newcommand{\JMM}{{\it J. Micromech. Microeng.\/} }
+%
+% Other commonly quoted journals
+%
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+\newcommand{\AM}{{\it Acta Metall.} }
+\newcommand{\AP}{{\it Ann. Phys., Lpz.} }
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+\newcommand{\APP}{{\it Ann. Phys., Paris\/} }
+\newcommand{\CJP}{{\it Can. J. Phys.} }
+\newcommand{\JAP}{{\it J. Appl. Phys.} }
+\newcommand{\JCP}{{\it J. Chem. Phys.} }
+\newcommand{\JJAP}{{\it Japan. J. Appl. Phys.} }
+\newcommand{\JP}{{\it J. Physique\/} }
+\newcommand{\JPhCh}{{\it J. Phys. Chem.} }
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+\newcommand{\JMP}{{\it J. Math. Phys.} }
+\newcommand{\JOSA}{{\it J. Opt. Soc. Am.} }
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+\newcommand{\SSC}{{\it Solid State Commun.} }
+\newcommand{\ZP}{{\it Z. Phys.} }
+
+\newcommand{\etal}{{et al.\/}}
+%
+%
+%----------------------------------------------------------------------------
+\begin{document}
+%
+\title{The $\theta_{13}$ and $\delta_{CP}$ sensitivities of the SPL-Fréjus project revisited}
+\author{Jean Eric Campagne, Antoine Cazes}
+\institute{ Laboratoire de l'Accélérateur Linéaire -
+Université Paris-Sud - B\^at. 200 - BP 34 -
+91898 Orsay Cedex, France}
+\mail{campagne@lal.in2p3.fr}
+\date{\today}
+%
+%
+%
+%\selectlanguage{francais}
+%
+\abstract{
+An optimization of the CERN SPL beam line has been performed guided by the sensitivities to the $\theta_{13}$ mixing angle and to the $\delta_{CP}$ Dirac CP violating phase. A UNO-like 440 ktons water \v{C}erenkov detector located at 130~km from the target in a new foreseen Fréjus laboratory has been used as a generic detector. Concerning the $\delta_{CP}$ independent $\theta_{13}$ sensitivity, a gain of about $20\%$ may be reached using a $3.5$~GeV proton beam with a 40~m long, 2~m radius decay tunnel compared to the up to now considered $2.2$~GeV beam energy and 20~m long, 1~m radius decay tunnel. This may motivate new machine developments to upgrade the nominal SPL proton beam energy.}
+%\pacs{14.60.Pq, 14.60.Lm}
+
+\maketitle
+
+
+\section{Introduction}
+The very near future of the neutrino long baseline experiments is devoted to the study of the oscillation mechanism in the range of $\Delta m^2 = \Delta m^2_{atm} \approx 2.4\times10^{-3}\mathrm{eV}^2$ \cite{SKNU04,K2KNU04}
+ using conventional $\nu_\mu$ beams. The current K2K experiment in Japan \cite{K2KNU04}, and the forthcoming MINOS in the USA \cite{MINOS} take benefit of low energy beam to measure the $\Delta m^2$ parameter using the disappearance mode $\nu_\mu\rightarrow\nu_\mu$, while OPERA/ICARUS experiments \cite{OPERA,ICARUS} using the high energy CNGS beam \cite{CNGS} will be able to detect $\nu_\tau$ appearance. If we do not consider the LSND anomaly \cite{LSND} that will be further studied soon by MiniBooNE experiment \cite{MINIBOONE}, the three flavor family scenario will be confirmed and accommodated by a $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix \cite{PMNS} with three angles ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase $\delta_{CP}$.  
+
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/cernSuperBeam_English}
+\caption{\label{fig:Sbeam}Sketch of the SPL neutrino Superbeam from CERN to the Fréjus tunnel.}	
+\end{figure}
+
+Beyond this medium term plan, two of the next future tasks of neutrino physics are to improve the sensitivity of the last unknown mixing angle parameter, the so-called $\theta_{13}$, and to explore the CP violation mechanism in the leptonic sector. The present upper bound on $\theta_{13}$ is $\sin^22\theta_{13}<0.14$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$~CL) \cite{CHOOZ}. This sensitivity can be improved using reactor and accelerator experiments. In reactor experiments, one uses $\bar{\nu}_e$ in disappearance mode and may reach $\sin^22\theta_{13}<0.024$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$CL) \cite{Wpaper}. In accelerator experiments, one can use $\nu_e$ and $\bar{\nu}_e$ from $\beta$ beams \cite{BETABEAM} in both  disappearance and appearance modes (\textit{i.e.} $\stackrel{\scriptscriptstyle (-)}{\nu}_e\rightarrow \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$), and also $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu$ in appearance mode (\textit{i.e.} $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu\rightarrow\stackrel{\scriptscriptstyle(-)}{\nu}_e$) with conventional beams either with sub-mega watt proton drivers \cite{NOVA,T2K} or with multi-mega watt proton drivers \cite{T2K,BNLHS,CERN}. The later neutrino beam type, called Superbeam, is foreseen to be extended to produce $\nu_\mu$ beam and $\bar{\nu}_\mu$ beam from muon decays, the so-called Neutrino Factory, in order to study the eventual leptonic CP violation. Such Neutrino Complex is under study in Japan, in USA and also in Europe at CERN and details may be found in reference \cite{CERN}. A comparison of the performances of $\beta$ beam and Superbeam may be found for instance in reference \cite{DONINI}.  The reactor experiment result on $\theta_{13}$ is straight forward as compared to Superbeam and Neutrino Factory results that are on one hand reacher but in an other hand more complex to analyse due to the interplay between the different physics factors $\theta_{13}$, $\delta_{CP}$, sign$(\Delta m^2_{23})$, sign$(\tan(2\theta_{23}))$ \cite{DONINI,DOUBLE-CHOOZ}. 
+
+This paper presents results of a new simulation of the SPL (Super Proton Linac) Superbeam that could take place at CERN \cite{SPL}, using for definitiveness a UNO-like 440kT fiducial water \v{C}erenkov detector \cite{UNO} located in a new enlarged underground laboratory under study in the Fréjus tunnel, $130$~km away from CERN \cite{mosca}. The SPL neutrino beam is created by  decays of pions, muons and kaons produced by the interactions of a $4$~MW proton beam impinging a liquid mercury jet \cite{CERN}. Pions, muons and kaons are collected using two concentric electromagnetic lenses (horns), the inner one and the outer one are hereafter called "Horn" and "Reflector" respectively \cite{Meer}. The horns are followed by a decay tunnel where most of the neutrinos are produced. A sketch of the beam line is shown on figure~\ref{fig:Sbeam}.  
+
+
+The analysis chain consists of different stages: the simulation of the interactions between the proton beam and the mercury target, the propagation of the resulting secondary particles through the magnetic field and the materials of the horns, the tracking of $\pi^\pm$, $K^{\pm,0}$ and $\mu^\pm$ until they decay, the computation of the neutrino flux at the detector site, and finally the statistical analysis. A part of the simulation chain has already been described in reference \cite{nuFact134,MMWPSCazes}. 
+
+
+Compared to recent papers on the same subject \cite{DONINI,JJG,Mezzetto}, we have reoptimized the Horn and Reflector shapes \cite{nuFact138}, and introduced the kaon background simulation which allows us to update the SPL beam energy. The organization of this document follows the simulation chain: the interaction between the proton beam and the mercury target is presented in the second section. The kaon production is detailed in the third section. The simulation of the horns is described in the forth section, while the algorithms used to compute the neutrino fluxes are explained in the fifth section. Then, the sensitivities to $\theta_{13}$ and $\delta_{CP}$ are revisited with new studies about the optimization of the proton beam energy, the pion collection and the decay tunnel geometry.
+
+\section{Target simulation}
+\label{sec:target}
+Since hadronic processes are crucial to describe the interactions of the proton beam on the target, the FLUKA simulator \cite{fluka} has been chosen for this first step of the simulation. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:targ}Liquid mercury jet parameters.}
+\begin{tabular}{ll}
+\hline\noalign{\smallskip}
+    \centre{2}{Hg target}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+      Hg jet speed & $20$~m/s \\
+      density & $13.546$ \\
+      Length, radius & $30$~cm, $7.5$~mm \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+The target used in the present study is a mercury liquid jet \cite{CERN} simulated for a sake of simplicity by a cylinder $30$~cm long (representing two hadronic lengths) and $1.5$~cm diameter (see table~\ref{tab:targ}) \cite{JJG}. Other types of target are under study \cite{CERN}. The pencil like simulated proton beam is composed with  $10^6$ mono-energetic protons, and no beam-target dynamical effects are taken into account. The beam axis is also the symmetry axis of the target and the horns and the decay tunnel. Simulations have been performed for $2.2$~GeV proton kinetic energy, the up to now nominal design \cite{SPL}, as well as for $3.5$~GeV, $4.5$~GeV, $6.5$~GeV and $8$~GeV according to possible new designs \cite{MMWPSGaroby}.
+
+Particle production yields are summarized in table~\ref{tab:nbPart}. The pion momentum spectra obtained at different energies and normalized to a 4MW SPL beam power are presented in figure~\ref{fig:compEner2}(a). At low energy, pions come from $\Delta$ decays while the high energy part is dominated with multi pion production. At very mow energy, for $P<200$~MeV/c, pions come from $\Delta$ produced by protons of the target excited by the beam interactions, while for  higher energy, pion production is due to transformation of protons of the beam into $\Delta$.
+
+The horns are designed to focus the $600$~MeV/c pions (see section~\ref{sec:horn}) and the variation of the number of such pions is rather smooth with respect to the beam energy considering a 4MW fixed beam power: $4.19\times10^{13}\pi$/s for the $2.2$~GeV beam, $4.91\times10^{13}\pi$/s for the $3.5$~GeV beam, $5.14\times10^{13}\pi$/s for the $4.5$~GeV beam, and $4.92\times10^{13}\pi$/s for the $6.5$~GeV beam. The main difference is made by the angular distribution. Figure~\ref{fig:compEner2}(b) shows this distribution for the $\pi^+$ exiting the target with a momentum between $500$~MeV/c and $700$~MeV/c. The acceptance of the horns is limited to the pion below $25^\circ$, and we see that more pions are accepted by the horns for the $3.5$~GeV and $4.5$~GeV proton beams compared to other beam energies.
+
+
+
+The secondary proton and neutron rates induce important radiation damages and power dissipation in the horns which have been addressed in reference \cite{nuFact134}, and which will require specific R\&D effort. At $2.2$~GeV, kaon yields are very low, but it has a dramatic energy dependence as further studied in section~\ref{sec:kaon}. It is worth to mention that the numbers in table~\ref{tab:nbPart} are not to be taken as face values, because the cross sections of pion and kaon productions using proton beam are still under studies as for instance by the HARP experiment \cite{harp}.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbPart}Average numbers of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA). The $\mu^+/\mu^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+$E_k$ (GeV) & p & n & $\gamma$ & $e^+$ & $e^-$ & $\pi^+$ & $\pi^-$ & $\mu^+$ & $\mu^-$ & $K^+$ & $K^0$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$2.2$ & $1.4$     &  $17$   & $5.0$  &   $0.08$  &  $0.17$    &  $0.24$   &  $0.18$ & $4$ & $1$ & $7$ & $6$ \\
+
+$3.5$ & $1.8$    &  $23$  & $7.0$   &  $0.15$  &  $0.28$    &  $0.41$   &  $0.37$ & $10$ & $3$ & $35$ & $30$ \\
+
+$4.5$ &  $2.3$  &  $25$ & $7.7$  & $0.21$  &  $0.35$    &  $0.57$ & $0.39$&  $11$ & $3.3$  &  $93$ &  $68$       \\
+
+$8$   &  $3.1$  &  $33$ & $11.0$ & $0.41$ & $0.63$    &  $1.00$  &  $0.85$ &  $30$ &  $9.5$ &  $413$ &    $340$         \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compEner2.eps}
+\caption{\label{fig:compEner2} (a) $\pi^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$~GeV/c and $0.7$~GeV/c. The different SPL beam kinetic energies presented are (\full) $2.2$~GeV, (\dashed) $3.5$~GeV, (\dotted) $4.5$~GeV and (\chain) $6.5$~GeV.}
+\end{figure*}
+%
+The cross section uncertainties are the main source of discrepancy between simulator programs. Some comparisons between FLUKA and MARS \cite{MARS} have already been presented in the same context \cite{nuFact134}. The energy distribution of the pions exiting the target, computed with the two simulator programs FLUKA and MARS, is shown on figure~\ref{fig:compFlukaMars}(a).  The discrepancy is quite large for the low energy part. However, the horns are designed to focus the high energy part of the spectrum (see section~\ref{sec:horn}), and therefore, MARS and FLUKA are in better agreement for the energy spectrum computed at the entrance of the decay tunnel, as shows figure~\ref{fig:compFlukaMars}(b). 
+%A difference of $10\%$ has been found between the  $\theta_{13}$ sensitivity computed with the two generators (see section~\ref{sec:results}), that can be taken as systematic error. 
+For a 2.2~GeV beam and a positive focusing,  $27\%$ more $\nu_\mu$ and $6\%$ more $\nu_e$ neutrinos are produced around the oscillation probability maximum with the FLUKA generator. It turns out that 
+a sensitivity $10\%$ better for FLUKA compared to MARS has been found for the $\sin^2(2\theta_{13})$ sensitivity
+(see section~\ref{sec:results}). So, the discrepancy  at low energy between MARS and FLUKA does not matter too much for the present application, and the sensitivity difference can be taken as a systematic error. 
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compMarsFlukav2.eps}
+\caption{\label{fig:compFlukaMars}$\pi^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\dashed) and by MARS (\full).}
+\end{figure*}
+%
+\section{Kaon production}
+\label{sec:kaon}
+The possibility to increase the SPL energy in order to study the optimization of the physics program has been recently pointed out \cite{MMWPSGaroby}. Then, the kaon production should be clearly addressed because it is a source of $\nu_e$ and $\bar{\nu}_e$ background events. The kaon decay channels and branching ratios are presented in table~\ref{tab:BRKP0SL} in \ref{sec:kaons}.
+
+The target simulation described in section~\ref{sec:target} has been used with $10^6$ p.o.t with kinetic energy uniformly distributed between $2.2$~GeV and $5$~GeV. The momentum of outgoing pions and kaons are recorded when they exit the target. The number of produced $K^{o,\pm}$ at different proton beam energies are presented on figure~\ref{fig:KaonsPions} (left). In one hand the $K^o$ production rate is similar to the $K^+$ production rate, but in an other hand the $K^-$ production rate is almost forty times smaller. For comparison, the numbers of $\pi^+$ and $\pi^-$  produced in the same conditions are presented on figure~\ref{fig:KaonsPions} (right). Pion production rate is about two orders of magnitude greater than the kaon production rate.
+%
+\begin{figure*}
+\centering
+%\includegraphics[height=95mm]{../picts/KaonProd.eps}
+\includegraphics[height=95mm]{../picts/KaonPionProdFluka2003v2.eps}
+%\caption{\label{fig:KaonsPions}Kaon production (a) as a function of the incident proton beam kinetic energy ($E_k$) for $10^6$ incident protons with (\full) curve for $K^+$, (\dashed) curve for $K^-$ and (\dotted) curve for $K^0$. Pion production (b) in the same conditions with (\full) curve for $\pi^+$ and (\dashed) curve for $\pi^-$.}
+\caption{\label{fig:KaonsPions} Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).} 
+\end{figure*}
+%
+The behavior of the two pion and kaon production rates are quite different. The $\pi^+$ yield grows smoothly with the proton energy while the production of kaons seams to have two origins, which has been confirmed by FLUKA's authors \cite{FLUKAprivate}. For beam energy below approximatively $4$~GeV, the resonance production model is used, and one notices a low production rate with a maximum at about $3.4$~GeV. For beam energy above  $4$~GeV, the dual parton model is used, and the production rate experiences a threshold effect with a rapid rise. The ratio between positive kaon and pion production rates is about $0.5\%$ between $2.2$~GeV and $4$~GeV and grow up to $2.3\%$ at $5$~GeV. One notices that the transition between the two kaon production models may not be optimal.
+%
+\section{Horns simulation}
+\label{sec:horn}
+The simulation code of the electromagnetic horns is written using GEANT 3.2.1 \cite{geant} for convenience and since electromagnetic processes are dominant, FLUKA has not been considered as mandatory, but this may be revised in a future work. The geometry of the horns has been inspired by an existing CERN prototype and a Reflector design proposed in reference \cite{SIMONE1}. Depending of the current injection, only positive secondary particles or negative secondary particles are focused. The relevant parameters are detailed in table~\ref{tab:specif}.
+
+The mercury target is localized inside the Horn because of the low energy and the large emittance of the secondary pions produced: $$<P_{\pi T}>/<P_\pi> \approx 240~\mathrm{MeV}/400~\mathrm{MeV}$$ ($2.2$~GeV proton beam energy). This explains the Horn design (figure~\ref{fig:plan}), with a cylindrical part around the target, called the neck, which is larger than the transversal size of the target to simulate the room for target handling, and a conic part designed such that the relevant pions are focused as much as possible to exit the magnetic field parallel to the beam axis.
+
+\begin{table}
+\centering
+\caption{\label{tab:specif}Relevant parameters of the horns in case of the generation of a $260$~MeV neutrino beam (or $350$~MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$~MeV/c (or $800$~MeV/c) pion momentum.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+ & Horn & Reflector \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+  neck inner radius & $3.7$~cm &  $20.3$~cm \\
+  neck length & $40$~cm        &  $120 (140)$~cm \\ 
+  end cone inner radius & $16$~cm        &  $35.7$~cm \\
+  outer radius & $20.3$~cm      & $40$~cm \\ 
+  total length & $120 (140)$~cm       & $190 (220)$~cm \\  
+  Alu thickness  & $3$~mm       & $3$~mm \\            
+  Peak current & $300$~kA       & $600$~kA \\
+  Frequency & $50$~Hz            & $50$~Hz \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The shape of the horn conductors is a crucial point since it determines the energy spectrum of the neutrino at the detector site. The details of the conductor shape optimization for the present context may be found in reference \cite{nuFact138}. We just recall here some ingredients. For a $\theta_{13}$ driven $\nu_\mu \rightarrow \nu_e$ oscillation, a $\Delta m^2_{23}$ parameter value of $2.4\times10^{-3}\mathrm{eV}^2$, and a baseline distance of $130$~km, the first oscillation maximum occurs for a neutrino energy of $260$~MeV. The   optimization of the physics potential depends at first approximation on the pion neutrino characteristics, which energy is fully determined by the pion 2-body decay and boost. To reach an energy of $260$~MeV, the pion needs a $\beta=0.97$, which in turn induces a pion momentum of $600$~MeV/c. Then, the shape of the conic part of the horns is determined such that these $600$~MeV/c pions exit parallel to the beam axis. 
+
+An other shape of the horn conductors has been used to produce a $350$~MeV neutrino beam to compare the sensitivity potential (see section \ref{sec:results}). In that case, keeping the current intensity unchanged ($300/600$~kA), the lengths of the Horn and the Reflector should be increased by $16$\% and $18.5$\%, respectively (see table~\ref{tab:specif}).
+
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/corne350.eps}
+\caption{\label{fig:plan}Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350~MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}
+\end{figure}
+
+Before closing this section, it is worth to quote that the Horn/Reflector conductor shapes optimized in the present study to focus a given pion momentum value, is not affected at first order by a proton beam energy change. What is affected is the production rate of the relevant pions. This Horn/Reflector design consideration would be different if one wishes to focus as much as possible all the pions produced for which the mean energy is of course affected by a proton beam energy change.    
+%
+\section{Particle decay treatment and flux calculation}
+%
+The decay tunnel representation is a simple cylinder with variable length ($L_T$) and radius ($R_T$) filled with "vacuum" and located right after the horns. The default design is a $20$~m long and $1$~m radius cylinder, but simulations have also been conducted with lengths of $10$~m, $40$~m and $60$~m, and radius of $1.5$~m and $2$~m in the spirit of reference \cite{donega}. In the GEANT simulation, to gain in CPU time, only pions, muons and kaons are tracked in the volume of the tunnel, and all particles exiting this volume are discarded. 
+
+Beyond the $1/L^2$ solid angle factor due to the source-detector distance ($L$) which decreases dramatically the fluxes, the neutrino beam focusing is very limited due to the small pion boost factor ($\approx 4$). Therefore, computational algorithms have been used to avoid a too prohibitive CPU time resulting from the simulation of each secondary particle decay. Otherwise, about $10^{15}$ p.o.t would have been necessary to obtain reliable statistics for the estimation of the $\bar{\nu}_e$ flux for instance.
+
+It is worth to mention that the particle decays occurring before the entrance of the decay tunnel are also taken into account and treated in the same manner, which is not the case in reference \cite{donega}. 
+%
+\subsection{Algorithm description}
+\label{sec:algo}
+The decay code has been included in the GEANT code. The basic idea of this algorithm is to compute the neutrino fluxes using the probability of reaching the detector for each neutrino produced by a $\pi$ or a $K$ or a $\mu$ particle (on-axis neutrino beam). This method has already been used in reference \cite{donega} and has been modified and extended to the kaon decay chain for the present study. 
+
+Muon neutrino comes mostly from pion decay. In a first stage, each pion is tracked by GEANT until it decays. Then, the probability for the produced muon neutrino to reach the detector is computed. The flux is obtained applying the probability as a weight for each neutrino. All the pions produced in the simulation are therefore useful to compute the flux, and this allows to reduce the number of events in the simulation to $10^6$ p.o.t. In this computation, the decay region (horns and tunnel) is considered as point like compared to the source-detector distance. 
+
+The same method is applied for neutrino coming from muons and kaons with some modifications  because most of the muons do not decay, and there are very few kaons produced (see table~\ref{tab:nbPart}).
+The probability computation is presented in appendix~\ref{sec:decayprobcomp}. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:proton}Number of protons on target for different beam energy at 4~MW constant power. One year is defined as $10^7$~s.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			Beam energy  & Number of proton \\
+			  (GeV)      & per year ($10^{23}$ p.o.t/y) \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			2.2 & 1.10 \\
+			3.5 & 0.70 \\
+			4.5 & 0.56 \\
+			6.5 & 0.40 \\
+			8.0 & 0.30 \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22p.eps}
+\caption{	\label{fig:flux22p}Neutrino fluxes, $100$~km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$~GeV (4~MW), a decay tunnel with a length of $20$~m and a radius of $1$~m. The top left panel contains the $\nu_\mu$ fluxes, and the top right panel shows the $\bar{\nu}_\mu$ fluxes. The bottom left panel presents the $\nu_e$ fluxes while the bottom right panel displays the $\bar{\nu}_e$ fluxes. The (\full) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\dashed) curve is the contribution from the charged kaon decay chain, and the (\dotted) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22m.eps}
+\caption{\label{fig:flux22m}Same legend as for figure~\ref{fig:flux22p} but the horns are focusing negative particles.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35p.eps}
+\caption{\label{fig:flux45p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35m.eps}
+\caption{\label{fig:flux45m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8p.eps}
+\caption{\label{fig:flux8p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8m.eps}
+\caption{\label{fig:flux8m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{table*}
+\centering
+\caption{\label{tab:speciesfluxes}Integral of the total flux of the different species with different settings. The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are expressed in $10^{13}/100\mathrm{m}^2/y$ unit while the $\nu_e$ and $\bar{\nu}_e$ fluxes are expressed in $10^{11}/100\mathrm{m}^2/y$ unit. The positive focusing  and negative focusing  are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. %Setting (1) means $L_T = 10$~m and $R_T = 1$~m. Setting (2) is the default option and means $L_T = 20$~m and $R_T = 1$~m. Setting (3) means $L_T = 20$~m and $R_T = 1.5$~m. Setting (4) means $L_T = 30$~m and $R_T = 1$~m. Setting (5) means $L_T = 40$~m and $R_T = 1$~m. Setting (6) means $L_T = 40$~m and $R_T = 1.5$~m. Setting (7) means $L_T = 40$~m and $R_T = 2$~m.  Setting (8) means $L_T = 60$~m and $R_T = 1$~m, and finally, setting (9) means $L_T = 60$~m and $R_T = 1.5$~m.
+}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+
+			\centre{3}{Settings}  & \centre{2}{$\nu_\mu$} & \centre{2}{$\nu_e$} 
+								&	\centre{2}{$\bar{\nu}_\mu$} & \centre{2}{$\bar{\nu}_e$} \\
+								$E_p$ & $L_T$ & $R_T$ & $+$ & $-$ & $+$ & $-$ & $+$ & $-$ 
+								& $+$ & $-$ \\ 
+\noalign{\smallskip}\hline\noalign{\smallskip}
+
+$2.2$~GeV & $10$~m &  $1$~m 
+	& $5.5$          & $0.4$ 
+	& $1.7$          & $0.2$
+	& $0.3$          & $4.3$  
+	& $0.1$ 	 & $0.8$ \\		
+
+$3.5$~GeV  & $10$~m &  $1$~m  
+	& $7.7$          & $0.7$ 
+	& $2.6$          & $0.6$
+	& $0.6$          & $6.6$  
+	& $0.3$ 	 & $1.3$ \\		
+	
+$4.5$~GeV  & $10$~m &  $1$~m  
+	& $7.1$          & $1.0$ 
+	& $2.8$          & $0.9$
+	& $0.5$          & $5.2$  
+	& $0.3$ 	 & $1.1$ \\		  
+
+$6.5$~GeV  & $10$~m &  $1$~m  
+	& $8.3$          & $1.2$ 
+	& $4.7$          & $1.9$
+	& $0.8$          & $5.6$  
+	& $0.9$          & $1.8$ \\
+
+$8.0$~GeV  & $10$~m &  $1$~m  
+	& $7.7$          & $1.2$ 
+	& $5.1$          & $2.2$
+	& $0.9$          & $5.6$  
+	& $1.1$ 	 & $2.1$ \\
+
+$2.2$~GeV & $20$~m &  $1$~m   
+	& $7.6$         & $0.4$ 
+	& $3.2$ 	& $0.2$
+	& $0.3$ 	& $5.8$  
+	& $0.1$ 	& $1.6$ \\		  
+
+$3.5$~GeV & $20$~m &  $1$~m    
+	& $10.0$          & $0.9$ 
+	& $4.4$           & $0.6$
+	& $0.7$ 	  & $8.5$  
+	& $0.3$ 	  & $2.2$ \\		  
+
+$4.5$~GeV & $20$~m &  $1$~m    
+	& $10.9$          & $1.1$ 
+	& $5.1$           & $1.0$
+	& $0.7$ 	  & $6.7$  
+	& $0.4$ 	  & $1.8$ \\		  
+
+$6.5$~GeV & $20$~m &  $1$~m    
+	& $10.4$          & $1.4$ 
+	& $6.4$           & $2.0$
+	& $1.0$           & $7.1$  
+	& $0.9$ 	  & $2.5$ \\	
+
+$8.0$~GeV & $20$~m &  $1$~m    
+	& $9.7$           & $1.5$ 
+	& $6.7$           & $2.3$
+	& $1.2$           & $7.1$  
+	& $1.1$ 	  & $2.8$ \\
+
+$2.2$~GeV & $20$~m &  $1.5$~m    
+	& $9.0$           & $0.6$ 
+	& $4.4$           & $0.4$
+	& $0.4$           & $6.7$  
+	& $0.2$  	  & $2.2$ \\
+
+$4.5$~GeV & $20$~m &  $1.5$~m    
+	& $13.2$          & $1.5$ 
+	& $6.9$           & $1.4$
+	& $0.9$           & $8.1$  
+	& $0.6$  	  & $2.7$ \\
+
+$3.5$~GeV & $30$~m &  $1$~m    
+	& $10.9$          & $0.9$ 
+	& $5.7$           & $0.7$
+	& $0.7$           & $9.4$  
+	& $0.3$  	  & $2.9$ \\
+
+$4.5$~GeV & $30$~m &  $1$~m   
+	& $11.6$          & $1.2$ 
+	& $6.3$           & $1.0$
+	& $0.7$           & $7.1$  
+	& $0.4$    	  & $2.3$ \\
+
+$2.2$~GeV & $40$~m &  $1$~m    
+	& $8.9$           & $0.5$ 
+	& $5.1$           & $0.3$
+	& $0.5$           & $6.7$  
+	& $0.1$   	  & $2.4$ \\	
+
+$3.5$~GeV & $40$~m &  $1$~m  
+	& $11.3$          & $0.9$ 
+	& $6.5$           & $0.6$
+	& $0.8$           & $9.7$  
+	& $0.3$ 	  & $3.3$ \\	
+
+$4.5$~GeV & $40$~m &  $1$~m  
+	& $12.3$          & $1.2$ 
+	& $7.2$           & $1.0$
+	& $0.8$           & $7.5$  
+	& $0.4$   	  & $2.6$ \\	
+
+$6.5$~GeV & $40$~m &  $1$~m  
+	& $11.7$          & $1.6$ 
+	& $8.3$           & $2.2$
+	& $1.1$           & $8.0$  
+	& $0.9$   	  & $3.3$ \\	
+
+$8.0$~GeV & $40$~m &  $1$~m  
+	& $10.9$          & $1.7$ 
+	& $8.5$           & $2.4$
+	& $1.3$           & $8.0$  
+	& $1.2$    	  & $3.6$ \\	
+
+$3.5$~GeV & $40$~m &  $1.5$~m  
+	& $14.5$          & $1.3$ 
+	& $10.0$          & $1.0$
+	& $1.0$           & $12.3$  
+	& $0.5$  	  & $5.3$ \\
+	
+$4.5$~GeV & $40$~m &  $1.5$~m 
+	& $15.5$          & $1.7$ 
+	& $10.8$          & $1.5$
+	& $1.0$           & $9.5$  
+	& $0.6$  	  & $4.2$ \\
+		
+$3.5$~GeV & $40$~m &  $2$~m 
+	& $16.6$          & $1.5$ 
+	& $12.9$          & $1.3$
+	& $1.3$           & $13.9$  
+	& $0.7$  	  & $6.9$ \\
+	
+$4.5$~GeV & $40$~m &  $2$~m 
+	& $18.2$          & $2.1$ 
+	& $14.3$          & $1.9$
+	& $1.3$           & $11.1$  
+	& $0.8$  	  & $5.6$ \\
+	
+$3.5$~GeV & $60$~m &  $1$~m 
+	& $11.7$          & $0.9$ 
+	& $7.6$           & $0.7$
+	& $0.7$           & $10.1$  
+	& $0.3$      	  & $3.7$ \\
+	
+$4.5$~GeV & $60$~m &  $1$~m 
+	& $12.5$          & $1.3$ 
+	& $8.1$           & $1.1$
+	& $0.7$           & $7.7$  
+	& $0.4$ 	  & $2.9$ \\
+	
+$3.5$~GeV & $60$~m &  $1.5$~m 
+	& $15.1$          & $1.3$ 
+	& $12.2$          & $1.0$
+	& $1.0$           & $12.8$  
+	& $0.5$  	  & $6.3$ \\
+	
+$4.5$~GeV & $60$~m &  $1.5$~m 
+	& $16.2$          & $1.8$ 
+	& $13.1$          & $1.6$
+	& $1.0$           & $9.9$  
+	& $0.6$ 	  & $4.9$ \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\subsection{Validation of the algorithm}
+The validity of the method presented in the previous section have been tested against a straight forward  algorithm consisting of decaying each pion $N$ times ($N \approx 10^6$) in a full GEANT simulation of the event (decays included). Such method presents the advantage to keep all the information of the neutrino available for further studies. It can be a good approach to compute the muon neutrino flux coming from pion decays. It can also provide the beam profile, but it shows its limits for the muon induced fluxes, especially the $\bar{\nu}_e$ flux. Indeed, this means that each muon is duplicated $N$ times and when a muon decays, it must decay $N$ times again. For $N\approx 10^6$, this is a prohibitive CPU time consuming.
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compGeantDonega.eps}
+\caption{\label{fig:compGeantDonega}Comparison between the probability method, (\full) curve, and the full GEANT simulation method, (\dashed) curve, for the $\nu_\mu$ from $\pi^+$ flux (a) and the $\bar{\nu}_\mu$ from $\pi^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu_e$ and $\bar{\nu}_e$ fluxes contrary to the former simulation.}
+\end{figure*}
+%
+The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are displayed on figure~\ref{fig:compGeantDonega} for both methods. The two spectra shows a clear agreement, and this makes confidence on the probability method.
+%
+\subsection{Simulated fluxes}
+The fluxes are computed at a distance of $100$~km from the source by convention and can be rescaled at any desired distance. They provide the number of the four neutrino species ($\nu_\mu$, $\bar{\nu}_\mu$, $\nu_e$, $\bar{\nu}_e$) passing through a $100$~m$^2$ fiducial area during $1$~year.
+
+In practice, the fluxes are given as a function of the neutrino energy via histograms composed of $20$~MeV bin width.  These histograms are filled with the energy of each neutrino weighted by the probability to reach the detector (section~\ref{sec:algo}). To obtain the fluxes, the histograms are rescaled to the number of p.o.t per year depending on the beam energy. Table~\ref{tab:proton} reports on the number of p.o.t per year for the different energies studied using the definition of one year being $10^7$~s and keeping the beam power constant (\textit{i.e.} $4$~MW).
+
+Three origins are identified in the composition of each neutrino flux:
+\begin{description}
+	\item[-] neutrinos from pions, which includes neutrinos created by primary pion decays and neutrinos coming from the muons produced by pion decays or muons directly exiting the target. This is the component studied in reference \cite{donega} but with different settings and event generator;
+	\item[-] neutrinos emitted during the decay chain of the charged kaons, either by direct production, or produced by the daughter pions and muons;
+	\item[-] neutrinos coming from the decay chain of the neutral kaons.
+\end{description}
+
+The three components of the fluxes for the four neutrino species are presented on figure~\ref{fig:flux22p} for positive particle focusing and a proton beam kinetic energy of $2.2$~GeV. The $\nu_\mu$ flux is dominated by the neutrinos of pion decays, but a tail above $500$~MeV (insert on the top left part) is created by the $K^+\rightarrow \mu^+\nu_\mu$ channel, which is anyway at least three order of magnitude below the flux maximum. The $\bar{\nu}_\mu$ flux is mostly due to the decays of $\pi^-$ that are not unfocused by the horns, but the higher energy part comes from $\mu^+$ decays. It is noticable that the $\nu_e$ and $\bar{\nu}_e$ fluxes are respectively more than $200$ and more than $7000$ times smaller than the $\nu_\mu$ flux. The $\bar{\nu}_e$ are produced in a large part by the $K^0_L\rightarrow\pi^+e^-\bar{\nu}_e$ decay channel and by $\mu^-$ decays, while the  $\nu_e$ flux is dominated by the $\mu^+$ decays.
+
+On figure~\ref{fig:flux22m}, the horns are set to focus negative particles keeping other parameters identical. By comparison with positive focusing, one can at first approximation translate the results by exchanging particles and anti-particles, except that the $K^+/K^-$ ratio is about 50 in the beam-target interactions (see table~\ref{tab:nbPart}).
+
+On figures~\ref{fig:flux45p} and \ref{fig:flux8p}, one observes the evolution of figure~\ref{fig:flux22p} when the proton beam kinetic energy increases to $3.5$~GeV and $8$~GeV, respectively. Correspondingly, the results for negative particle focusing are presented on figures~\ref{fig:flux45m} and \ref{fig:flux8m}. One clearly notices the increase of the kaon induced neutrino contents as the beam energy grows.
+%
+On table~\ref{tab:speciesfluxes} are reported the integral of the fluxes when one modifies the decay tunnel length and radius, as well as the beam kinetic energy. Changing the length from $10$~m to $40$~m will increase the $\nu_\mu$ flux by $50\%$ to $70\%$ and in the same time, the number of $\nu_e$ will be multiply by a factor $1.5$ to $2$. One can notice that going from $40$~m to $60$~m does not increase the signal-like events but increase the background-like events. For a $40$~m length of the decay tunnel, the increase of the radius improve the number of signal-like events by $50\%$, and the backgroud increase by $70\%$ to $100\%$. Notice that the $\nu_\mu/\bar{\nu}_\mu$ flux ratio is rather insensitive to the decay tunnel length. The feeling that $L_T = 40$~m and $R_T = 2$~m is a good signal over background compromise is confirmed by sensitivity quantitative studies reported in section~\ref{sec:results}.
+
+Looking at the evolution of $\nu_\mu$ flux with respect to the beam energy, one notices that a maximum is reached around $4.5$~GeV. This is due to the competition between the cross section rise with respect to the energy and the decrease of the number of p.o.t due to the constant SPL power ($4$~MW).
+%
+\section{Sensitivity computation ingredients}
+%
+The sensitivity to $\theta_{13}$ and $\delta_{CP}$ is computed for a $\nu_\mu\rightarrow\nu_e$ appearance experiment. The detector considered for definitiveness is similar to the UNO detector, \textit{i.e.} a $440$~kt fiducial water \v{C}erenkov detector \cite{UNO}. The detector simulation has been presented in reference \cite{JJG} and the analysis program described in reference \cite{MEZZETTONUFACT060} has been used for sensitivity computation following previous work of reference \cite{Mezzetto}. See table~\ref{tab:param} for the default user parameter values used in this paper. We just remind here some key points of the sensitivity analysis program. 
+
+It is included a full 3-flavors oscillation probability computation with matter effects, but no ambiguities are taken into account. This latest point may be revisited in a future work using reference \cite{DONINI-2}. Concerning the background events, the $\nu_e/\bar{\nu}_e$ from the beam, the $\nu_\mu e^-$ elastic scattering process, the $\pi^o$ production as well as the $\mu/e$ misidentification are taken into account. The cross-sections from the NUANCE program are used \cite{NUANCE}. The systematics error on the total $\nu_e$ and $\bar{\nu}_e$ fluxes determination is a user parameter and we have used the $2\%$ value considered as a final goal, but also $5\%$ and $10\%$ \cite{MEZZETTONUFACT060}. The detector is located at $L = 130$~km from CERN, in the foreseen new Fréjus laboratory \cite{mosca}. It is worth to mention that if one wants to evaluate the influence of $L$ on the sensitivity, it would mean a re-optimization of the horns for each $L$ envisaged (see section~\ref{sec:horn}).  
+%
+\begin{table}
+\centering
+\caption{\label{tab:param}Default parameters used to compute the sensitivity curves \cite{MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite{KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite{JJG}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			$\Delta m^2_{12} = 8.2 (0.5)\times 10^{-5}~\mathrm{eV}^2$ & $\sin^22\theta_{12} = 0.82 (9\%)$ \\
+			$\Delta m^2_{23} = 2.5 (0.1)\times 10^{-3}~\mathrm{eV}^2$ & $\sin^22\theta_{23} = 1.0 (1\%)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		  $L_T = 20$~m & $R_T = 1$~m \\ 
+		  $M=440$~kT   & $\epsilon_{syst}=2\%$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+\centre{2}{Horn/Reflector shapes to produce a $260$~MeV neutrino beam} \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The running time scenario has been fixed either by focusing positive particles during 5 years, either  by focusing positive particles during 1 (or 2) year(s) followed by focusing negative particles during 4 (or 8) years.
+%
+\section{Results}
+\label{sec:results}
+\subsection{The positive only focusing scenario}
+The $\theta_{13}$ and $\delta_{CP}$ sensitivities are computed with $\theta_{13} = 0^\circ$ and $\delta_{CP} = 0^\circ$ if not explicitly mentioned. It is worth to stress that the default parameters of table~\ref{tab:param} are used if not contrary mentioned, in particular, the decay tunnel geometry parameters ($L_T=20$~m and $R_T=1$~m), and the horn design to generate a $260$~MeV neutrino beam. 
+
+Table~\ref{tab:nbvsE} presents the number of signal and background events for a $5$ years positive focusing experiment, but with different beam energy settings. 
+%The quality factor ($S$) is defined in reference \cite{MEZZETTONUFACT060} as\footnote{Contrary to the definition of the significance of reference \cite{MEZZETTONUFACT060}, the systematical factor is applied to the total $\nu_e$ flux in agreement with the sensitivity contour computation.}:
+%\begin{equation}
+%\begin{aligned}
+%\mathcal{S} &= \frac{N^{osc}_{\nu_e}}{\sqrt{ N^{tot}_{\nu_e} + \left(N^{tot}_{\nu_e}\times\epsilon_{syst}\right)^2}}\\
+%\mathrm{with}\quad N^{tot}_{\nu_e} &= N^{osc}_{\nu_e} + N^{beam}_{\nu_e} + N^{oth. bkg}
+%\label{eq:significance}
+%\end{aligned}
+%\end{equation}
+%and $N^{osc}_{\nu_e}$ the number of $\nu_e$ events due to $\nu_\mu$ oscillations, $N^{beam}_{\nu_e}$ the number of background events coming from the $\nu_e+\bar{\nu}_e$ contamination of the beam, $N^{oth. bkg}$ the other kinds of background events and $\epsilon_{syst}$ the systematical factor.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbvsE}Number of events for 5 years positive focusing scenario with default parameters of table~\ref{tab:param}. Other backgrounds are $\pi^0$, $\nu_\mu$-elast., $\mu/e$-missId. 
+%The $S$ factor is defined by equation~\ref{eq:significance}.
+}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		 & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			non oscillated $\nu_\mu$       & $36917$  & $60969$  & $73202$  & $78024$ & $76068$ \\ 
+			oscillated $\nu_e$             & $43$     & $60$     & $64$     & $61$    & $56$ \\
+			beam $\nu_e$                   & $165$    & $222$    & $242$    & $288$   & $299$ \\
+			other background               & $70$     & $105$    & $127$    & $148$   & $152$ \\
+%			S factor                       & $1.88$   & $2.16$   & $2.17$   & $1.87$  & $1.69$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+The contours at $90\%$, $95\%$ and $99\%$~CL of the $\theta_{13}$ sensitivity are presented in the ($\sin^22\theta_{13}$, $\Delta m^2_{23}$) plane on figure~\ref{fig:sensi45} for $3.5$~GeV proton beam kinetic energy. 
+The comparison between the contours at $90\%$~CL with $2.2$~GeV, $3.5$~GeV, $4.5$~GeV and $8$~GeV beam energies is shown on figure~\ref{fig:compSensi}. One notices in this scenario a better perfomence reached with a $4.5$~GeV energy beam. 
+%as a confirmation of significance parameter value. 
+But, in fact there is not much visual difference between a sensitivity obtained with $3.5$~GeV and $4.5$~GeV, even if one should keep in mind that kaon production models are different at these two energies (see section~\ref{sec:kaon}). These two energy settings have been studied with different decay tunnel geometry and  results are reported on table~\ref{tab:thvsE_3545}. One notice that similar results can be reached with a $3.5$~GeV beam, compared to a $4.5$~GeV beam.
+
+Quantitative studies of the minimum $\sin^22\theta_{13}$ with respect to the kinetic beam energy $E_k(proton)$, and the decay length $L_T$, and the systematics $\epsilon_{syst}$ are presented in tables~\ref{tab:thvsE} and \ref{tab:thvseps}. One notices that for $\epsilon_{syst} = 5\%$ there is no difference between a $3.5$~GeV and a $4.5$~GeV beam.
+%
+We have also considered the $3.5$~GeV and $4.5$~GeV beam energies with the tunnel geometry parameters $L_T=40$~m and $R_T=2$~m, and the horn design producing a $350$~MeV neutrino beam (see section~\ref{sec:horn}). In table~\ref{tab:thvsE_3545} are reported numerical values, and on figure~\ref{fig:comp5year} are shown the $90$\% CL sensitivity contours. With the $350$~MeV neutrino beam, one can expect a $16$\% improvment with respect to the $260$~MeV neutrino beam. One notices also that there is marginal gain to increase the beam energy from $3.5$~GeV to $4.5$~GeV, as already mentioned. 
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensi35.eps}
+\caption{\label{fig:sensi45}Sensitivity contours obtained with a SPL energy of $3.5$~GeV and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m. (\full), (\dashed) and (\dotted) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compSensi.eps}
+\caption{\label{fig:compSensi}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comp5year.eps}
+\caption{\label{fig:comp5year}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$~GeV or $4.5$~GeV, and either a $260$~MeV (default) neutrino beam or a $350$~MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$~m and $R_T = 2$~m. The (\chain) curve corresponds to a $350$~MeV/$4.5$~GeV (neutrino beam/SPL beam energy) setting; the (\dotted) curve corresponds to a $350$~MeV/$3.5$~GeV setting; the (\dashed) curve corresponds to a $260$~MeV/$4.5$~GeV setting and the (\full) curve corresponds to a  $260$~MeV/$3.5$~GeV setting.}
+\end{figure}
+%
+\begin{table}
+\centering
+\caption{\label{tab:thvsE}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		        & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV  \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$10$~m & $1.10$ & $0.92$ & $1.04$ & $1.07$ & $1.16$ \\
+			$20$~m & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$40$~m & $1.23$ & $1.00$ & $0.99$ & $1.08$ & $1.19$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+
+There are also variations on the minimum $\sin^22\theta_{13}$ value that may be reached in a $\nu_\mu \rightarrow \nu_e$ experiment which are due to the $\mathrm{sign}(\Delta m^2_{23})$ ambiguity and the $\delta_{CP}$ value. On table~\ref{tab:sign} are presented these kind of variations. Other ambiguities coming from the sign$(\tan(2\theta_{23}))$ ignorance also take place as studied in reference \cite{DONINI}. From figure~9 of this reference, we estimate a 30\% effect on $\sin^2(2\theta_{13})$ sensivity due to these ambiguities.
+%
+\subsection{Mixed positive/negative focusing scenario}
+%
+The combined $\sin^22\theta_{13}$ and $\delta_{CP}$ sensitivity for the 5 years positive focusing scenario and the default parameters of table~\ref{tab:param} is presented on figure~\ref{fig:compDeltaTheta}(a). The results obtained with a $3.5$~GeV and $4.5$~GeV SPL beam are similar and better than with the other energy settings. On figure~\ref{fig:sensiDeltaTheta}(a) the results obtained with a $260$~MeV neutrino beam and a $350$~MeV neutrino beam are presented with a $40$~m long, $2$~m radius decay tunnel. With the $350$~MeV neutrino beam, one can reached better sensitivity results in the range $|\delta_{CP}| < 120^o$, and comparatively the gain obtained when switching from a $3.5$~GeV proton beam to a $4.5$~GeV proton beam is marginal. 
+%
+To improve the $\delta_{CP}$-independent limit on $\sin^22\theta_{13}$, especially around $\delta_{CP}=90^\circ$, one may envisaged a combination of 2 years with positive focusing and 8 years negative focusing as in references \cite{DONINI,JJG,Mezzetto}. The comparison of the results obtained with different SPL beam energies on the combined sensitivity contours are presented in figure~\ref{fig:compDeltaTheta}(b). Quantitative results with this kind of mixed focusing scenario are reported table \ref{tab:thvsE_td}. One generally gets $10\%$ to $20\%$ better limit on $\sin^22\theta_{13}$ independently of $\delta_{CP}$ with a $3.5$~GeV kinetic energy beam compare to a $2.2$~GeV beam. Doubling the length and the radius of the decay tunnel allows to reach a $10\%$ better limit.
+
+On figure~\ref{fig:sensiDeltaTheta}(b) are presented the results considering the effects of a $350$~MeV neutrino beam obtained either with a $3.5$~GeV proton beam or a $4.5$~GeV proton beam compared to a $260$~MeV neutrino beam obtained with a $4.5$~GeV proton beam. The tunnel geometry parameters are $L_T=40$~m and $R_T=2$~m (other tunnel geometry have been studied but the results are worse and so are not reported). Except in the region $|\delta_{CP}|>150^o$, the results obtained with the $350$~MeV neutrino beam ($3.5$~GeV proton beam) are somewhat better, even if a $11\%$ improvement of the $\delta_{CP}$-independent $\sin^22\theta_{13}$ limit can be reached with the $260$~MeV neutrino beam obtained with the $3.5$~GeV proton beam.
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compDeltaTheta.eps}
+\caption{\label{fig:compDeltaTheta}90\% sensitivity contours obtained with SPL beam energy of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) at $90\%$ CL. Default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensiDeltaTheta.eps}
+\caption{\label{fig:sensiDeltaTheta}90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$~m and $R_T=2$~m and different SPL beam energies ($3.5$~GeV or $4.5$~GeV) and different horn designs ($260$~MeV or $350$~MeV neutrino beams): (\full) curve for a $350$~MeV/$4.5$~GeV setting, (\dotted) curve for a $350$~MeV/$3.5$~GeV setting, (\dashed) curve for a $260$~MeV/$3.5$~GeV setting. Other default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}
+\end{figure}
+%
+\begin{table*}
+\centering
+\caption{\label{tab:thvsE_3545}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) at and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings in parenthesis are identical to those of table~\ref{tab:speciesfluxes}, except that the setting (7b) corresponds to the tunnel geometry of setting (7) but the horn geometry producing a $350$~MeV neutrino beam is used. We remind that the setting (2) is the default one, and the settings (7) and (7b) corresponds to $L_T = 40$~m and $R_T = 2$~m.}
+
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+setting & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (7b) & (8) & (9)\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$3.5$~GeV   & $0.92$ & $0.92$ & $0.83$ & $0.98$ & $1.00$ & $0.93$ & $0.91$ & $0.76$ & $1.05$ & $1.01$ \\
+$4.5$~GeV   & $1.04$ & $0.89$ & $0.82$ & $0.94$ & $0.99$ & $0.92$ & $0.87$ & $0.71$ & $1.03$ & $1.00$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{table}
+\centering
+\caption{\label{tab:thvseps}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon_{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			      & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$2\%$ & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$5\%$ & $1.48$ & $1.25$ & $1.25$ & $1.48$ & $1.64$ \\
+			$10\%$ & $2.40$ & $2.14$ & $2.21$ & $2.72$ & $3.09$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table}
+\centering
+\caption{\label{tab:sign}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$~GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta_{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			    & $-180^\circ$ & $-90^\circ$ & $0^\circ$ & $90^\circ$ & $180^\circ$\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$+$ & $1.40$ & $0.43$ & $1.16$ & $11.48$ & $1.40$\\
+			$-$ & $1.45$ & $11.75$& $1.11$ & $0.43$  & $1.45$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table*}
+\centering
+\caption{\label{tab:thvsE_td}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta_{CP}$ case, and for different decay tunnel length ($L_T$) and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 2 years of positive focusing plus 8 years of negative focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings are identical to those of table~\ref{tab:speciesfluxes}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+setting & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (7b) & (8) & (9)\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$2.2$~GeV &        & $2.52$ &        &        & $2.58$ &        & $2.30$ &        &         &       \\
+$3.5$~GeV & $2.34$ & $2.22$ & $2.10$ & $2.13$ & $2.09$ & $2.08$ & $2.02$ & $2.28$ &  $2.16$ & $2.09$\\
+$4.5$~GeV & $2.91$ & $2.60$ & $2.43$ & $2.48$ & $2.52$ & $2.39$ & $2.34$ & $2.55$ &  $2.53$ & $2.47$\\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\section{Summary and outlook}
+A complete chain of simulation has been set up for the SPL-Fréjus project. The neutrino production has been extended to the kaon decay contribution, which is important to test SPL energy scenario above $2.2$~GeV.
+The beam line optimization has been performed using the sensitivity to $\sin^22\theta_{13}$ and $\delta_{CP}$. The shape of the focusing system has been updated to obtain a neutrino beam energy around $260$~MeV or $350$~MeV.
+
+In a positive only focusing scenario, the best limit on $\sin^22\theta_{13}$ is $0.82\times10^{-3}$
+ ($90\%$ CL, $\delta_{CP}=0$), with a $4.5$~GeV beam energy and a $20$~m long, $1.5$~m radius decay tunnel. However, the $3.5$~GeV beam may also obtain rather similar limit with $0.83\times10^{-3}$ ($90\%$ CL) with the same tunnel parameters. The $\delta_{CP}$ independant $\sin^22\theta_{13}$ sensitivity is limited to $\approx 10^{-2}$ due to the $\delta_{CP} \approx 90^o$ region.
+ 
+In a mixed focusing scenario, the best limit on $\sin^22\theta_{13}$ independent of $\delta_{CP}$ is $2.02\times10^{-3}$ ($90\%$ CL) obtained with a $3.5$~GeV beam energy and a $40$~m long, $2$~m radius decay tunnel.
+
+The comparison of the optimization presented in this paper with the results obtained by other projects is displayed on figure \ref{fig:deltathetaFinal}. It is presented the 5 years positive focusing scenario, and two versions of a mixed scenario using positive and negative focusing: one scenario duration is 5 years in total and the other one is 10 years running in total and has been used in the previous section. It shows the complementarity of the SPL-Fr\'ejus project with the beta beam-Fr\'ejus project. Especially when considering the sensitivity to $\sin^22\theta_{13}$ for $\delta_{CP}<0$. 
+
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comparaisonFinale.eps}
+\caption{\label{fig:deltathetaFinal}90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite{CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite{Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite{MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite{KOBAYASHI}. The BNL contour has been obtained from reference \cite{BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu_e$ and $\bar{\nu}_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta$ beam was analysed like a reactor experiment with 1\% systematic error \cite{MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$~GeV beam and a decay tunnel of $40$~m length, and $2$~m radius.}
+\end{figure}
+%
+The authors think that the present study may be extended in many respects. The beam line simulation part may be performed with a single simulator as FLUKA (or GEANT4 \cite{GEANT4} for comparison). Other targets may be envisaged (tantalum, carbon) as well as other detector types as a Large Liquid Argon detector \cite{BIGICARUS}. The baseline length may also be revisited as well as the off axis option. The sensitivity analysis may be deeper investigated using the complete set of possible ambiguities as in reference \cite{DONINI}, and the $\theta_{13}$ or $\delta_{CP}$ measurement accuracy with new beam energy scenario may be investigated too.     
+%
+\begin{acknowledgement}
+The authors would like to thank M.~Mezzetto to have expressed his interest since the early stage of this work and to have provided us with his sensitivity computation program. Also the authors thank S.~Gilardoni for fruitful discussions.
+\end{acknowledgement}
+%
+\appendix
+\setcounter{section}{0}
+\section{Decay probability computations}
+\label{sec:decayprobcomp}
+This appendix contains the probability formulas and the algorithms used in the flux computation (see section~\ref{sec:algo}).
+
+\subsection{Pion neutrino probability computation}
+\label{sec:Ppi}
+Pions decay only as $\pi^+\rightarrow \mu^+ + \nu_\mu$ or $\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$ and the neutrinos are emitted isotropically in the pion rest frame, with an energy of about $30$~MeV given by the 2-body decay kinematics. Applying a Lorentz boost knowing the pion momentum and direction, it is possible to compute the probability to reach the detector for the neutrinos. Only neutrino parallel to the beam axis are supposed to pass through the detector fiducial area, and therefore, the neutrino must be emitted by the pion with an angle opposite to the angle between the pion and the beam axis (see figure~\ref{fig:pionDecay}). This gives:
+\begin{equation}
+\mathcal{P}_\pi = \frac{1}{4\pi}\frac{A}{L^2}\frac{1-\beta^2}{(\beta\cos\alpha-1)^2}
+\label{probaPi}
+\end{equation}
+where $\beta$ is the velocity of the pion in the tunnel frame, $A$ is the fiducial detector surface, $L$ the distance between the neutrino source and the detector, and $\alpha$ the angle between the pion direction and the beam axis in the laboratory frame.
+
+\begin{figure}
+\centering
+\includegraphics{../picts/pionDecay.eps}
+\caption{\label{fig:pionDecay}Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha$ is needed.}
+\end{figure}
+
+\subsection{Muon neutrino probability computation}
+\label{sec:Pmu}
+Muons decay only as $\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_\mu$ or $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$, and will produce background events. The mean decay length of the muons is $2$~km, therefore, most of them do not decay in the tunnel. This induces a lack of statistics to estimate the corresponding level of background. This problem has been solved using each muon appearing in the simulation in the following steps:
+\begin{enumerate}
+	\item the probability for the muon to decay into the tunnel has been computed using a straight line propagation;
+	\item the available energy for the neutrino in the tunnel frame has been divided in $20$~MeV energy bins; 
+	% (the number of bin depending of the muon energy).
+	\item one $\nu_e$ and one $\nu_\mu$ have been simulated in each of the energy bins (step 2). Then, the probability to reach the detector has been computed, and multiplied by the probability computed at step (1).%the neutrino energy is stored in an histogram, weighted with this probability and 
+\end{enumerate}
+After the probability computation, the non useful muon is discarded by GEANT to gain in CPU time. 
+
+The probability for the muon neutrino and the electron neutrino to be emitted parallel to the beam axis is \cite{donega}:
+\begin{multline}
+\frac{d\mathcal{P}_\mu}{dE_\nu} = \frac{1}{4\pi}\frac{A}{L^2}\frac{2}{m_\mu}\frac{1}{\gamma_\mu(1+\beta_\mu\cos\theta^*)}\\ \times \frac{1-\beta_\mu^2}{(\beta_\mu\cos\rho-1)^2}\left[f_0(x)\mp \Pi_\mu^L f_1(x)\cos\theta^*\right]
+\label{probaMu}
+\end{multline}
+where $\beta_\mu$ and $\gamma_\mu$ are the velocity and the Lorentz boost of the muon in the tunnel frame, $\theta^*$ is the angle with respect to the beam axis of the muon in the muon rest frame, $\rho$ is the corresponding angle in the tunnel frame. Like in the pion case, this angle appears because the neutrino must be parallel to the beam axis. $\Pi_\mu^L$ is the muon longitudinal polarization, the parameter $x$ is defined as $x=2E_\nu^*/m_\mu$ where $E_\nu^*$ is the neutrino energy in the muon rest frame, and the function $f_0(x)$ and $f_1(x)$ coming from the matrix element of the muon decay are given in table~\ref{tab:Function}. The sign in front of $\Pi_\mu^L$ in equation~\ref{probaMu} is $(-)$ for the $\mu^+$ decays and $(+)$ for the $\mu^-$ decays, respectively.
+
+%\Table{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%\br
+%		      &  $f_0(x)$ & $f_1(x)$ \\
+%\mr
+%		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+%		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		      &  $f_0(x)$ & $f_1(x)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+Muon polarization is computed using the conservation of the transverse component of the velocity four-vector $\gamma(1,\beta)$ between the muon rest frame (where the polarization is computed) and the pion rest frame, where the muon helicity is $-1$, due to the parity non conservation. It yields \cite{picasso}:
+\begin{equation}
+\Pi_\mu^T = \frac{\gamma_\pi\beta_\pi}{\gamma_\mu\beta_\mu}\sin\theta^*
+\mbox{ and }\Pi_\mu^L = \sqrt{1-\Pi_\mu^{T2}}
+\label{pola}
+\end{equation}
+where $\gamma_\pi$, $\beta_\pi$, $\gamma_\mu$, and $\beta_\mu$ are the Lorentz boost and velocity of the pion and of the muon in the tunnel frame, and $\theta^*$ the angle with respect to the beam axis of the muon in the pion rest frame.
+
+\subsection{The treatment of the kaons}
+\label{sec:kaons}
+Contrary to pions and muons, kaons have many decay channels. They are summarized in table~\ref{tab:BRKP0SL}.
+
+%\Table{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%\br
+%\centre{2}{$K^\pm$}                                               & \centre{2}{$K^0_L$}     &          \centre{2}{$K^0_S$}\\
+%\mr
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu$   & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+%$\pi^\pm\pi^0$ & $21.17\%$                                        & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+%$\pi^\pm\pi^+\pi^-$ & $5.59\%$                                    & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+%$e^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+%$\pi^\pm\pi^0\pi^0$ & $1.73\%$                                    & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+\centre{2}{$K^\pm$}         & \centre{2}{$K^0_L$}     & \centre{2}{$K^0_S$}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$\mu^\pm\nu_\mu$ & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+$\pi^\pm\pi^0$ & $21.17\%$   & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+$\pi^\pm\pi^+\pi^-$ & $5.59\%$ & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+$e^\pm\nu_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+$\mu^\pm\nu_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+$\pi^\pm\pi^0\pi^0$ & $1.73\%$ & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+There is a very small amount of kaons produced (section~\ref{sec:kaon}), and this number has been artificially increased in order to obtain statistically significant results.  The multiplicity of decay channels makes impossible the method used for the muon case (\ref{sec:Pmu}). The method chosen for the good compromise between the gain in CPU and the statistical uncertainty of the results, is to duplicate many times each kaon exiting the target. The number of duplication varies between 10 and 300. It depends on the initial kaon rate and therefore on the beam energy.
+
+All the kaons daughter particles are tracked by GEANT until they decay. Three different types of daughter particles are identified in the kaon decays. The first type corresponds to primary neutrinos, the second type concerns charged pions and muons, and the neutral pions are left for the last type.
+
+In the $K^\pm\rightarrow\mu^\pm \nu_\mu(\bar{\nu}_\mu)$ decay modes, the computation of the probability for a neutrino to reach the detector is the same than the 2-body decay formula used to in the pion decay (equation~\ref{probaPi}), where $\beta$ is now the kaon velocity, and $\alpha$ the angle of the kaon with respect to the beam axis. 
+
+When a neutrino is produced by a kaon 3-body decay, the probability to reach the detector is computed using a pure phase space formula. It yields:
+\begin{multline}
+\mathcal{P}_K = \frac{1}{4\pi}\frac{A}{L^2}\frac{1}{m_K-m_\pi-m_l} \\ \times \frac{1}{\gamma_K(1+\beta_K\cos\theta^*)}
+\frac{1-\beta_K^2}{(\beta_K\cos\delta-1)^2}
+\label{probaL}
+\end{multline}
+where $m_K$ is the kaon mass (charged or neutral), $m_\pi$ is the pion mass ($\pi^0$ mass in $K^\pm$ decays and $\pi^\pm$ mass in $K_L^0$ decays), and $m_l$ is the mass of the lepton associated with the neutrino. The $\beta_K$ and $\gamma_K$ are the velocity and the Lorentz boost of the kaon, $\theta^*$ is the angle between the neutrino direction and the kaon direction, in the kaon rest frame. Finally, $\delta$ is the angle between the kaon direction and the beam axis in the tunnel frame.
+
+When a $\pi^\pm$ is produced in the kaon decay chain, it is tracked by GEANT until it decays, and the probability of equation~\ref{probaPi} is applied to the produced neutrino. In case of a muon, it is treated as explained in \ref{sec:Pmu}. The muon polarization is computed this time using the kaon decay informations. Finally, when a $\pi^0$ is produced, as it cannot create neutrinos, it is simply discarded.
+
+%
+%\section*{References}
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+I. Ambats \etal,  NO$\nu$A proposal FNAL P929, 2004 (unpublished)
+
+\bibitem{T2K}
+Y. Itow, KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05 (unpublished),
+see also arXiv:hep-ex/0106019
+
+\bibitem{BNLHS}
+M. V. Diwan, \PR D {\bf 68}, 012002 (2003)
+
+\bibitem{CERN}
+A. Blondel \etal, CERN-2004-002 (unpublished)
+
+\bibitem{DONINI}
+A. Donini \etal, IFT-UAM/CSIC-04-30, 2004 (unpublished);
+see also arXiv:hep-ph/0406132
+
+\bibitem{DOUBLE-CHOOZ}
+F. Dalnoki-Veress, the Double-CHOOZ project arXiv:hep-ex/0406070 (unpublished)
+
+\bibitem{SPL}
+B. Autin \etal, CERN-2000-12 (unpublished)
+
+\bibitem{UNO} 
+The UNO whitepaper, \textsl{Physics Potential and Feasibility of UNO}, SBHEP01-3 (unpublished), see also http://ale.physics.sunysb.edu/uno/
+
+\bibitem{mosca}
+L. Mosca, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Meer}
+S. van der Meer, CERN-Report No 61-7, 1961 (unpublished)
+
+\bibitem{nuFact134} 
+J.E. Campagne and A. Cazes, CERN-NUFACT-Note-134, 2003 (unpublished), see http://slac.web.cern.ch/slap/NuFact/NuFact/\\
+NFNotes.html
+
+\bibitem{MMWPSCazes} 
+J.E. Campagne and A. Cazes, Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004,
+see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{JJG}
+J.J. G\'omez Gadenas \etal,  IFIC/01-31, Proceedings of Venice 2001, Neutrino telescopes, vol. 2, p463-481;
+see also arXiv:hep-ph/0105297; A. Blondel \etal, \NIM A {\bf 503} 173 (2001);
+A. Blondel \etal, CERN-2004-002
+
+\bibitem{Mezzetto}
+M. Mezzetto,  \jpg {\bf 29}, 1781-1784 (2003),
+see also arXiv:hep-ex/0302005
+
+
+\bibitem{nuFact138} 
+J.E. Campagne, CERN-NUFACT-Note-138, 2004 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{fluka}
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p159-164 (2001);
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+
+\bibitem{MMWPSGaroby} 
+R. Garoby, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{harp}
+C. Catanesi \etal, CERN-SPSC 2002/019 (unpublished)
+
+\bibitem{minerva} 
+D. Drakoulakos \etal, Fermilab P-938 (unpublished),
+see also arXiv:hep-ex/405002
+
+\bibitem{MARS}
+N.V. Mokhov \etal, The MARS Code System User Guide, Version 13(95), Fermilab-FN-628 (1995);
+N.V. Mokhov  \etal, MARS oed Develepments, LANL Report LA-UR-98-5716 (1998), nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+
+\bibitem{FLUKAprivate}
+G. Battistoni and A. Ferrari, \textsl{private communication}
+
+\bibitem{geant}
+Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+
+\bibitem{SIMONE1}
+S. Gilardoni, Talk at NuFact03 (2003), see http://www.cap.bnl.gov/nufact03/
+
+\bibitem{donega}
+A. Blondel \etal, CERN-NUFACT-Note-78, 2001 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{MEZZETTONUFACT060}
+M. Mezzetto, CERN-NUFACT-Note-60, 2000 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{DONINI-2}
+A. Donini, D. Meloni and S. Rigolin, J. High Energy Phys. \textbf{0406}, 011 (2004),
+see also arXiv:hep-ph/0312072
+
+\bibitem{NUANCE}
+D. Casper, \textsl{ Nucl. Phys. Proc. Suppl.} \textbf{112}, 161-170 (2002),
+see also arXiv:hep-ph/0208030
+
+\bibitem{KAMLAND}
+G. Gratta,  talk at the International Conference NEUTRINO 2004, 14-19 June 2004, http://neutrino2004.in2p3.fr/
+
+\bibitem{MIGLIOZZITERANOVA}
+M. Komatsu, P Migliozzi and F. Terranova,  \jpg {\bf 29}, 443 (2003); see also arXiv:hep-ph/0210043
+
+\bibitem{KOBAYASHI}
+T. Kobayashi, \NP B (Proceedings Supplement) {\bf 143}, 303 (2005)
+
+\bibitem{BNL}
+ M.V. Diwan \etal, \PR D \textbf{68}, 012002 (2003); see also figure~8 of 
+arXiv:hep-ph/0303081
+
+\bibitem{MAOROPRIVATE}
+M. Mezzetto, \textsl{private communication}: the corresponding $\theta_{13}$ limit is $3.4^o$.
+
+\bibitem{GEANT4}
+A. Agostinelli \etal, \NIM A \textbf{506}, 250-503 (2003) 
+
+\bibitem{BIGICARUS}
+A. Ereditato and A. Rubia, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Gaisser}
+T.K. Gaisser, \textsl{Cosmic Rays and Particle Physics} (Cambridge University Press, 1990)  
+
+\bibitem{picasso}
+F. Combley and E. Picasso, \textsl{Phys. Rept.} {\bf 14}, 1 (1974) 
+
+\bibitem{pdg}
+K. Hagiwara \etal,  \PR D {\bf 66},  010001 (2002)
+
+
+%
+\end{thebibliography}
+%
+\end{document}
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r1.aux
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r1.aux	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r1.aux	(revision 392)
@@ -0,0 +1,222 @@
+\relax 
+\citation{SKNU04,K2KNU04}
+\citation{K2KNU04}
+\citation{MINOS}
+\citation{OPERA,ICARUS}
+\citation{CNGS}
+\citation{LSND}
+\citation{MINIBOONE}
+\citation{PMNS}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{BETABEAM}
+\citation{NOVA,T2K}
+\citation{T2K,BNLHS,CERN}
+\citation{CERN}
+\citation{DONINI}
+\citation{DONINI,DOUBLE-CHOOZ}
+\citation{SPL}
+\citation{UNO}
+\citation{mosca}
+\citation{CERN}
+\citation{Meer}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Sketch of the SPL neutrino Superbeam from CERN to the Fr\'ejus tunnel.}}{1}}
+\newlabel{fig:Sbeam}{{1}{1}}
+\citation{nuFact134,MMWPSCazes}
+\citation{DONINI,JJG,Mezzetto}
+\citation{nuFact138}
+\citation{fluka}
+\citation{CERN}
+\citation{JJG}
+\citation{CERN}
+\citation{SPL}
+\citation{MMWPSGaroby}
+\citation{nuFact134}
+\citation{harp}
+\citation{MARS}
+\citation{nuFact134}
+\citation{MMWPSGaroby}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Liquid mercury jet parameters.}}{2}}
+\newlabel{tab:targ}{{1}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Target simulation}{2}}
+\newlabel{sec:target}{{2}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Kaon production}{2}}
+\newlabel{sec:kaon}{{3}{2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  (a) $\pi ^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi ^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$\nobreakspace  {}GeV/c and $0.7$\nobreakspace  {}GeV/c. The different SPL beam kinetic energies presented are (\mbox {------}) $2.2$\nobreakspace  {}GeV, (\mbox {- - - -}) $3.5$\nobreakspace  {}GeV, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) $4.5$\nobreakspace  {}GeV and (\mbox {--- $\cdot $ ---}) $6.5$\nobreakspace  {}GeV.}}{3}}
+\newlabel{fig:compEner2}{{2}{3}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces $\pi ^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\mbox {- - - -}) and by MARS (\mbox {------}).}}{3}}
+\newlabel{fig:compFlukaMars}{{3}{3}}
+\citation{FLUKAprivate}
+\citation{geant}
+\citation{SIMONE1}
+\citation{nuFact138}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Average numbers of the most relevant secondary particles exiting the $30$\nobreakspace  {}cm long, $1.5$\nobreakspace  {}cm diameter mercury target per incident proton (FLUKA). The $\mu ^+/\mu ^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}}{4}}
+\newlabel{tab:nbPart}{{2}{4}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Horns simulation}{4}}
+\newlabel{sec:horn}{{4}{4}}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Relevant parameters of the horns in case of the generation of a $260$\nobreakspace  {}MeV neutrino beam (or $350$\nobreakspace  {}MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$\nobreakspace  {}MeV/c (or $800$\nobreakspace  {}MeV/c) pion momentum.}}{4}}
+\newlabel{tab:specif}{{3}{4}}
+\citation{donega}
+\citation{donega}
+\citation{donega}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).}}{5}}
+\newlabel{fig:KaonsPions}{{4}{5}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350\nobreakspace  {}MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}}{5}}
+\newlabel{fig:plan}{{5}{5}}
+\@writefile{toc}{\contentsline {section}{\numberline {5}Particle decay treatment and flux calculation}{5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Algorithm description}{5}}
+\newlabel{sec:algo}{{5.1}{5}}
+\citation{donega}
+\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Number of protons on target for different beam energy at 4\nobreakspace  {}MW constant power. One year is defined as $10^7$\nobreakspace  {}s.}}{6}}
+\newlabel{tab:proton}{{4}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Validation of the algorithm}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Simulated fluxes}{6}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  Neutrino fluxes, $100$\nobreakspace  {}km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$\nobreakspace  {}GeV (4\nobreakspace  {}MW), a decay tunnel with a length of $20$\nobreakspace  {}m and a radius of $1$\nobreakspace  {}m. The top left panel contains the $\nu _\mu $ fluxes, and the top right panel shows the $\mathaccentV {bar}016{\nu }_\mu $ fluxes. The bottom left panel presents the $\nu _e$ fluxes while the bottom right panel displays the $\mathaccentV {bar}016{\nu }_e$ fluxes. The (\mbox {------}) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\mbox {- - - -}) curve is the contribution from the charged kaon decay chain, and the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}}{7}}
+\newlabel{fig:flux22p}{{6}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but the horns are focusing negative particles.}}{7}}
+\newlabel{fig:flux22m}{{7}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{8}}
+\newlabel{fig:flux45p}{{8}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{8}}
+\newlabel{fig:flux45m}{{9}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{9}}
+\newlabel{fig:flux8p}{{10}{9}}
+\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{9}}
+\newlabel{fig:flux8m}{{11}{9}}
+\citation{UNO}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{Mezzetto}
+\citation{DONINI-2}
+\citation{NUANCE}
+\citation{MEZZETTONUFACT060}
+\citation{mosca}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Integral of the total flux of the different species with different settings. The $\nu _\mu $ and $\mathaccentV {bar}016{\nu }_\mu $ fluxes are expressed in $10^{13}/100\@mathrm {m}^2/y$ unit while the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes are expressed in $10^{11}/100\@mathrm {m}^2/y$ unit. The positive focusing and negative focusing are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. }}{10}}
+\newlabel{tab:speciesfluxes}{{5}{10}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Sensitivity computation ingredients}{10}}
+\@writefile{toc}{\contentsline {section}{\numberline {7}Results}{10}}
+\newlabel{sec:results}{{7}{10}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}The positive only focusing scenario}{10}}
+\citation{DONINI}
+\citation{DONINI,JJG,Mezzetto}
+\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Comparison between the probability method, (\mbox {------}) curve, and the full GEANT simulation method, (\mbox {- - - -}) curve, for the $\nu _\mu $ from $\pi ^+$ flux (a) and the $\mathaccentV {bar}016{\nu }_\mu $ from $\pi ^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes contrary to the former simulation.}}{11}}
+\newlabel{fig:compGeantDonega}{{12}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Default parameters used to compute the sensitivity curves \cite  {MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite  {KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite  {JJG}.}}{11}}
+\newlabel{tab:param}{{6}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Number of events for 5 years positive focusing scenario with default parameters of table\nobreakspace  {}6\hbox {}. Other backgrounds are $\pi ^0$, $\nu _\mu $-elast., $\mu /e$-missId. }}{12}}
+\newlabel{tab:nbvsE}{{7}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Sensitivity contours obtained with a SPL energy of $3.5$\nobreakspace  {}GeV and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m. (\mbox {------}), (\mbox {- - - -}) and (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}}{12}}
+\newlabel{fig:sensi45}{{13}{12}}
+\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{12}}
+\newlabel{tab:thvsE}{{8}{12}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Mixed positive/negative focusing scenario}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{12}}
+\newlabel{fig:compSensi}{{14}{12}}
+\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Study of the sensitivity of different beam energy, decay tunnel length ($L_T$) at and radius ($R_T$), and horn design in two different scenarios. First scenario is 5 years of positive focusing, in wich sensitivity is given as the minimum of $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL. Second scenario is 2 years of positive focusing plus 8 years of negative focusing, in wich sensitivity is given as the minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta _{CP}$ case. A star $^{(*)}$ indicates the use of the the horn geometry producing a $350$\nobreakspace  {}MeV neutrino beam. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:thvsE_3545}{{9}{13}}
+\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV, and either a $260$\nobreakspace  {}MeV (default) neutrino beam or a $350$\nobreakspace  {}MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$\nobreakspace  {}m and $R_T = 2$\nobreakspace  {}m. The (\mbox {--- $\cdot $ ---}) curve corresponds to a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV (neutrino beam/SPL beam energy) setting; the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve corresponds to a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting; the (\mbox {- - - -}) curve corresponds to a $260$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting and the (\mbox {------}) curve corresponds to a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting.}}{13}}
+\newlabel{fig:comp5year}{{15}{13}}
+\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces 90\% sensitivity contours obtained with SPL beam energy of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) at $90\%$ CL. Default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{13}}
+\newlabel{fig:compDeltaTheta}{{16}{13}}
+\@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{13}}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\citation{GEANT4}
+\citation{BIGICARUS}
+\citation{DONINI}
+\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces 90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$\nobreakspace  {}m and $R_T=2$\nobreakspace  {}m and different SPL beam energies ($3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV) and different horn designs ($260$\nobreakspace  {}MeV or $350$\nobreakspace  {}MeV neutrino beams): (\mbox {------}) curve for a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve for a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting, (\mbox {- - - -}) curve for a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting. Other default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}}{14}}
+\newlabel{fig:sensiDeltaTheta}{{17}{14}}
+\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon _{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{14}}
+\newlabel{tab:thvseps}{{10}{14}}
+\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$\nobreakspace  {}GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta _{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{14}}
+\newlabel{tab:sign}{{11}{14}}
+\@writefile{toc}{\contentsline {section}{\numberline {A}Decay probability computations}{14}}
+\newlabel{sec:decayprobcomp}{{A}{14}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}Pion neutrino probability computation}{14}}
+\newlabel{sec:Ppi}{{A.1}{14}}
+\citation{donega}
+\citation{Gaisser}
+\citation{picasso}
+\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces 90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite  {CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite  {Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite  {MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite  {KOBAYASHI}. The BNL contour has been obtained from reference \cite  {BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta $ beam was analysed like a reactor experiment with 1\% systematic error \cite  {MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$\nobreakspace  {}GeV beam and a decay tunnel of $40$\nobreakspace  {}m length, and $2$\nobreakspace  {}m radius.}}{15}}
+\newlabel{fig:deltathetaFinal}{{18}{15}}
+\newlabel{probaPi}{{1}{15}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Muon neutrino probability computation}{15}}
+\newlabel{sec:Pmu}{{A.2}{15}}
+\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha $ is needed.}}{15}}
+\newlabel{fig:pionDecay}{{19}{15}}
+\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Flux function in the muon rest frame \cite  {Gaisser}.}}{15}}
+\newlabel{tab:Function}{{12}{15}}
+\newlabel{probaMu}{{2}{15}}
+\newlabel{pola}{{3}{15}}
+\citation{pdg}
+\bibcite{SKNU04}{1}
+\bibcite{K2KNU04}{2}
+\bibcite{MINOS}{3}
+\bibcite{OPERA}{4}
+\bibcite{ICARUS}{5}
+\bibcite{CNGS}{6}
+\bibcite{LSND}{7}
+\bibcite{MINIBOONE}{8}
+\bibcite{PMNS}{9}
+\bibcite{CHOOZ}{10}
+\bibcite{Wpaper}{11}
+\bibcite{BETABEAM}{12}
+\bibcite{NOVA}{13}
+\bibcite{T2K}{14}
+\bibcite{BNLHS}{15}
+\bibcite{CERN}{16}
+\bibcite{DONINI}{17}
+\bibcite{DOUBLE-CHOOZ}{18}
+\bibcite{SPL}{19}
+\bibcite{UNO}{20}
+\bibcite{mosca}{21}
+\bibcite{Meer}{22}
+\bibcite{nuFact134}{23}
+\@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces Charged and neutral kaon decay channels \cite  {pdg}.}}{16}}
+\newlabel{tab:BRKP0SL}{{13}{16}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.3}The treatment of the kaons}{16}}
+\newlabel{sec:kaons}{{A.3}{16}}
+\newlabel{probaL}{{4}{16}}
+\bibcite{MMWPSCazes}{24}
+\bibcite{JJG}{25}
+\bibcite{Mezzetto}{26}
+\bibcite{nuFact138}{27}
+\bibcite{fluka}{28}
+\bibcite{MMWPSGaroby}{29}
+\bibcite{harp}{30}
+\bibcite{minerva}{31}
+\bibcite{MARS}{32}
+\bibcite{FLUKAprivate}{33}
+\bibcite{geant}{34}
+\bibcite{SIMONE1}{35}
+\bibcite{donega}{36}
+\bibcite{MEZZETTONUFACT060}{37}
+\bibcite{DONINI-2}{38}
+\bibcite{NUANCE}{39}
+\bibcite{KAMLAND}{40}
+\bibcite{MIGLIOZZITERANOVA}{41}
+\bibcite{KOBAYASHI}{42}
+\bibcite{BNL}{43}
+\bibcite{MAOROPRIVATE}{44}
+\bibcite{GEANT4}{45}
+\bibcite{BIGICARUS}{46}
+\bibcite{Gaisser}{47}
+\bibcite{picasso}{48}
+\bibcite{pdg}{49}
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r1.blg
===================================================================
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+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r1.blg	(revision 392)
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r1.log
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r1.tex
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r1.tex	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r1.tex	(revision 392)
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+\newcommand{\DSE}{{\it Distrib. Syst. Engng\/} }
+\newcommand{\EJP}{{\it Eur. J. Phys.} } 
+\newcommand{\HPP}{{\it High Perform. Polym.} }              % added 4/5/93
+\newcommand{\IP}{{\it Inverse Problems\/} }
+\newcommand{\JHM}{{\it J. Hard Mater.} }                    % added 4/5/93
+\newcommand{\JO}{{\it J. Opt.} }
+\newcommand{\JOA}{{\it J. Opt. A: Pure Appl. Opt.} }
+\newcommand{\JOB}{{\it J. Opt. B: Quantum Semiclass. Opt.} }
+\newcommand{\JPA}{{\it J. Phys. A: Math. Gen.} }
+\newcommand{\JPB}{{\it J. Phys. B: At. Mol. Phys.} }      %1968-87
+\newcommand{\jpb}{{\it J. Phys. B: At. Mol. Opt. Phys.} } %1988 and onwards
+\newcommand{\JPC}{{\it J. Phys. C: Solid State Phys.} }   %1968--1988
+\newcommand{\JPCM}{{\it J. Phys.: Condens. Matter\/} }    %1989 and onwards
+\newcommand{\JPD}{{\it J. Phys. D: Appl. Phys.} }
+\newcommand{\JPE}{{\it J. Phys. E: Sci. Instrum.} }
+\newcommand{\JPF}{{\it J. Phys. F: Met. Phys.} }
+\newcommand{\JPG}{{\it J. Phys. G: Nucl. Phys.} }         %1975--1988
+\newcommand{\jpg}{{\it J. Phys. G: Nucl. Part. Phys.} }   %1989 and onwards
+\newcommand{\MSMSE}{{\it Modelling Simulation Mater. Sci. Eng.} }
+\newcommand{\MST}{{\it Meas. Sci. Technol.} }                 %1990 and onwards
+\newcommand{\NET}{{\it Network: Comput. Neural Syst.} }
+\newcommand{\NJP}{{\it New J. Phys.} }
+\newcommand{\NL}{{\it Nonlinearity\/} }
+\newcommand{\NT}{{\it Nanotechnology} }
+\newcommand{\PAO}{{\it Pure Appl. Optics\/} }
+\newcommand{\PM}{{\it Physiol. Meas.} }                        % added 4/5/93
+\newcommand{\PMB}{{\it Phys. Med. Biol.} }
+\newcommand{\PPCF}{{\it Plasma Phys. Control. Fusion\/} }      % added 4/5/93
+\newcommand{\PSST}{{\it Plasma Sources Sci. Technol.} }
+\newcommand{\PUS}{{\it Public Understand. Sci.} }
+\newcommand{\QO}{{\it Quantum Opt.} }
+\newcommand{\QSO}{{\em Quantum Semiclass. Opt.} }
+\newcommand{\RPP}{{\it Rep. Prog. Phys.} }
+\newcommand{\SLC}{{\it Sov. Lightwave Commun.} }               % added 4/5/93 
+\newcommand{\SST}{{\it Semicond. Sci. Technol.} }
+\newcommand{\SUST}{{\it Supercond. Sci. Technol.} }
+\newcommand{\WRM}{{\it Waves Random Media\/} }
+\newcommand{\JMM}{{\it J. Micromech. Microeng.\/} }
+%
+% Other commonly quoted journals
+%
+\newcommand{\AC}{{\it Acta Crystallogr.} }
+\newcommand{\AM}{{\it Acta Metall.} }
+\newcommand{\AP}{{\it Ann. Phys., Lpz.} }
+\newcommand{\APNY}{{\it Ann. Phys., NY\/} }
+\newcommand{\APP}{{\it Ann. Phys., Paris\/} }
+\newcommand{\CJP}{{\it Can. J. Phys.} }
+\newcommand{\JAP}{{\it J. Appl. Phys.} }
+\newcommand{\JCP}{{\it J. Chem. Phys.} }
+\newcommand{\JJAP}{{\it Japan. J. Appl. Phys.} }
+\newcommand{\JP}{{\it J. Physique\/} }
+\newcommand{\JPhCh}{{\it J. Phys. Chem.} }
+\newcommand{\JMMM}{{\it J. Magn. Magn. Mater.} }
+\newcommand{\JMP}{{\it J. Math. Phys.} }
+\newcommand{\JOSA}{{\it J. Opt. Soc. Am.} }
+\newcommand{\JPSJ}{{\it J. Phys. Soc. Japan\/} }
+\newcommand{\JQSRT}{{\it J. Quant. Spectrosc. Radiat. Transfer\/} }
+\newcommand{\NC}{{\it Nuovo Cimento\/} }
+\newcommand{\NIM}{{\it Nucl. Instrum. Methods\/} }
+\newcommand{\NP}{{\it Nucl. Phys.} }
+\newcommand{\PL}{{\it Phys. Lett.} }
+\newcommand{\PR}{{\it Phys. Rev.} }
+\newcommand{\PRL}{{\it Phys. Rev. Lett.} }
+\newcommand{\PRS}{{\it Proc. R. Soc.} }
+\newcommand{\PS}{{\it Phys. Scr.} }
+\newcommand{\PSS}{{\it Phys. Status Solidi\/} }
+\newcommand{\PTRS}{{\it Phil. Trans. R. Soc.} }
+\newcommand{\RMP}{{\it Rev. Mod. Phys.} }
+\newcommand{\RSI}{{\it Rev. Sci. Instrum.} }
+\newcommand{\SSC}{{\it Solid State Commun.} }
+\newcommand{\ZP}{{\it Z. Phys.} }
+
+\newcommand{\etal}{{et al.\/}}
+%
+%
+%----------------------------------------------------------------------------
+\begin{document}
+%
+\title{The $\theta_{13}$ and $\delta_{CP}$ sensitivities of the SPL-Fréjus project revisited}
+\author{Jean Eric Campagne, Antoine Cazes}
+\institute{ Laboratoire de l'Accélérateur Linéaire -
+Université Paris-Sud - B\^at. 200 - BP 34 -
+91898 Orsay Cedex, France}
+\mail{campagne@lal.in2p3.fr}
+\date{\today}
+%
+%
+%
+%\selectlanguage{francais}
+%
+\abstract{
+An optimization of the CERN SPL beam line has been performed guided by the sensitivities to the $\theta_{13}$ mixing angle and to the $\delta_{CP}$ Dirac CP violating phase. A UNO-like 440 ktons water \v{C}erenkov detector located at 130~km from the target in a new foreseen Fréjus laboratory has been used as a generic detector. Concerning the $\delta_{CP}$ independent $\theta_{13}$ sensitivity, a gain of about $20\%$ may be reached using a $3.5$~GeV proton beam with a 40~m long, 2~m radius decay tunnel compared to the up to now considered $2.2$~GeV beam energy and 20~m long, 1~m radius decay tunnel. This may motivate new machine developments to upgrade the nominal SPL proton beam energy.}
+%\pacs{14.60.Pq, 14.60.Lm}
+
+\maketitle
+
+
+\section{Introduction}
+The very near future of the neutrino long baseline experiments is devoted to the study of the oscillation mechanism in the range of $\Delta m^2 = \Delta m^2_{atm} \approx 2.4\times10^{-3}\mathrm{eV}^2$ \cite{SKNU04,K2KNU04}
+ using conventional $\nu_\mu$ beams. The current K2K experiment in Japan \cite{K2KNU04}, and the forthcoming MINOS in the USA \cite{MINOS} take benefit of low energy beam to measure the $\Delta m^2$ parameter using the disappearance mode $\nu_\mu\rightarrow\nu_\mu$, while OPERA/ICARUS experiments \cite{OPERA,ICARUS} using the high energy CNGS beam \cite{CNGS} will be able to detect $\nu_\tau$ appearance. If we do not consider the LSND anomaly \cite{LSND} that will be further studied soon by MiniBooNE experiment \cite{MINIBOONE}, the three flavor family scenario will be confirmed and accommodated by a $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix \cite{PMNS} with three angles ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase $\delta_{CP}$.  
+
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/cernSuperBeam_English}
+\caption{\label{fig:Sbeam}Sketch of the SPL neutrino Superbeam from CERN to the Fréjus tunnel.}	
+\end{figure}
+
+Beyond this medium term plan, two of the next future tasks of neutrino physics are to improve the sensitivity of the last unknown mixing angle parameter, the so-called $\theta_{13}$, and to explore the CP violation mechanism in the leptonic sector. The present upper bound on $\theta_{13}$ is $\sin^22\theta_{13}<0.14$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$~CL) \cite{CHOOZ}. This sensitivity can be improved using reactor and accelerator experiments. In reactor experiments, one uses $\bar{\nu}_e$ in disappearance mode and may reach $\sin^22\theta_{13}<0.024$ for $\Delta m^2 = \Delta m^2_{atm}$ ($90\%$CL) \cite{Wpaper}. In accelerator experiments, one can use $\nu_e$ and $\bar{\nu}_e$ from $\beta$ beams \cite{BETABEAM} in both  disappearance and appearance modes (\textit{i.e.} $\stackrel{\scriptscriptstyle (-)}{\nu}_e\rightarrow \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$), and also $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu$ in appearance mode (\textit{i.e.} $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu\rightarrow\stackrel{\scriptscriptstyle(-)}{\nu}_e$) with conventional beams either with sub-mega watt proton drivers \cite{NOVA,T2K} or with multi-mega watt proton drivers \cite{T2K,BNLHS,CERN}. The later neutrino beam type, called Superbeam, is foreseen to be extended to produce $\nu_\mu$ beam and $\bar{\nu}_\mu$ beam from muon decays, the so-called Neutrino Factory, in order to study the eventual leptonic CP violation. Such Neutrino Complex is under study in Japan, in USA and also in Europe at CERN and details may be found in reference \cite{CERN}. A comparison of the performances of $\beta$ beam and Superbeam may be found for instance in reference \cite{DONINI}.  The reactor experiment result on $\theta_{13}$ is straight forward as compared to Superbeam and Neutrino Factory results that are on one hand reacher but in an other hand more complex to analyse due to the interplay between the different physics factors $\theta_{13}$, $\delta_{CP}$, sign$(\Delta m^2_{23})$, sign$(\tan(2\theta_{23}))$ \cite{DONINI,DOUBLE-CHOOZ}. 
+
+This paper presents results of a new simulation of the SPL (Super Proton Linac) Superbeam that could take place at CERN \cite{SPL}, using for definitiveness a UNO-like 440kT fiducial water \v{C}erenkov detector \cite{UNO} located in a new enlarged underground laboratory under study in the Fréjus tunnel, $130$~km away from CERN \cite{mosca}. The SPL neutrino beam is created by  decays of pions, muons and kaons produced by the interactions of a $4$~MW proton beam impinging a liquid mercury jet \cite{CERN}. Pions, muons and kaons are collected using two concentric electromagnetic lenses (horns), the inner one and the outer one are hereafter called "Horn" and "Reflector" respectively \cite{Meer}. The horns are followed by a decay tunnel where most of the neutrinos are produced. A sketch of the beam line is shown on figure~\ref{fig:Sbeam}.  
+
+
+The analysis chain consists of different stages: the simulation of the interactions between the proton beam and the mercury target, the propagation of the resulting secondary particles through the magnetic field and the materials of the horns, the tracking of $\pi^\pm$, $K^{\pm,0}$ and $\mu^\pm$ until they decay, the computation of the neutrino flux at the detector site, and finally the statistical analysis. A part of the simulation chain has already been described in reference \cite{nuFact134,MMWPSCazes}. 
+
+
+Compared to recent papers on the same subject \cite{DONINI,JJG,Mezzetto}, we have reoptimized the Horn and Reflector shapes \cite{nuFact138}, and introduced the kaon background simulation which allows us to update the SPL beam energy. The organization of this document follows the simulation chain: the interaction between the proton beam and the mercury target is presented in the second section. The kaon production is detailed in the third section. The simulation of the horns is described in the forth section, while the algorithms used to compute the neutrino fluxes are explained in the fifth section. Then, the sensitivities to $\theta_{13}$ and $\delta_{CP}$ are revisited with new studies about the optimization of the proton beam energy, the pion collection and the decay tunnel geometry.
+
+\section{Target simulation}
+\label{sec:target}
+Since hadronic processes are crucial to describe the interactions of the proton beam on the target, the FLUKA simulator \cite{fluka} has been chosen for this first step of the simulation. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:targ}Liquid mercury jet parameters.}
+\begin{tabular}{ll}
+\hline\noalign{\smallskip}
+    \centre{2}{Hg target}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+      Hg jet speed & $20$~m/s \\
+      density & $13.546$ \\
+      Length, radius & $30$~cm, $7.5$~mm \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+The target used in the present study is a mercury liquid jet \cite{CERN} simulated for a sake of simplicity by a cylinder $30$~cm long (representing two hadronic lengths) and $1.5$~cm diameter (see table~\ref{tab:targ}) \cite{JJG}. Other types of target are under study \cite{CERN}. The pencil like simulated proton beam is composed with  $10^6$ mono-energetic protons, and no beam-target dynamical effects are taken into account. The beam axis is also the symmetry axis of the target and the horns and the decay tunnel. Simulations have been performed for $2.2$~GeV proton kinetic energy, the up to now nominal design \cite{SPL}, as well as for $3.5$~GeV, $4.5$~GeV, $6.5$~GeV and $8$~GeV according to possible new designs \cite{MMWPSGaroby}.
+
+Particle production yields are summarized in table~\ref{tab:nbPart}. The pion momentum spectra obtained at different energies and normalized to a 4MW SPL beam power are presented in figure~\ref{fig:compEner2}(a). At low energy, pions come from $\Delta$ decays while the high energy part is dominated with multi pion production. At very mow energy, for $P<200$~MeV/c, pions come from $\Delta$ produced by protons of the target excited by the beam interactions, while for  higher energy, pion production is due to transformation of protons of the beam into $\Delta$.
+
+The horns are designed to focus the $600$~MeV/c pions (see section~\ref{sec:horn}) and the variation of the number of such pions is rather smooth with respect to the beam energy considering a 4MW fixed beam power: $4.19\times10^{13}\pi$/s for the $2.2$~GeV beam, $4.91\times10^{13}\pi$/s for the $3.5$~GeV beam, $5.14\times10^{13}\pi$/s for the $4.5$~GeV beam, and $4.92\times10^{13}\pi$/s for the $6.5$~GeV beam. The main difference is made by the angular distribution. Figure~\ref{fig:compEner2}(b) shows this distribution for the $\pi^+$ exiting the target with a momentum between $500$~MeV/c and $700$~MeV/c. The acceptance of the horns is limited to the pion below $25^\circ$, and we see that more pions are accepted by the horns for the $3.5$~GeV and $4.5$~GeV proton beams compared to other beam energies.
+
+
+
+The secondary proton and neutron rates induce important radiation damages and power dissipation in the horns which have been addressed in reference \cite{nuFact134}, and which will require specific R\&D effort. At $2.2$~GeV, kaon yields are very low, but it has a dramatic energy dependence as further studied in section~\ref{sec:kaon}. It is worth to mention that the numbers in table~\ref{tab:nbPart} are not to be taken as face values, because the cross sections of pion and kaon productions using proton beam are still under studies as for instance by the HARP experiment \cite{harp}.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbPart}Average numbers of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA). The $\mu^+/\mu^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+$E_k$ (GeV) & p & n & $\gamma$ & $e^+$ & $e^-$ & $\pi^+$ & $\pi^-$ & $\mu^+$ & $\mu^-$ & $K^+$ & $K^0$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$2.2$ & $1.4$     &  $17$   & $5.0$  &   $0.08$  &  $0.17$    &  $0.24$   &  $0.18$ & $4$ & $1$ & $7$ & $6$ \\
+
+$3.5$ & $1.8$    &  $23$  & $7.0$   &  $0.15$  &  $0.28$    &  $0.41$   &  $0.37$ & $10$ & $3$ & $35$ & $30$ \\
+
+$4.5$ &  $2.3$  &  $25$ & $7.7$  & $0.21$  &  $0.35$    &  $0.57$ & $0.39$&  $11$ & $3.3$  &  $93$ &  $68$       \\
+
+$8$   &  $3.1$  &  $33$ & $11.0$ & $0.41$ & $0.63$    &  $1.00$  &  $0.85$ &  $30$ &  $9.5$ &  $413$ &    $340$         \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compEner2.eps}
+\caption{\label{fig:compEner2} (a) $\pi^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$~GeV/c and $0.7$~GeV/c. The different SPL beam kinetic energies presented are (\full) $2.2$~GeV, (\dashed) $3.5$~GeV, (\dotted) $4.5$~GeV and (\chain) $6.5$~GeV.}
+\end{figure*}
+%
+The cross section uncertainties are the main source of discrepancy between simulator programs. Some comparisons between FLUKA and MARS \cite{MARS} have already been presented in the same context \cite{nuFact134}. The energy distribution of the pions exiting the target, computed with the two simulator programs FLUKA and MARS, is shown on figure~\ref{fig:compFlukaMars}(a).  The discrepancy is quite large for the low energy part. However, the horns are designed to focus the high energy part of the spectrum (see section~\ref{sec:horn}), and therefore, MARS and FLUKA are in better agreement for the energy spectrum computed at the entrance of the decay tunnel, as shows figure~\ref{fig:compFlukaMars}(b). 
+%A difference of $10\%$ has been found between the  $\theta_{13}$ sensitivity computed with the two generators (see section~\ref{sec:results}), that can be taken as systematic error. 
+For a 2.2~GeV beam and a positive focusing,  $27\%$ more $\nu_\mu$ and $6\%$ more $\nu_e$ neutrinos are produced around the oscillation probability maximum with the FLUKA generator. It turns out that 
+a sensitivity $10\%$ better for FLUKA compared to MARS has been found for the $\sin^2(2\theta_{13})$ sensitivity
+(see section~\ref{sec:results}). So, the discrepancy  at low energy between MARS and FLUKA does not matter too much for the present application, and the sensitivity difference can be taken as a systematic error. 
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compMarsFlukav2.eps}
+\caption{\label{fig:compFlukaMars}$\pi^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\dashed) and by MARS (\full).}
+\end{figure*}
+%
+\section{Kaon production}
+\label{sec:kaon}
+The possibility to increase the SPL energy in order to study the optimization of the physics program has been recently pointed out \cite{MMWPSGaroby}. Then, the kaon production should be clearly addressed because it is a source of $\nu_e$ and $\bar{\nu}_e$ background events. The kaon decay channels and branching ratios are presented in table~\ref{tab:BRKP0SL} in \ref{sec:kaons}.
+
+The target simulation described in section~\ref{sec:target} has been used with $10^6$ p.o.t with kinetic energy uniformly distributed between $2.2$~GeV and $5$~GeV. The momentum of outgoing pions and kaons are recorded when they exit the target. The number of produced $K^{o,\pm}$ at different proton beam energies are presented on figure~\ref{fig:KaonsPions} (left). In one hand the $K^o$ production rate is similar to the $K^+$ production rate, but in an other hand the $K^-$ production rate is almost forty times smaller. For comparison, the numbers of $\pi^+$ and $\pi^-$  produced in the same conditions are presented on figure~\ref{fig:KaonsPions} (right). Pion production rate is about two orders of magnitude greater than the kaon production rate.
+%
+\begin{figure*}
+\centering
+%\includegraphics[height=95mm]{../picts/KaonProd.eps}
+\includegraphics[height=95mm]{../picts/KaonPionProdFluka2003v2.eps}
+%\caption{\label{fig:KaonsPions}Kaon production (a) as a function of the incident proton beam kinetic energy ($E_k$) for $10^6$ incident protons with (\full) curve for $K^+$, (\dashed) curve for $K^-$ and (\dotted) curve for $K^0$. Pion production (b) in the same conditions with (\full) curve for $\pi^+$ and (\dashed) curve for $\pi^-$.}
+\caption{\label{fig:KaonsPions} Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).} 
+\end{figure*}
+%
+The behavior of the two pion and kaon production rates are quite different. The $\pi^+$ yield grows smoothly with the proton energy while the production of kaons seams to have two origins, which has been confirmed by FLUKA's authors \cite{FLUKAprivate}. For beam energy below approximatively $4$~GeV, the resonance production model is used, and one notices a low production rate with a maximum at about $3.4$~GeV. For beam energy above  $4$~GeV, the dual parton model is used, and the production rate experiences a threshold effect with a rapid rise. The ratio between positive kaon and pion production rates is about $0.5\%$ between $2.2$~GeV and $4$~GeV and grow up to $2.3\%$ at $5$~GeV. One notices that the transition between the two kaon production models may not be optimal.
+%
+\section{Horns simulation}
+\label{sec:horn}
+The simulation code of the electromagnetic horns is written using GEANT 3.2.1 \cite{geant} for convenience and since electromagnetic processes are dominant, FLUKA has not been considered as mandatory, but this may be revised in a future work. The geometry of the horns has been inspired by an existing CERN prototype and a Reflector design proposed in reference \cite{SIMONE1}. Depending of the current injection, only positive secondary particles or negative secondary particles are focused. The relevant parameters are detailed in table~\ref{tab:specif}.
+
+The mercury target is localized inside the Horn because of the low energy and the large emittance of the secondary pions produced: $$<P_{\pi T}>/<P_\pi> \approx 240~\mathrm{MeV}/400~\mathrm{MeV}$$ ($2.2$~GeV proton beam energy). This explains the Horn design (figure~\ref{fig:plan}), with a cylindrical part around the target, called the neck, which is larger than the transversal size of the target to simulate the room for target handling, and a conic part designed such that the relevant pions are focused as much as possible to exit the magnetic field parallel to the beam axis.
+
+\begin{table}
+\centering
+\caption{\label{tab:specif}Relevant parameters of the horns in case of the generation of a $260$~MeV neutrino beam (or $350$~MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$~MeV/c (or $800$~MeV/c) pion momentum.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+ & Horn & Reflector \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+  neck inner radius & $3.7$~cm &  $20.3$~cm \\
+  neck length & $40$~cm        &  $120 (140)$~cm \\ 
+  end cone inner radius & $16$~cm        &  $35.7$~cm \\
+  outer radius & $20.3$~cm      & $40$~cm \\ 
+  total length & $120 (140)$~cm       & $190 (220)$~cm \\  
+  Alu thickness  & $3$~mm       & $3$~mm \\            
+  Peak current & $300$~kA       & $600$~kA \\
+  Frequency & $50$~Hz            & $50$~Hz \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The shape of the horn conductors is a crucial point since it determines the energy spectrum of the neutrino at the detector site. The details of the conductor shape optimization for the present context may be found in reference \cite{nuFact138}. We just recall here some ingredients. For a $\theta_{13}$ driven $\nu_\mu \rightarrow \nu_e$ oscillation, a $\Delta m^2_{23}$ parameter value of $2.4\times10^{-3}\mathrm{eV}^2$, and a baseline distance of $130$~km, the first oscillation maximum occurs for a neutrino energy of $260$~MeV. The   optimization of the physics potential depends at first approximation on the pion neutrino characteristics, which energy is fully determined by the pion 2-body decay and boost. To reach an energy of $260$~MeV, the pion needs a $\beta=0.97$, which in turn induces a pion momentum of $600$~MeV/c. Then, the shape of the conic part of the horns is determined such that these $600$~MeV/c pions exit parallel to the beam axis. 
+
+An other shape of the horn conductors has been used to produce a $350$~MeV neutrino beam to compare the sensitivity potential (see section \ref{sec:results}). In that case, keeping the current intensity unchanged ($300/600$~kA), the lengths of the Horn and the Reflector should be increased by $16$\% and $18.5$\%, respectively (see table~\ref{tab:specif}).
+
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/corne350.eps}
+\caption{\label{fig:plan}Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350~MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}
+\end{figure}
+
+Before closing this section, it is worth to quote that the Horn/Reflector conductor shapes optimized in the present study to focus a given pion momentum value, is not affected at first order by a proton beam energy change. What is affected is the production rate of the relevant pions. This Horn/Reflector design consideration would be different if one wishes to focus as much as possible all the pions produced for which the mean energy is of course affected by a proton beam energy change.    
+%
+\section{Particle decay treatment and flux calculation}
+%
+The decay tunnel representation is a simple cylinder with variable length ($L_T$) and radius ($R_T$) filled with "vacuum" and located right after the horns. The default design is a $20$~m long and $1$~m radius cylinder, but simulations have also been conducted with lengths of $10$~m, $40$~m and $60$~m, and radius of $1.5$~m and $2$~m in the spirit of reference \cite{donega}. In the GEANT simulation, to gain in CPU time, only pions, muons and kaons are tracked in the volume of the tunnel, and all particles exiting this volume are discarded. 
+
+Beyond the $1/L^2$ solid angle factor due to the source-detector distance ($L$) which decreases dramatically the fluxes, the neutrino beam focusing is very limited due to the small pion boost factor ($\approx 4$). Therefore, computational algorithms have been used to avoid a too prohibitive CPU time resulting from the simulation of each secondary particle decay. Otherwise, about $10^{15}$ p.o.t would have been necessary to obtain reliable statistics for the estimation of the $\bar{\nu}_e$ flux for instance.
+
+It is worth to mention that the particle decays occurring before the entrance of the decay tunnel are also taken into account and treated in the same manner, which is not the case in reference \cite{donega}. 
+%
+\subsection{Algorithm description}
+\label{sec:algo}
+The decay code has been included in the GEANT code. The basic idea of this algorithm is to compute the neutrino fluxes using the probability of reaching the detector for each neutrino produced by a $\pi$ or a $K$ or a $\mu$ particle (on-axis neutrino beam). This method has already been used in reference \cite{donega} and has been modified and extended to the kaon decay chain for the present study. 
+
+Muon neutrino comes mostly from pion decay. In a first stage, each pion is tracked by GEANT until it decays. Then, the probability for the produced muon neutrino to reach the detector is computed. The flux is obtained applying the probability as a weight for each neutrino. All the pions produced in the simulation are therefore useful to compute the flux, and this allows to reduce the number of events in the simulation to $10^6$ p.o.t. In this computation, the decay region (horns and tunnel) is considered as point like compared to the source-detector distance. 
+
+The same method is applied for neutrino coming from muons and kaons with some modifications  because most of the muons do not decay, and there are very few kaons produced (see table~\ref{tab:nbPart}).
+The probability computation is presented in appendix~\ref{sec:decayprobcomp}. 
+%
+\begin{table}
+\centering
+\caption{\label{tab:proton}Number of protons on target for different beam energy at 4~MW constant power. One year is defined as $10^7$~s.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			Beam energy  & Number of proton \\
+			  (GeV)      & per year ($10^{23}$ p.o.t/y) \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			2.2 & 1.10 \\
+			3.5 & 0.70 \\
+			4.5 & 0.56 \\
+			6.5 & 0.40 \\
+			8.0 & 0.30 \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22p.eps}
+\caption{	\label{fig:flux22p}Neutrino fluxes, $100$~km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$~GeV (4~MW), a decay tunnel with a length of $20$~m and a radius of $1$~m. The top left panel contains the $\nu_\mu$ fluxes, and the top right panel shows the $\bar{\nu}_\mu$ fluxes. The bottom left panel presents the $\nu_e$ fluxes while the bottom right panel displays the $\bar{\nu}_e$ fluxes. The (\full) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\dashed) curve is the contribution from the charged kaon decay chain, and the (\dotted) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux22m.eps}
+\caption{\label{fig:flux22m}Same legend as for figure~\ref{fig:flux22p} but the horns are focusing negative particles.}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35p.eps}
+\caption{\label{fig:flux45p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux35m.eps}
+\caption{\label{fig:flux45m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $3.5$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8p.eps}
+\caption{\label{fig:flux8p}Same legend as for figure~\ref{fig:flux22p} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/flux8m.eps}
+\caption{\label{fig:flux8m}Same legend as for figure~\ref{fig:flux22m} but for proton beam kinetic energy of $8$~GeV (4~MW).}
+\end{figure*}
+%
+\begin{table*}
+\centering
+\caption{\label{tab:speciesfluxes}Integral of the total flux of the different species with different settings. The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are expressed in $10^{13}/100\mathrm{m}^2/y$ unit while the $\nu_e$ and $\bar{\nu}_e$ fluxes are expressed in $10^{11}/100\mathrm{m}^2/y$ unit. The positive focusing  and negative focusing  are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. %Setting (1) means $L_T = 10$~m and $R_T = 1$~m. Setting (2) is the default option and means $L_T = 20$~m and $R_T = 1$~m. Setting (3) means $L_T = 20$~m and $R_T = 1.5$~m. Setting (4) means $L_T = 30$~m and $R_T = 1$~m. Setting (5) means $L_T = 40$~m and $R_T = 1$~m. Setting (6) means $L_T = 40$~m and $R_T = 1.5$~m. Setting (7) means $L_T = 40$~m and $R_T = 2$~m.  Setting (8) means $L_T = 60$~m and $R_T = 1$~m, and finally, setting (9) means $L_T = 60$~m and $R_T = 1.5$~m.
+}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+
+			\centre{3}{Settings}  & \centre{2}{$\nu_\mu$} & \centre{2}{$\nu_e$} 
+								&	\centre{2}{$\bar{\nu}_\mu$} & \centre{2}{$\bar{\nu}_e$} \\
+								$E_p$ & $L_T$ & $R_T$ & $+$ & $-$ & $+$ & $-$ & $+$ & $-$ 
+								& $+$ & $-$ \\ 
+\noalign{\smallskip}\hline\noalign{\smallskip}
+
+$2.2$~GeV & $10$~m &  $1$~m 
+	& $5.5$          & $0.4$ 
+	& $1.7$          & $0.2$
+	& $0.3$          & $4.3$  
+	& $0.1$ 	 & $0.8$ \\		
+
+$3.5$~GeV  & $10$~m &  $1$~m  
+	& $7.7$          & $0.7$ 
+	& $2.6$          & $0.6$
+	& $0.6$          & $6.6$  
+	& $0.3$ 	 & $1.3$ \\		
+	
+$4.5$~GeV  & $10$~m &  $1$~m  
+	& $7.1$          & $1.0$ 
+	& $2.8$          & $0.9$
+	& $0.5$          & $5.2$  
+	& $0.3$ 	 & $1.1$ \\		  
+
+$6.5$~GeV  & $10$~m &  $1$~m  
+	& $8.3$          & $1.2$ 
+	& $4.7$          & $1.9$
+	& $0.8$          & $5.6$  
+	& $0.9$          & $1.8$ \\
+
+$8.0$~GeV  & $10$~m &  $1$~m  
+	& $7.7$          & $1.2$ 
+	& $5.1$          & $2.2$
+	& $0.9$          & $5.6$  
+	& $1.1$ 	 & $2.1$ \\
+
+$2.2$~GeV & $20$~m &  $1$~m   
+	& $7.6$         & $0.4$ 
+	& $3.2$ 	& $0.2$
+	& $0.3$ 	& $5.8$  
+	& $0.1$ 	& $1.6$ \\		  
+
+$3.5$~GeV & $20$~m &  $1$~m    
+	& $10.0$          & $0.9$ 
+	& $4.4$           & $0.6$
+	& $0.7$ 	  & $8.5$  
+	& $0.3$ 	  & $2.2$ \\		  
+
+$4.5$~GeV & $20$~m &  $1$~m    
+	& $10.9$          & $1.1$ 
+	& $5.1$           & $1.0$
+	& $0.7$ 	  & $6.7$  
+	& $0.4$ 	  & $1.8$ \\		  
+
+$6.5$~GeV & $20$~m &  $1$~m    
+	& $10.4$          & $1.4$ 
+	& $6.4$           & $2.0$
+	& $1.0$           & $7.1$  
+	& $0.9$ 	  & $2.5$ \\	
+
+$8.0$~GeV & $20$~m &  $1$~m    
+	& $9.7$           & $1.5$ 
+	& $6.7$           & $2.3$
+	& $1.2$           & $7.1$  
+	& $1.1$ 	  & $2.8$ \\
+
+$2.2$~GeV & $20$~m &  $1.5$~m    
+	& $9.0$           & $0.6$ 
+	& $4.4$           & $0.4$
+	& $0.4$           & $6.7$  
+	& $0.2$  	  & $2.2$ \\
+
+$4.5$~GeV & $20$~m &  $1.5$~m    
+	& $13.2$          & $1.5$ 
+	& $6.9$           & $1.4$
+	& $0.9$           & $8.1$  
+	& $0.6$  	  & $2.7$ \\
+
+$3.5$~GeV & $30$~m &  $1$~m    
+	& $10.9$          & $0.9$ 
+	& $5.7$           & $0.7$
+	& $0.7$           & $9.4$  
+	& $0.3$  	  & $2.9$ \\
+
+$4.5$~GeV & $30$~m &  $1$~m   
+	& $11.6$          & $1.2$ 
+	& $6.3$           & $1.0$
+	& $0.7$           & $7.1$  
+	& $0.4$    	  & $2.3$ \\
+
+$2.2$~GeV & $40$~m &  $1$~m    
+	& $8.9$           & $0.5$ 
+	& $5.1$           & $0.3$
+	& $0.5$           & $6.7$  
+	& $0.1$   	  & $2.4$ \\	
+
+$3.5$~GeV & $40$~m &  $1$~m  
+	& $11.3$          & $0.9$ 
+	& $6.5$           & $0.6$
+	& $0.8$           & $9.7$  
+	& $0.3$ 	  & $3.3$ \\	
+
+$4.5$~GeV & $40$~m &  $1$~m  
+	& $12.3$          & $1.2$ 
+	& $7.2$           & $1.0$
+	& $0.8$           & $7.5$  
+	& $0.4$   	  & $2.6$ \\	
+
+$6.5$~GeV & $40$~m &  $1$~m  
+	& $11.7$          & $1.6$ 
+	& $8.3$           & $2.2$
+	& $1.1$           & $8.0$  
+	& $0.9$   	  & $3.3$ \\	
+
+$8.0$~GeV & $40$~m &  $1$~m  
+	& $10.9$          & $1.7$ 
+	& $8.5$           & $2.4$
+	& $1.3$           & $8.0$  
+	& $1.2$    	  & $3.6$ \\	
+
+$3.5$~GeV & $40$~m &  $1.5$~m  
+	& $14.5$          & $1.3$ 
+	& $10.0$          & $1.0$
+	& $1.0$           & $12.3$  
+	& $0.5$  	  & $5.3$ \\
+	
+$4.5$~GeV & $40$~m &  $1.5$~m 
+	& $15.5$          & $1.7$ 
+	& $10.8$          & $1.5$
+	& $1.0$           & $9.5$  
+	& $0.6$  	  & $4.2$ \\
+		
+$3.5$~GeV & $40$~m &  $2$~m 
+	& $16.6$          & $1.5$ 
+	& $12.9$          & $1.3$
+	& $1.3$           & $13.9$  
+	& $0.7$  	  & $6.9$ \\
+	
+$4.5$~GeV & $40$~m &  $2$~m 
+	& $18.2$          & $2.1$ 
+	& $14.3$          & $1.9$
+	& $1.3$           & $11.1$  
+	& $0.8$  	  & $5.6$ \\
+	
+$3.5$~GeV & $60$~m &  $1$~m 
+	& $11.7$          & $0.9$ 
+	& $7.6$           & $0.7$
+	& $0.7$           & $10.1$  
+	& $0.3$      	  & $3.7$ \\
+	
+$4.5$~GeV & $60$~m &  $1$~m 
+	& $12.5$          & $1.3$ 
+	& $8.1$           & $1.1$
+	& $0.7$           & $7.7$  
+	& $0.4$ 	  & $2.9$ \\
+	
+$3.5$~GeV & $60$~m &  $1.5$~m 
+	& $15.1$          & $1.3$ 
+	& $12.2$          & $1.0$
+	& $1.0$           & $12.8$  
+	& $0.5$  	  & $6.3$ \\
+	
+$4.5$~GeV & $60$~m &  $1.5$~m 
+	& $16.2$          & $1.8$ 
+	& $13.1$          & $1.6$
+	& $1.0$           & $9.9$  
+	& $0.6$ 	  & $4.9$ \\
+ \noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\subsection{Validation of the algorithm}
+The validity of the method presented in the previous section have been tested against a straight forward  algorithm consisting of decaying each pion $N$ times ($N \approx 10^6$) in a full GEANT simulation of the event (decays included). Such method presents the advantage to keep all the information of the neutrino available for further studies. It can be a good approach to compute the muon neutrino flux coming from pion decays. It can also provide the beam profile, but it shows its limits for the muon induced fluxes, especially the $\bar{\nu}_e$ flux. Indeed, this means that each muon is duplicated $N$ times and when a muon decays, it must decay $N$ times again. For $N\approx 10^6$, this is a prohibitive CPU time consuming.
+%
+\begin{figure*}
+\centering
+\includegraphics[height=95mm]{../picts/compGeantDonega.eps}
+\caption{\label{fig:compGeantDonega}Comparison between the probability method, (\full) curve, and the full GEANT simulation method, (\dashed) curve, for the $\nu_\mu$ from $\pi^+$ flux (a) and the $\bar{\nu}_\mu$ from $\pi^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu_e$ and $\bar{\nu}_e$ fluxes contrary to the former simulation.}
+\end{figure*}
+%
+The $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes are displayed on figure~\ref{fig:compGeantDonega} for both methods. The two spectra shows a clear agreement, and this makes confidence on the probability method.
+%
+\subsection{Simulated fluxes}
+The fluxes are computed at a distance of $100$~km from the source by convention and can be rescaled at any desired distance. They provide the number of the four neutrino species ($\nu_\mu$, $\bar{\nu}_\mu$, $\nu_e$, $\bar{\nu}_e$) passing through a $100$~m$^2$ fiducial area during $1$~year.
+
+In practice, the fluxes are given as a function of the neutrino energy via histograms composed of $20$~MeV bin width.  These histograms are filled with the energy of each neutrino weighted by the probability to reach the detector (section~\ref{sec:algo}). To obtain the fluxes, the histograms are rescaled to the number of p.o.t per year depending on the beam energy. Table~\ref{tab:proton} reports on the number of p.o.t per year for the different energies studied using the definition of one year being $10^7$~s and keeping the beam power constant (\textit{i.e.} $4$~MW).
+
+Three origins are identified in the composition of each neutrino flux:
+\begin{description}
+	\item[-] neutrinos from pions, which includes neutrinos created by primary pion decays and neutrinos coming from the muons produced by pion decays or muons directly exiting the target. This is the component studied in reference \cite{donega} but with different settings and event generator;
+	\item[-] neutrinos emitted during the decay chain of the charged kaons, either by direct production, or produced by the daughter pions and muons;
+	\item[-] neutrinos coming from the decay chain of the neutral kaons.
+\end{description}
+
+The three components of the fluxes for the four neutrino species are presented on figure~\ref{fig:flux22p} for positive particle focusing and a proton beam kinetic energy of $2.2$~GeV. The $\nu_\mu$ flux is dominated by the neutrinos of pion decays, but a tail above $500$~MeV (insert on the top left part) is created by the $K^+\rightarrow \mu^+\nu_\mu$ channel, which is anyway at least three order of magnitude below the flux maximum. The $\bar{\nu}_\mu$ flux is mostly due to the decays of $\pi^-$ that are not unfocused by the horns, but the higher energy part comes from $\mu^+$ decays. It is noticable that the $\nu_e$ and $\bar{\nu}_e$ fluxes are respectively more than $200$ and more than $7000$ times smaller than the $\nu_\mu$ flux. The $\bar{\nu}_e$ are produced in a large part by the $K^0_L\rightarrow\pi^+e^-\bar{\nu}_e$ decay channel and by $\mu^-$ decays, while the  $\nu_e$ flux is dominated by the $\mu^+$ decays.
+
+On figure~\ref{fig:flux22m}, the horns are set to focus negative particles keeping other parameters identical. By comparison with positive focusing, one can at first approximation translate the results by exchanging particles and anti-particles, except that the $K^+/K^-$ ratio is about 50 in the beam-target interactions (see table~\ref{tab:nbPart}).
+
+On figures~\ref{fig:flux45p} and \ref{fig:flux8p}, one observes the evolution of figure~\ref{fig:flux22p} when the proton beam kinetic energy increases to $3.5$~GeV and $8$~GeV, respectively. Correspondingly, the results for negative particle focusing are presented on figures~\ref{fig:flux45m} and \ref{fig:flux8m}. One clearly notices the increase of the kaon induced neutrino contents as the beam energy grows.
+%
+On table~\ref{tab:speciesfluxes} are reported the integral of the fluxes when one modifies the decay tunnel length and radius, as well as the beam kinetic energy. Changing the length from $10$~m to $40$~m will increase the $\nu_\mu$ flux by $50\%$ to $70\%$ and in the same time, the number of $\nu_e$ will be multiply by a factor $1.5$ to $2$. One can notice that going from $40$~m to $60$~m does not increase the signal-like events but increase the background-like events. For a $40$~m length of the decay tunnel, the increase of the radius improve the number of signal-like events by $50\%$, and the backgroud increase by $70\%$ to $100\%$. Notice that the $\nu_\mu/\bar{\nu}_\mu$ flux ratio is rather insensitive to the decay tunnel length. The feeling that $L_T = 40$~m and $R_T = 2$~m is a good signal over background compromise is confirmed by sensitivity quantitative studies reported in section~\ref{sec:results}.
+
+Looking at the evolution of $\nu_\mu$ flux with respect to the beam energy, one notices that a maximum is reached around $4.5$~GeV. This is due to the competition between the cross section rise with respect to the energy and the decrease of the number of p.o.t due to the constant SPL power ($4$~MW).
+%
+\section{Sensitivity computation ingredients}
+%
+The sensitivity to $\theta_{13}$ and $\delta_{CP}$ is computed for a $\nu_\mu\rightarrow\nu_e$ appearance experiment. The detector considered for definitiveness is similar to the UNO detector, \textit{i.e.} a $440$~kt fiducial water \v{C}erenkov detector \cite{UNO}. The detector simulation has been presented in reference \cite{JJG} and the analysis program described in reference \cite{MEZZETTONUFACT060} has been used for sensitivity computation following previous work of reference \cite{Mezzetto}. See table~\ref{tab:param} for the default user parameter values used in this paper. We just remind here some key points of the sensitivity analysis program. 
+
+It is included a full 3-flavors oscillation probability computation with matter effects, but no ambiguities are taken into account. This latest point may be revisited in a future work using reference \cite{DONINI-2}. Concerning the background events, the $\nu_e/\bar{\nu}_e$ from the beam, the $\nu_\mu e^-$ elastic scattering process, the $\pi^o$ production as well as the $\mu/e$ misidentification are taken into account. The cross-sections from the NUANCE program are used \cite{NUANCE}. The systematics error on the total $\nu_e$ and $\bar{\nu}_e$ fluxes determination is a user parameter and we have used the $2\%$ value considered as a final goal, but also $5\%$ and $10\%$ \cite{MEZZETTONUFACT060}. The detector is located at $L = 130$~km from CERN, in the foreseen new Fréjus laboratory \cite{mosca}. It is worth to mention that if one wants to evaluate the influence of $L$ on the sensitivity, it would mean a re-optimization of the horns for each $L$ envisaged (see section~\ref{sec:horn}).  
+%
+\begin{table}
+\centering
+\caption{\label{tab:param}Default parameters used to compute the sensitivity curves \cite{MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite{KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite{JJG}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			$\Delta m^2_{12} = 8.2 (0.5)\times 10^{-5}~\mathrm{eV}^2$ & $\sin^22\theta_{12} = 0.82 (9\%)$ \\
+			$\Delta m^2_{23} = 2.5 (0.1)\times 10^{-3}~\mathrm{eV}^2$ & $\sin^22\theta_{23} = 1.0 (1\%)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		  $L_T = 20$~m & $R_T = 1$~m \\ 
+		  $M=440$~kT   & $\epsilon_{syst}=2\%$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+\centre{2}{Horn/Reflector shapes to produce a $260$~MeV neutrino beam} \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+The running time scenario has been fixed either by focusing positive particles during 5 years, either  by focusing positive particles during 1 (or 2) year(s) followed by focusing negative particles during 4 (or 8) years.
+%
+\section{Results}
+\label{sec:results}
+\subsection{The positive only focusing scenario}
+The $\theta_{13}$ and $\delta_{CP}$ sensitivities are computed with $\theta_{13} = 0^\circ$ and $\delta_{CP} = 0^\circ$ if not explicitly mentioned. It is worth to stress that the default parameters of table~\ref{tab:param} are used if not contrary mentioned, in particular, the decay tunnel geometry parameters ($L_T=20$~m and $R_T=1$~m), and the horn design to generate a $260$~MeV neutrino beam. 
+
+Table~\ref{tab:nbvsE} presents the number of signal and background events for a $5$ years positive focusing experiment, but with different beam energy settings. 
+%The quality factor ($S$) is defined in reference \cite{MEZZETTONUFACT060} as\footnote{Contrary to the definition of the significance of reference \cite{MEZZETTONUFACT060}, the systematical factor is applied to the total $\nu_e$ flux in agreement with the sensitivity contour computation.}:
+%\begin{equation}
+%\begin{aligned}
+%\mathcal{S} &= \frac{N^{osc}_{\nu_e}}{\sqrt{ N^{tot}_{\nu_e} + \left(N^{tot}_{\nu_e}\times\epsilon_{syst}\right)^2}}\\
+%\mathrm{with}\quad N^{tot}_{\nu_e} &= N^{osc}_{\nu_e} + N^{beam}_{\nu_e} + N^{oth. bkg}
+%\label{eq:significance}
+%\end{aligned}
+%\end{equation}
+%and $N^{osc}_{\nu_e}$ the number of $\nu_e$ events due to $\nu_\mu$ oscillations, $N^{beam}_{\nu_e}$ the number of background events coming from the $\nu_e+\bar{\nu}_e$ contamination of the beam, $N^{oth. bkg}$ the other kinds of background events and $\epsilon_{syst}$ the systematical factor.
+%
+\begin{table*}
+\centering
+\caption{\label{tab:nbvsE}Number of events for 5 years positive focusing scenario with default parameters of table~\ref{tab:param}. Other backgrounds are $\pi^0$, $\nu_\mu$-elast., $\mu/e$-missId. 
+%The $S$ factor is defined by equation~\ref{eq:significance}.
+}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		 & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			non oscillated $\nu_\mu$       & $36917$  & $60969$  & $73202$  & $78024$ & $76068$ \\ 
+			oscillated $\nu_e$             & $43$     & $60$     & $64$     & $61$    & $56$ \\
+			beam $\nu_e$                   & $165$    & $222$    & $242$    & $288$   & $299$ \\
+			other background               & $70$     & $105$    & $127$    & $148$   & $152$ \\
+%			S factor                       & $1.88$   & $2.16$   & $2.17$   & $1.87$  & $1.69$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+The contours at $90\%$, $95\%$ and $99\%$~CL of the $\theta_{13}$ sensitivity are presented in the ($\sin^22\theta_{13}$, $\Delta m^2_{23}$) plane on figure~\ref{fig:sensi45} for $3.5$~GeV proton beam kinetic energy. 
+The comparison between the contours at $90\%$~CL with $2.2$~GeV, $3.5$~GeV, $4.5$~GeV and $8$~GeV beam energies is shown on figure~\ref{fig:compSensi}. One notices in this scenario a better perfomence reached with a $4.5$~GeV energy beam. 
+%as a confirmation of significance parameter value. 
+But, in fact there is not much visual difference between a sensitivity obtained with $3.5$~GeV and $4.5$~GeV, even if one should keep in mind that kaon production models are different at these two energies (see section~\ref{sec:kaon}). These two energy settings have been studied with different decay tunnel geometry and  results are reported on table~\ref{tab:thvsE_3545}. One notice that similar results can be reached with a $3.5$~GeV beam, compared to a $4.5$~GeV beam.
+
+Quantitative studies of the minimum $\sin^22\theta_{13}$ with respect to the kinetic beam energy $E_k(proton)$, and the decay length $L_T$, and the systematics $\epsilon_{syst}$ are presented in tables~\ref{tab:thvsE} and \ref{tab:thvseps}. One notices that for $\epsilon_{syst} = 5\%$ there is no difference between a $3.5$~GeV and a $4.5$~GeV beam.
+%
+We have also considered the $3.5$~GeV and $4.5$~GeV beam energies with the tunnel geometry parameters $L_T=40$~m and $R_T=2$~m, and the horn design producing a $350$~MeV neutrino beam (see section~\ref{sec:horn}). In table~\ref{tab:thvsE_3545} are reported numerical values, and on figure~\ref{fig:comp5year} are shown the $90$\% CL sensitivity contours. With the $350$~MeV neutrino beam, one can expect a $16$\% improvment with respect to the $260$~MeV neutrino beam. One notices also that there is marginal gain to increase the beam energy from $3.5$~GeV to $4.5$~GeV, as already mentioned. 
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensi35.eps}
+\caption{\label{fig:sensi45}Sensitivity contours obtained with a SPL energy of $3.5$~GeV and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m. (\full), (\dashed) and (\dotted) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compSensi.eps}
+\caption{\label{fig:compSensi}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) and default parameters of table~\ref{tab:param}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comp5year.eps}
+\caption{\label{fig:comp5year}Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$~GeV or $4.5$~GeV, and either a $260$~MeV (default) neutrino beam or a $350$~MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$~m and $R_T = 2$~m. The (\chain) curve corresponds to a $350$~MeV/$4.5$~GeV (neutrino beam/SPL beam energy) setting; the (\dotted) curve corresponds to a $350$~MeV/$3.5$~GeV setting; the (\dashed) curve corresponds to a $260$~MeV/$4.5$~GeV setting and the (\full) curve corresponds to a  $260$~MeV/$3.5$~GeV setting.}
+\end{figure}
+%
+\begin{table}
+\centering
+\caption{\label{tab:thvsE}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		        & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV  \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$10$~m & $1.10$ & $0.92$ & $1.04$ & $1.07$ & $1.16$ \\
+			$20$~m & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$40$~m & $1.23$ & $1.00$ & $0.99$ & $1.08$ & $1.19$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+
+There are also variations on the minimum $\sin^22\theta_{13}$ value that may be reached in a $\nu_\mu \rightarrow \nu_e$ experiment which are due to the $\mathrm{sign}(\Delta m^2_{23})$ ambiguity and the $\delta_{CP}$ value. On table~\ref{tab:sign} are presented these kind of variations. Other ambiguities coming from the sign$(\tan(2\theta_{23}))$ ignorance also take place as studied in reference \cite{DONINI}. From figure~9 of this reference, we estimate a 30\% effect on $\sin^2(2\theta_{13})$ sensivity due to these ambiguities.
+%
+\subsection{Mixed positive/negative focusing scenario}
+%
+The combined $\sin^22\theta_{13}$ and $\delta_{CP}$ sensitivity for the 5 years positive focusing scenario and the default parameters of table~\ref{tab:param} is presented on figure~\ref{fig:compDeltaTheta}(a). The results obtained with a $3.5$~GeV and $4.5$~GeV SPL beam are similar and better than with the other energy settings. On figure~\ref{fig:sensiDeltaTheta}(a) the results obtained with a $260$~MeV neutrino beam and a $350$~MeV neutrino beam are presented with a $40$~m long, $2$~m radius decay tunnel. With the $350$~MeV neutrino beam, one can reached better sensitivity results in the range $|\delta_{CP}| < 120^o$, and comparatively the gain obtained when switching from a $3.5$~GeV proton beam to a $4.5$~GeV proton beam is marginal. 
+%
+To improve the $\delta_{CP}$-independent limit on $\sin^22\theta_{13}$, especially around $\delta_{CP}=90^\circ$, one may envisaged a combination of 2 years with positive focusing and 8 years negative focusing as in references \cite{DONINI,JJG,Mezzetto}. The comparison of the results obtained with different SPL beam energies on the combined sensitivity contours are presented in figure~\ref{fig:compDeltaTheta}(b). Quantitative results with this kind of mixed focusing scenario are reported table \ref{tab:thvsE_td}. One generally gets $10\%$ to $20\%$ better limit on $\sin^22\theta_{13}$ independently of $\delta_{CP}$ with a $3.5$~GeV kinetic energy beam compare to a $2.2$~GeV beam. Doubling the length and the radius of the decay tunnel allows to reach a $10\%$ better limit.
+
+On figure~\ref{fig:sensiDeltaTheta}(b) are presented the results considering the effects of a $350$~MeV neutrino beam obtained either with a $3.5$~GeV proton beam or a $4.5$~GeV proton beam compared to a $260$~MeV neutrino beam obtained with a $4.5$~GeV proton beam. The tunnel geometry parameters are $L_T=40$~m and $R_T=2$~m (other tunnel geometry have been studied but the results are worse and so are not reported). Except in the region $|\delta_{CP}|>150^o$, the results obtained with the $350$~MeV neutrino beam ($3.5$~GeV proton beam) are somewhat better, even if a $11\%$ improvement of the $\delta_{CP}$-independent $\sin^22\theta_{13}$ limit can be reached with the $260$~MeV neutrino beam obtained with the $3.5$~GeV proton beam.
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/compDeltaTheta.eps}
+\caption{\label{fig:compDeltaTheta}90\% sensitivity contours obtained with SPL beam energy of $2.2$~GeV (\dashed), $3.5$~GeV (\chain), $4.5$~GeV (\full) and $8$~GeV (\dotted) at $90\%$ CL. Default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$~m and $R_T = 1$~m.}
+\end{figure}
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/sensiDeltaTheta.eps}
+\caption{\label{fig:sensiDeltaTheta}90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$~m and $R_T=2$~m and different SPL beam energies ($3.5$~GeV or $4.5$~GeV) and different horn designs ($260$~MeV or $350$~MeV neutrino beams): (\full) curve for a $350$~MeV/$4.5$~GeV setting, (\dotted) curve for a $350$~MeV/$3.5$~GeV setting, (\dashed) curve for a $260$~MeV/$3.5$~GeV setting. Other default parameters of table~\ref{tab:param} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}
+\end{figure}
+%
+\begin{table*}
+\centering
+%\caption{\label{tab:thvsE_3545}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) at and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings in parenthesis are identical to those of table~\ref{tab:speciesfluxes}, except that the setting (7b) corresponds to the tunnel geometry of setting (7) but the horn geometry producing a $350$~MeV neutrino beam is used. We remind that the setting (2) is the default one, and the settings (7) and (7b) corresponds to $L_T = 40$~m and $R_T = 2$~m.}
+\caption{\label{tab:thvsE_3545}Study of the sensitivity of different beam energy, decay tunnel length ($L_T$) at and radius ($R_T$), and horn design in two different scenarios. First scenario is 5 years of positive focusing, in wich sensitivity is given as the minimum of $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL. Second scenario is 2 years of positive focusing plus 8 years of negative focusing, in wich sensitivity is given as the minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta_{CP}$ case. A star $^{(*)}$ indicates the use of the the horn geometry producing a $350$~MeV neutrino beam. Other parameters are fixed to default values (table~\ref{tab:param}).}
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+setting & $L_T$ & $10$~m & $20$~m &  $20$~m & $30$~m & $40$~m &  $40$~m & $40$~m & $40$~m$^{(*)}$ & $60$~m &  $60$~m\\
+        & $R_T$ & $1$~m  & $1$~m & $1.5$~m &  $1$~m &  $1$~m & $1.5$~m &  $2$~m &  $2$~m$^{(*)}$ &  $1$~m & $1.5$~m\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+5 years of positive &
+    $3.5$~GeV   & $0.92$ & $0.92$ & $0.83$ & $0.98$ & $1.00$ & $0.93$ & $0.91$ & $0.76$ & $1.05$ & $1.01$ \\
+focusing scenario &
+    $4.5$~GeV   & $1.04$ & $0.89$ & $0.82$ & $0.94$ & $0.99$ & $0.92$ & $0.87$ & $0.71$ & $1.03$ & $1.00$ \\
+\noalign{\smallskip}\hline
+ 2 years of positive  &
+    $2.2$~GeV &        & $2.52$ &        &        & $2.58$ &        & $2.30$ &        &         &       \\
+focusing $+$ 8 year of &
+    $3.5$~GeV & $2.34$ & $2.22$ & $2.10$ & $2.13$ & $2.09$ & $2.08$ & $2.02$ & $2.28$ &  $2.16$ & $2.09$\\
+negative focusing scenario &
+    $4.5$~GeV & $2.91$ & $2.60$ & $2.43$ & $2.48$ & $2.52$ & $2.39$ & $2.34$ & $2.55$ &  $2.53$ & $2.47$\\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table*}
+%
+\begin{table}
+\centering
+\caption{\label{tab:thvseps}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon_{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			      & $2.2$~GeV & $3.5$~GeV & $4.5$~GeV & $6.5$~GeV & $8$~GeV \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$2\%$ & $1.16$ & $0.92$ & $0.89$ & $1.01$ & $1.12$ \\
+			$5\%$ & $1.48$ & $1.25$ & $1.25$ & $1.48$ & $1.64$ \\
+			$10\%$ & $2.40$ & $2.14$ & $2.21$ & $2.72$ & $3.09$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+\begin{table}
+\centering
+\caption{\label{tab:sign}Minimum $\sin^22\theta_{13}\times 10^3$ in the $(\sin^22\theta_{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$~GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta_{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table~\ref{tab:param}).}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+			    & $-180^\circ$ & $-90^\circ$ & $0^\circ$ & $90^\circ$ & $180^\circ$\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+			$+$ & $1.40$ & $0.43$ & $1.16$ & $11.48$ & $1.40$\\
+			$-$ & $1.45$ & $11.75$& $1.11$ & $0.43$  & $1.45$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+%
+%\begin{table*}
+%\centering
+%\caption{\label{tab:thvsE_td}Minimum $\sin^22\theta_{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta_{CP}$ case, and for different decay tunnel length ($L_T$) and radius ($R_T$) for the $3.5$~GeV and $4.5$~GeV scenarios and 2 years of positive focusing plus 8 years of negative focusing. Other parameters are fixed to default values (table~\ref{tab:param}). Settings are identical to those of table~\ref{tab:speciesfluxes}.}
+%
+%\begin{tabular}{@{}l*{15}{l}}
+%\hline\noalign{\smallskip}
+%setting & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (7b) & (8) & (9)\\
+%\noalign{\smallskip}\hline\noalign{\smallskip}
+%$2.2$~GeV &        & $2.52$ &        &        & $2.58$ &        & $2.30$ &        &         &       \\
+%$3.5$~GeV & $2.34$ & $2.22$ & $2.10$ & $2.13$ & $2.09$ & $2.08$ & $2.02$ & $2.28$ &  $2.16$ & $2.09$\\
+%$4.5$~GeV & $2.91$ & $2.60$ & $2.43$ & $2.48$ & $2.52$ & $2.39$ & $2.34$ & $2.55$ &  $2.53$ & $2.47$\\
+%\noalign{\smallskip}\hline
+%\end{tabular}
+%\end{table*}
+%
+\section{Summary and outlook}
+A complete chain of simulation has been set up for the SPL-Fréjus project. The neutrino production has been extended to the kaon decay contribution, which is important to test SPL energy scenario above $2.2$~GeV.
+The beam line optimization has been performed using the sensitivity to $\sin^22\theta_{13}$ and $\delta_{CP}$. The shape of the focusing system has been updated to obtain a neutrino beam energy around $260$~MeV or $350$~MeV.
+
+In a positive only focusing scenario, the best limit on $\sin^22\theta_{13}$ is $0.82\times10^{-3}$
+ ($90\%$ CL, $\delta_{CP}=0$), with a $4.5$~GeV beam energy and a $20$~m long, $1.5$~m radius decay tunnel. However, the $3.5$~GeV beam may also obtain rather similar limit with $0.83\times10^{-3}$ ($90\%$ CL) with the same tunnel parameters. The $\delta_{CP}$ independant $\sin^22\theta_{13}$ sensitivity is limited to $\approx 10^{-2}$ due to the $\delta_{CP} \approx 90^o$ region.
+ 
+In a mixed focusing scenario, the best limit on $\sin^22\theta_{13}$ independent of $\delta_{CP}$ is $2.02\times10^{-3}$ ($90\%$ CL) obtained with a $3.5$~GeV beam energy and a $40$~m long, $2$~m radius decay tunnel.
+
+The comparison of the optimization presented in this paper with the results obtained by other projects is displayed on figure \ref{fig:deltathetaFinal}. It is presented the 5 years positive focusing scenario, and two versions of a mixed scenario using positive and negative focusing: one scenario duration is 5 years in total and the other one is 10 years running in total and has been used in the previous section. It shows the complementarity of the SPL-Fr\'ejus project with the beta beam-Fr\'ejus project. Especially when considering the sensitivity to $\sin^22\theta_{13}$ for $\delta_{CP}<0$. 
+
+%
+\begin{figure}
+\centering
+\includegraphics[width=85mm]{../picts/comparaisonFinale.eps}
+\caption{\label{fig:deltathetaFinal}90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite{CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite{Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite{MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite{KOBAYASHI}. The BNL contour has been obtained from reference \cite{BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu_e$ and $\bar{\nu}_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta$ beam was analysed like a reactor experiment with 1\% systematic error \cite{MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$~GeV beam and a decay tunnel of $40$~m length, and $2$~m radius.}
+\end{figure}
+%
+The authors think that the present study may be extended in many respects. The beam line simulation part may be performed with a single simulator as FLUKA (or GEANT4 \cite{GEANT4} for comparison). Other targets may be envisaged (tantalum, carbon) as well as other detector types as a Large Liquid Argon detector \cite{BIGICARUS}. The baseline length may also be revisited as well as the off axis option. The sensitivity analysis may be deeper investigated using the complete set of possible ambiguities as in reference \cite{DONINI}, and the $\theta_{13}$ or $\delta_{CP}$ measurement accuracy with new beam energy scenario may be investigated too.     
+%
+\begin{acknowledgement}
+The authors would like to thank M.~Mezzetto to have expressed his interest since the early stage of this work and to have provided us with his sensitivity computation program. Also the authors thank S.~Gilardoni for fruitful discussions.
+\end{acknowledgement}
+%
+\appendix
+\setcounter{section}{0}
+\section{Decay probability computations}
+\label{sec:decayprobcomp}
+This appendix contains the probability formulas and the algorithms used in the flux computation (see section~\ref{sec:algo}).
+
+\subsection{Pion neutrino probability computation}
+\label{sec:Ppi}
+Pions decay only as $\pi^+\rightarrow \mu^+ + \nu_\mu$ or $\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$ and the neutrinos are emitted isotropically in the pion rest frame, with an energy of about $30$~MeV given by the 2-body decay kinematics. Applying a Lorentz boost knowing the pion momentum and direction, it is possible to compute the probability to reach the detector for the neutrinos. Only neutrino parallel to the beam axis are supposed to pass through the detector fiducial area, and therefore, the neutrino must be emitted by the pion with an angle opposite to the angle between the pion and the beam axis (see figure~\ref{fig:pionDecay}). This gives:
+\begin{equation}
+\mathcal{P}_\pi = \frac{1}{4\pi}\frac{A}{L^2}\frac{1-\beta^2}{(\beta\cos\alpha-1)^2}
+\label{probaPi}
+\end{equation}
+where $\beta$ is the velocity of the pion in the tunnel frame, $A$ is the fiducial detector surface, $L$ the distance between the neutrino source and the detector, and $\alpha$ the angle between the pion direction and the beam axis in the laboratory frame.
+
+\begin{figure}
+\centering
+\includegraphics{../picts/pionDecay.eps}
+\caption{\label{fig:pionDecay}Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha$ is needed.}
+\end{figure}
+
+\subsection{Muon neutrino probability computation}
+\label{sec:Pmu}
+Muons decay only as $\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_\mu$ or $\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$, and will produce background events. The mean decay length of the muons is $2$~km, therefore, most of them do not decay in the tunnel. This induces a lack of statistics to estimate the corresponding level of background. This problem has been solved using each muon appearing in the simulation in the following steps:
+\begin{enumerate}
+	\item the probability for the muon to decay into the tunnel has been computed using a straight line propagation;
+	\item the available energy for the neutrino in the tunnel frame has been divided in $20$~MeV energy bins; 
+	% (the number of bin depending of the muon energy).
+	\item one $\nu_e$ and one $\nu_\mu$ have been simulated in each of the energy bins (step 2). Then, the probability to reach the detector has been computed, and multiplied by the probability computed at step (1).%the neutrino energy is stored in an histogram, weighted with this probability and 
+\end{enumerate}
+After the probability computation, the non useful muon is discarded by GEANT to gain in CPU time. 
+
+The probability for the muon neutrino and the electron neutrino to be emitted parallel to the beam axis is \cite{donega}:
+\begin{multline}
+\frac{d\mathcal{P}_\mu}{dE_\nu} = \frac{1}{4\pi}\frac{A}{L^2}\frac{2}{m_\mu}\frac{1}{\gamma_\mu(1+\beta_\mu\cos\theta^*)}\\ \times \frac{1-\beta_\mu^2}{(\beta_\mu\cos\rho-1)^2}\left[f_0(x)\mp \Pi_\mu^L f_1(x)\cos\theta^*\right]
+\label{probaMu}
+\end{multline}
+where $\beta_\mu$ and $\gamma_\mu$ are the velocity and the Lorentz boost of the muon in the tunnel frame, $\theta^*$ is the angle with respect to the beam axis of the muon in the muon rest frame, $\rho$ is the corresponding angle in the tunnel frame. Like in the pion case, this angle appears because the neutrino must be parallel to the beam axis. $\Pi_\mu^L$ is the muon longitudinal polarization, the parameter $x$ is defined as $x=2E_\nu^*/m_\mu$ where $E_\nu^*$ is the neutrino energy in the muon rest frame, and the function $f_0(x)$ and $f_1(x)$ coming from the matrix element of the muon decay are given in table~\ref{tab:Function}. The sign in front of $\Pi_\mu^L$ in equation~\ref{probaMu} is $(-)$ for the $\mu^+$ decays and $(+)$ for the $\mu^-$ decays, respectively.
+
+%\Table{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%\br
+%		      &  $f_0(x)$ & $f_1(x)$ \\
+%\mr
+%		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+%		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:Function}Flux function in the muon rest frame \cite{Gaisser}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+		      &  $f_0(x)$ & $f_1(x)$ \\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+		$\nu_\mu$ & $2x^2(3-2x)$ & $2x^2(1-2x)$ \\
+		$\nu_e$   & $12x^2(1-x)$ & $12x^2(1-x)$ \\
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+Muon polarization is computed using the conservation of the transverse component of the velocity four-vector $\gamma(1,\beta)$ between the muon rest frame (where the polarization is computed) and the pion rest frame, where the muon helicity is $-1$, due to the parity non conservation. It yields \cite{picasso}:
+\begin{equation}
+\Pi_\mu^T = \frac{\gamma_\pi\beta_\pi}{\gamma_\mu\beta_\mu}\sin\theta^*
+\mbox{ and }\Pi_\mu^L = \sqrt{1-\Pi_\mu^{T2}}
+\label{pola}
+\end{equation}
+where $\gamma_\pi$, $\beta_\pi$, $\gamma_\mu$, and $\beta_\mu$ are the Lorentz boost and velocity of the pion and of the muon in the tunnel frame, and $\theta^*$ the angle with respect to the beam axis of the muon in the pion rest frame.
+
+\subsection{The treatment of the kaons}
+\label{sec:kaons}
+Contrary to pions and muons, kaons have many decay channels. They are summarized in table~\ref{tab:BRKP0SL}.
+
+%\Table{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%\br
+%\centre{2}{$K^\pm$}                                               & \centre{2}{$K^0_L$}     &          \centre{2}{$K^0_S$}\\
+%\mr
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu$   & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+%$\pi^\pm\pi^0$ & $21.17\%$                                        & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+%$\pi^\pm\pi^+\pi^-$ & $5.59\%$                                    & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+%$e^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+%$\mu^\pm\stackrel{\scriptscriptstyle (-)}{\nu}_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+%$\pi^\pm\pi^0\pi^0$ & $1.73\%$                                    & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+%\br
+%\endTable
+\begin{table}
+\centering
+\caption{\label{tab:BRKP0SL}Charged and neutral kaon decay channels \cite{pdg}.}
+%
+\begin{tabular}{@{}l*{15}{l}}
+\hline\noalign{\smallskip}
+\centre{2}{$K^\pm$}         & \centre{2}{$K^0_L$}     & \centre{2}{$K^0_S$}\\
+\noalign{\smallskip}\hline\noalign{\smallskip}
+$\mu^\pm\nu_\mu$ & $63.51\%$ & $\pi^-e^+\nu_e$ & $19.35\%$        & $\pi^+\pi^-$ & $68.61\%$ \\
+$\pi^\pm\pi^0$ & $21.17\%$   & $\pi^+e^-\bar{\nu}_e$ & $19.35\%$  & $\pi^0\pi^0$ &  $31.39\%$ \\ 		
+$\pi^\pm\pi^+\pi^-$ & $5.59\%$ & $\pi^-\mu^+\nu_\mu$ & $13.5\%$ & & \\
+$e^\pm\nu_e\pi^0$ & $4.82\%$   & $\pi^+\mu^-\bar{\nu}_\mu$ & $13.5\%$ & & \\  			  			
+$\mu^\pm\nu_\mu\pi^0$ & $3.18\%$ & $\pi^0\pi^0\pi^0$ & $21.5\%$ & &\\
+$\pi^\pm\pi^0\pi^0$ & $1.73\%$ & $\pi^+\pi^-\pi^0$ & $12.38\%$ & & \\ 			
+\noalign{\smallskip}\hline
+\end{tabular}
+\end{table}
+
+There is a very small amount of kaons produced (section~\ref{sec:kaon}), and this number has been artificially increased in order to obtain statistically significant results.  The multiplicity of decay channels makes impossible the method used for the muon case (\ref{sec:Pmu}). The method chosen for the good compromise between the gain in CPU and the statistical uncertainty of the results, is to duplicate many times each kaon exiting the target. The number of duplication varies between 10 and 300. It depends on the initial kaon rate and therefore on the beam energy.
+
+All the kaons daughter particles are tracked by GEANT until they decay. Three different types of daughter particles are identified in the kaon decays. The first type corresponds to primary neutrinos, the second type concerns charged pions and muons, and the neutral pions are left for the last type.
+
+In the $K^\pm\rightarrow\mu^\pm \nu_\mu(\bar{\nu}_\mu)$ decay modes, the computation of the probability for a neutrino to reach the detector is the same than the 2-body decay formula used to in the pion decay (equation~\ref{probaPi}), where $\beta$ is now the kaon velocity, and $\alpha$ the angle of the kaon with respect to the beam axis. 
+
+When a neutrino is produced by a kaon 3-body decay, the probability to reach the detector is computed using a pure phase space formula. It yields:
+\begin{multline}
+\mathcal{P}_K = \frac{1}{4\pi}\frac{A}{L^2}\frac{1}{m_K-m_\pi-m_l} \\ \times \frac{1}{\gamma_K(1+\beta_K\cos\theta^*)}
+\frac{1-\beta_K^2}{(\beta_K\cos\delta-1)^2}
+\label{probaL}
+\end{multline}
+where $m_K$ is the kaon mass (charged or neutral), $m_\pi$ is the pion mass ($\pi^0$ mass in $K^\pm$ decays and $\pi^\pm$ mass in $K_L^0$ decays), and $m_l$ is the mass of the lepton associated with the neutrino. The $\beta_K$ and $\gamma_K$ are the velocity and the Lorentz boost of the kaon, $\theta^*$ is the angle between the neutrino direction and the kaon direction, in the kaon rest frame. Finally, $\delta$ is the angle between the kaon direction and the beam axis in the tunnel frame.
+
+When a $\pi^\pm$ is produced in the kaon decay chain, it is tracked by GEANT until it decays, and the probability of equation~\ref{probaPi} is applied to the produced neutrino. In case of a muon, it is treated as explained in \ref{sec:Pmu}. The muon polarization is computed this time using the kaon decay informations. Finally, when a $\pi^0$ is produced, as it cannot create neutrinos, it is simply discarded.
+
+%
+%\section*{References}
+\begin{thebibliography}{99}
+%
+%\bibitem{SKNU04}
+%Kearns E [SuperKamiokande Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%
+%\bibitem{K2KNU04}
+%Nakaya T [K2K Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%
+%\bibitem{MINOS}
+%Thomson T [MINOS Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%\nonum Adamson P \etal NuMi-L-337
+%
+%\bibitem{OPERA}
+%Autiero D [OPERA Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)\\
+%Guler M \etal \textit{ Experiment proposal} CERN/SPSC 2000-028 SPSC/P318 LNGS P25/2000 
+%
+%\bibitem{ICARUS}
+%Guler M \etal [ICARUS Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%\nonum Aprili P \etal CERN-SPSC-2002-027
+%
+%\bibitem{CNGS}
+%Acquistapace G \etal CERN-98-02
+%
+%\bibitem{LSND}
+%Athanassopoulos A \etal [LSND Collaboration] 1998 \PRL {\bf 81} 1774
+%\nonum Aguilar A \etal [LSND Collaboration] 2001 \PR D {\bf 64} 112007
+%
+%\bibitem{MINIBOONE}
+%Stancu I \etal [MiniBooNE Collaboration] FERMILAB-TM-2207
+%
+%\bibitem{PMNS}
+%Pontecorvo B  1957 \textit{Sov. Phys.--JETP} {\bf 6} 429 [1957 \textit{Zh. Eksp. Teor. Fiz.} \textbf{33} 549]
+%\nonum Maki Z, Nakagawa M and Sakata S 1962 \textit{Prog. Theor. Phys.} \textbf{28} 870\\
+%Pontecorvo B 1968 \textit{Sov. Phys.--JETP} \textbf{26}  984 [1967 \textit{Zh. Eksp. Teor. Fiz.} \textbf{53} 1717]
+%\nonum Gribov V N and Pontecorvo B 1969 \PL B \textbf{28} 493
+%
+%\bibitem{CHOOZ}
+%Apollonio M \etal  [CHOOZ Collaboration] 1999 \PL B {\bf 466} 415
+%\nonum Apollonio M \etal  [CHOOZ Collaboration] 2003 \EJP C {\bf 27}  331
+%
+%\bibitem{Wpaper}
+%Anderson K \etal 2004 \textit{White paper report on using nuclear reactors to search for a value of $\theta_{13}$} http://www.hep.anl.gov/minos/reactor13/reactor13.pdf
+%
+%\bibitem{BETABEAM}
+%Zucchelli P 2002 \PL B \textbf{532} 166
+%
+%\bibitem{NOVA}
+%Ambats I \etal 2004 NO$\nu$A proposal FNAL P929
+%
+%\bibitem{T2K}
+%Itow Y 2001 KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05 \\
+%see also arXiv:hep-ex/0106019
+%
+%\bibitem{BNLHS}
+%Diwan M V 2003 \PR D {\bf 68} 012002
+%
+%\bibitem{CERN}
+%Blondel A \etal CERN-2004-002
+%
+%\bibitem{DONINI}
+%Donini A \etal 2004 IFT-UAM/CSIC-04-30\\
+%see also arXiv:hep-ph/0406132.
+%
+%\bibitem{DOUBLE-CHOOZ}
+%Dalnoki-Veress F for the Double-CHOOZ project arXiv:hep-ex/0406070
+%
+%\bibitem{SPL}
+%Autin B \etal CERN-2000-12
+%
+%\bibitem{UNO} 
+%The UNO whitepaper \textit{Physics Potential and Feasibility of UNO} (preprint SBHEP01-3) (see also http://ale.physics.sunysb.edu/uno/)
+%
+%\bibitem{mosca}
+%Mosca L 2004 Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+%
+%\bibitem{Meer}
+%van der Meer S 1961 CERN-Report No 61-7
+%
+%\bibitem{nuFact134} 
+%Campagne J E and Cazes A 2003 CERN-NUFACT-Note-134\\ http://slac.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{MMWPSCazes} 
+%Campagne J E and Cazes A 2004 Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 \\
+%http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+%
+%\bibitem{JJG}
+%G\'omez Gadenas J J \etal 2001 IFIC/01-31 \\
+%see also arXiv:hep-ph/0105297
+%
+%\bibitem{Mezzetto}
+%Mezzetto M 2003 \jpg {\bf 29} 1781-1784\\
+%see also arXiv:hep-ex/0302005
+%
+%
+%\bibitem{nuFact138} 
+%Campagne J E 2004 CERN-NUFACT-Note-138\\
+% http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{fluka}
+%Fasso A \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, Kling A \etal - eds., Springer-Verlag Berlin, p159-164 (2001);
+%\nonum Fasso A \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, Kling A \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+%
+%\bibitem{MMWPSGaroby} 
+%Garoby R 2004 Talk in the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004 http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+%
+%\bibitem{harp}
+%Catanesi C \etal [HARP Collaboration] CERN-SPSC 2002/019
+%
+%\bibitem{MARS}
+%Mokhov N V \etal 1995 The MARS Code System User Guide, Version 13(95), Fermilab-FN-628
+%\nonum Mokhov N V \etal 1998 MARS oed Develepments; LANL Report LA-UR-98-5716, nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+%
+%\bibitem{FLUKAprivate}
+%Battistoni G and Ferrari A \textit{private communication}
+%
+%\bibitem{geant}
+%Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+%
+%\bibitem{SIMONE1}
+%Gilardoni S 2003 Talk at NuFact03 http://www.cap.bnl.gov/nufact03/
+%
+%\bibitem{donega}
+%Blondel A \etal 2001 CERN-NUFACT-Note-78\\
+% http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{MEZZETTONUFACT060}
+%Mezzetto M 2000 CERN-NUFACT-Note-60\\
+% http://slap.web.cern.ch/slap/NuFact/NuFact/NFNotes.html
+%
+%\bibitem{DONINI-2}
+%Donini A, Meloni D and Rigolin S 2004 J. High Energy Phys. \textbf{0406} 011\\
+%see also arXiv:hep-ph/0312072
+%
+%\bibitem{NUANCE}
+%Casper D  2002\textit{ Nucl. Phys. Proc. Suppl.} \textbf{112} 161-170\\
+%see also arXiv:hep-ph/0208030
+%
+%
+%\bibitem{KAMLAND}
+%Gratta G [KamLAND Collaboration] Talk at Neutrino 2004 to be published in \NP B (Proceedings Supplement)
+%
+%\bibitem{GEANT4}
+%Agostinelli A \etal [GEANT4 Collaboration] 2003 \NIM A \textbf{506} 250-503
+%
+%\bibitem{Gaisser}
+%Gaisser T K 1990 \textit{Cosmic Rays and Particle Physics} Cambridge University Press 
+%
+%\bibitem{picasso}
+%Combley F and Picasso E 1974 \textit{Phys. Rept.} {\bf 14} 1
+%
+%\bibitem{pdg}
+%Hagiwara K \etal 2002 \PR D {\bf 66}  010001
+%
+\bibitem{SKNU04}
+E. Kearns [SuperKamiokande Collaboration], talk at the International Conference NEUTRINO 2004, 14-19 June 2004, http://neutrino2004.in2p3.fr/
+
+\bibitem{K2KNU04}
+T. Nakaya [K2K Collaboration], \NP B (Proceedings Supplement) {\bf 143}, 96 (2005)
+
+\bibitem{MINOS}
+T. Thomson [MINOS Collaboration], \NP B (Proceedings Supplement) {\bf 143}, 249 (2005);
+P. Adamson \etal, NuMi-L-337 (unpublished)
+
+\bibitem{OPERA}
+D. Autiero [OPERA Collaboration], \NP B (Proceedings Supplement) {\bf 143}, 257 (2005);
+M. Guler  \etal, \textsl{Experiment proposal} CERN/SPSC 2000-028 SPSC/P318 LNGS P25/2000 (unpublished) 
+
+\bibitem{ICARUS}
+A. Bueno  [ICARUS Collaboration], \NP B (Proceedings Supplement) {\bf 143}, 262 (2005);
+P. Aprili \etal, CERN-SPSC-2002-027 (unpublished)
+
+\bibitem{CNGS}
+G. Acquistapace  \etal, CERN-98-02 (unpublished)
+
+\bibitem{LSND}
+A. Athanassopoulos \etal, \PRL {\bf 81}, 1774  (1998);
+A. Aguilar \etal, \PR D {\bf 64}, 112007 (2001) 
+
+\bibitem{MINIBOONE}
+I. Stancu \etal, FERMILAB-TM-2207 (unpublished)
+
+\bibitem{PMNS}
+B. Pontecorvo \textsl{Sov. Phys.--JETP} {\bf 6}, 429 (1957) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{33}, 549 (1957)];
+Z. Maki, M. Nakagawa and S. Sakata \textsl{Prog. Theor. Phys.} \textbf{28}, 870 (1962);
+Pontecorvo B \textsl{Sov. Phys.--JETP} \textbf{26},  984 (1968) [\textsl{Zh. Eksp. Teor. Fiz.} \textbf{53}, 1717 (1967)];
+V. N. Gribov and B. Pontecorvo \PL B \textbf{28}, 493 (1969) 
+
+\bibitem{CHOOZ}
+M. Apollonio \etal, \PL B {\bf 466}, 415 (1999);
+M. Apollonio \etal, \EJP C {\bf 27},  331 (2003)
+
+\bibitem{Wpaper}
+K. Anderson \etal, \textsl{White paper report on using nuclear reactors to search for a value of $\theta_{13}$} (2004), http://www.hep.anl.gov/minos/reactor13/reactor13.pdf (unpublished); 
+F.~Arbelier \etal, \textsl{Letter of Intend for Double-CHOOZ}, arXiv:hep-ex/0405032 (unpublished)
+
+\bibitem{BETABEAM}
+P. Zucchelli, \PL B \textbf{532}, 166 (2002) 
+
+\bibitem{NOVA}
+I. Ambats \etal,  NO$\nu$A proposal FNAL P929, 2004 (unpublished)
+
+\bibitem{T2K}
+Y. Itow, KEK report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05 (unpublished),
+see also arXiv:hep-ex/0106019
+
+\bibitem{BNLHS}
+M. V. Diwan, \PR D {\bf 68}, 012002 (2003)
+
+\bibitem{CERN}
+A. Blondel \etal, CERN-2004-002 (unpublished)
+
+\bibitem{DONINI}
+A. Donini \etal, IFT-UAM/CSIC-04-30, 2004 (unpublished);
+see also arXiv:hep-ph/0406132
+
+\bibitem{DOUBLE-CHOOZ}
+F. Dalnoki-Veress, the Double-CHOOZ project arXiv:hep-ex/0406070 (unpublished)
+
+\bibitem{SPL}
+B. Autin \etal, CERN-2000-12 (unpublished)
+
+\bibitem{UNO} 
+The UNO whitepaper, \textsl{Physics Potential and Feasibility of UNO}, SBHEP01-3 (unpublished), see also http://ale.physics.sunysb.edu/uno/
+
+\bibitem{mosca}
+L. Mosca, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Meer}
+S. van der Meer, CERN-Report No 61-7, 1961 (unpublished)
+
+\bibitem{nuFact134} 
+J.E. Campagne and A. Cazes, CERN-NUFACT-Note-134, 2003 (unpublished), see http://slac.web.cern.ch/slap/NuFact/NuFact/\\
+NFNotes.html
+
+\bibitem{MMWPSCazes} 
+J.E. Campagne and A. Cazes, Poster session at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004,
+see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{JJG}
+J.J. G\'omez Gadenas \etal,  IFIC/01-31, Proceedings of Venice 2001, Neutrino telescopes, vol. 2, p463-481;
+see also arXiv:hep-ph/0105297; A. Blondel \etal, \NIM A {\bf 503} 173 (2001);
+A. Blondel \etal, CERN-2004-002
+
+\bibitem{Mezzetto}
+M. Mezzetto,  \jpg {\bf 29}, 1781-1784 (2003),
+see also arXiv:hep-ex/0302005
+
+
+\bibitem{nuFact138} 
+J.E. Campagne, CERN-NUFACT-Note-138, 2004 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{fluka}
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p159-164 (2001);
+A. Fasso \etal, Proceedings of the MonteCarlo 2000 conference, Lisbon, October 26 2000, A. Kling \etal - eds., Springer-Verlag Berlin, p955-960 (2001)
+
+\bibitem{MMWPSGaroby} 
+R. Garoby, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{harp}
+C. Catanesi \etal, CERN-SPSC 2002/019 (unpublished)
+
+\bibitem{minerva} 
+D. Drakoulakos \etal, Fermilab P-938 (unpublished),
+see also arXiv:hep-ex/405002
+
+\bibitem{MARS}
+N.V. Mokhov \etal, The MARS Code System User Guide, Version 13(95), Fermilab-FN-628 (1995);
+N.V. Mokhov  \etal, MARS oed Develepments, LANL Report LA-UR-98-5716 (1998), nucl-th/9812038 v2 16 December 1998, http://www-ap.fnal.gov/MARS/
+
+\bibitem{FLUKAprivate}
+G. Battistoni and A. Ferrari, \textsl{private communication}
+
+\bibitem{geant}
+Application Software group, Computing and Network Division \etal GEANT Description and Simulation Tool, CERN Geneva, Switzerland
+
+\bibitem{SIMONE1}
+S. Gilardoni, Talk at NuFact03 (2003), see http://www.cap.bnl.gov/nufact03/
+
+\bibitem{donega}
+A. Blondel \etal, CERN-NUFACT-Note-78, 2001 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{MEZZETTONUFACT060}
+M. Mezzetto, CERN-NUFACT-Note-60, 2000 (unpublished), see
+ http://slap.web.cern.ch/slap/NuFact/NuFact/\\ NFNotes.html
+
+\bibitem{DONINI-2}
+A. Donini, D. Meloni and S. Rigolin, J. High Energy Phys. \textbf{0406}, 011 (2004),
+see also arXiv:hep-ph/0312072
+
+\bibitem{NUANCE}
+D. Casper, \textsl{ Nucl. Phys. Proc. Suppl.} \textbf{112}, 161-170 (2002),
+see also arXiv:hep-ph/0208030
+
+\bibitem{KAMLAND}
+G. Gratta,  talk at the International Conference NEUTRINO 2004, 14-19 June 2004, http://neutrino2004.in2p3.fr/
+
+\bibitem{MIGLIOZZITERANOVA}
+M. Komatsu, P Migliozzi and F. Terranova,  \jpg {\bf 29}, 443 (2003); see also arXiv:hep-ph/0210043
+
+\bibitem{KOBAYASHI}
+T. Kobayashi, \NP B (Proceedings Supplement) {\bf 143}, 303 (2005)
+
+\bibitem{BNL}
+ M.V. Diwan \etal, \PR D \textbf{68}, 012002 (2003); see also figure~8 of 
+arXiv:hep-ph/0303081
+
+\bibitem{MAOROPRIVATE}
+M. Mezzetto, \textsl{private communication}: the corresponding $\theta_{13}$ limit is $3.4^o$.
+
+\bibitem{GEANT4}
+A. Agostinelli \etal, \NIM A \textbf{506}, 250-503 (2003) 
+
+\bibitem{BIGICARUS}
+A. Ereditato and A. Rubia, Talk at the Physics with a Multi MegaWatt Proton Source Workshop at CERN 25-27 May 2004, see http://physicsatmwatt.web.cern.ch/physicsatmwatt/
+
+\bibitem{Gaisser}
+T.K. Gaisser, \textsl{Cosmic Rays and Particle Physics} (Cambridge University Press, 1990)  
+
+\bibitem{picasso}
+F. Combley and E. Picasso, \textsl{Phys. Rept.} {\bf 14}, 1 (1974) 
+
+\bibitem{pdg}
+K. Hagiwara \etal,  \PR D {\bf 66},  010001 (2002)
+
+
+%
+\end{thebibliography}
+%
+\end{document}
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r2.aux
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r2.aux	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r2.aux	(revision 392)
@@ -0,0 +1,222 @@
+\relax 
+\citation{SKNU04,K2KNU04}
+\citation{K2KNU04}
+\citation{MINOS}
+\citation{OPERA,ICARUS}
+\citation{CNGS}
+\citation{LSND}
+\citation{MINIBOONE}
+\citation{PMNS}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{BETABEAM}
+\citation{NOVA,T2K}
+\citation{T2K,BNLHS,CERN}
+\citation{CERN}
+\citation{DONINI}
+\citation{DONINI,DOUBLE-CHOOZ}
+\citation{SPL}
+\citation{UNO}
+\citation{mosca}
+\citation{CERN}
+\citation{Meer}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Sketch of the SPL neutrino Superbeam from CERN to the Fr\'ejus tunnel.}}{1}}
+\newlabel{fig:Sbeam}{{1}{1}}
+\citation{nuFact134,MMWPSCazes}
+\citation{DONINI,JJG,Mezzetto}
+\citation{nuFact138}
+\citation{fluka}
+\citation{CERN}
+\citation{JJG}
+\citation{CERN}
+\citation{SPL}
+\citation{MMWPSGaroby}
+\citation{nuFact134}
+\citation{harp}
+\citation{MARS}
+\citation{nuFact134}
+\citation{MMWPSGaroby}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Liquid mercury jet parameters.}}{2}}
+\newlabel{tab:targ}{{1}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Target simulation}{2}}
+\newlabel{sec:target}{{2}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Kaon production}{2}}
+\newlabel{sec:kaon}{{3}{2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  (a) $\pi ^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi ^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$\nobreakspace  {}GeV/c and $0.7$\nobreakspace  {}GeV/c. The different SPL beam kinetic energies presented are (\mbox {------}) $2.2$\nobreakspace  {}GeV, (\mbox {- - - -}) $3.5$\nobreakspace  {}GeV, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) $4.5$\nobreakspace  {}GeV and (\mbox {--- $\cdot $ ---}) $6.5$\nobreakspace  {}GeV.}}{3}}
+\newlabel{fig:compEner2}{{2}{3}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces $\pi ^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\mbox {- - - -}) and by MARS (\mbox {------}).}}{3}}
+\newlabel{fig:compFlukaMars}{{3}{3}}
+\citation{FLUKAprivate}
+\citation{geant}
+\citation{SIMONE1}
+\citation{nuFact138}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Average numbers of the most relevant secondary particles exiting the $30$\nobreakspace  {}cm long, $1.5$\nobreakspace  {}cm diameter mercury target per incident proton (FLUKA). The $\mu ^+/\mu ^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}}{4}}
+\newlabel{tab:nbPart}{{2}{4}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Horns simulation}{4}}
+\newlabel{sec:horn}{{4}{4}}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Relevant parameters of the horns in case of the generation of a $260$\nobreakspace  {}MeV neutrino beam (or $350$\nobreakspace  {}MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$\nobreakspace  {}MeV/c (or $800$\nobreakspace  {}MeV/c) pion momentum.}}{4}}
+\newlabel{tab:specif}{{3}{4}}
+\citation{donega}
+\citation{donega}
+\citation{donega}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).}}{5}}
+\newlabel{fig:KaonsPions}{{4}{5}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350\nobreakspace  {}MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}}{5}}
+\newlabel{fig:plan}{{5}{5}}
+\@writefile{toc}{\contentsline {section}{\numberline {5}Particle decay treatment and flux calculation}{5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Algorithm description}{5}}
+\newlabel{sec:algo}{{5.1}{5}}
+\citation{donega}
+\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Number of protons on target for different beam energy at 4\nobreakspace  {}MW constant power. One year is defined as $10^7$\nobreakspace  {}s.}}{6}}
+\newlabel{tab:proton}{{4}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Validation of the algorithm}{6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Simulated fluxes}{6}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  Neutrino fluxes, $100$\nobreakspace  {}km from the target and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$\nobreakspace  {}GeV (4\nobreakspace  {}MW), a decay tunnel with a length of $20$\nobreakspace  {}m and a radius of $1$\nobreakspace  {}m. The top left panel contains the $\nu _\mu $ fluxes, and the top right panel shows the $\mathaccentV {bar}016{\nu }_\mu $ fluxes. The bottom left panel presents the $\nu _e$ fluxes while the bottom right panel displays the $\mathaccentV {bar}016{\nu }_e$ fluxes. The (\mbox {------}) curve is the contribution from primary pions and the daughter muons, and from primary muons. The (\mbox {- - - -}) curve is the contribution from the charged kaon decay chain, and the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve is the contribution from the $K^0$ decay chain. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}}{7}}
+\newlabel{fig:flux22p}{{6}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but the horns are focusing negative particles.}}{7}}
+\newlabel{fig:flux22m}{{7}{7}}
+\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{8}}
+\newlabel{fig:flux45p}{{8}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{8}}
+\newlabel{fig:flux45m}{{9}{8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{9}}
+\newlabel{fig:flux8p}{{10}{9}}
+\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Same legend as for figure\nobreakspace  {}7\hbox {} but for proton beam kinetic energy of $8$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{9}}
+\newlabel{fig:flux8m}{{11}{9}}
+\citation{UNO}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{Mezzetto}
+\citation{DONINI-2}
+\citation{NUANCE}
+\citation{MEZZETTONUFACT060}
+\citation{mosca}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\citation{MEZZETTONUFACT060}
+\citation{KAMLAND}
+\citation{JJG}
+\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Integral of the total flux of the different species with different settings. The $\nu _\mu $ and $\mathaccentV {bar}016{\nu }_\mu $ fluxes are expressed in $10^{13}/100\@mathrm {m}^2/y$ unit while the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes are expressed in $10^{11}/100\@mathrm {m}^2/y$ unit. The positive focusing and negative focusing are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. }}{10}}
+\newlabel{tab:speciesfluxes}{{5}{10}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Sensitivity computation ingredients}{10}}
+\@writefile{toc}{\contentsline {section}{\numberline {7}Results}{10}}
+\newlabel{sec:results}{{7}{10}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}The positive only focusing scenario}{10}}
+\citation{DONINI}
+\citation{DONINI,JJG,Mezzetto}
+\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Comparison between the probability method, (\mbox {------}) curve, and the full GEANT simulation method, (\mbox {- - - -}) curve, for the $\nu _\mu $ from $\pi ^+$ flux (a) and the $\mathaccentV {bar}016{\nu }_\mu $ from $\pi ^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes contrary to the former simulation.}}{11}}
+\newlabel{fig:compGeantDonega}{{12}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Default parameters used to compute the sensitivity curves \cite  {MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masse square differences and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite  {KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite  {JJG}.}}{11}}
+\newlabel{tab:param}{{6}{11}}
+\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Number of events for 5 years positive focusing scenario with default parameters of table\nobreakspace  {}6\hbox {}. Other backgrounds are $\pi ^0$, $\nu _\mu $-elast., $\mu /e$-missId. }}{12}}
+\newlabel{tab:nbvsE}{{7}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Sensitivity contours obtained with a SPL energy of $3.5$\nobreakspace  {}GeV and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m. (\mbox {------}), (\mbox {- - - -}) and (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}}{12}}
+\newlabel{fig:sensi45}{{13}{12}}
+\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{12}}
+\newlabel{tab:thvsE}{{8}{12}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Mixed positive/negative focusing scenario}{12}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{12}}
+\newlabel{fig:compSensi}{{14}{12}}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\citation{CHOOZ}
+\citation{Wpaper}
+\citation{MIGLIOZZITERANOVA}
+\citation{KOBAYASHI}
+\citation{BNL}
+\citation{MAOROPRIVATE}
+\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Study of the sensitivity of different beam energy, decay tunnel length ($L_T$) at and radius ($R_T$), and horn design in two different scenarios. First scenario is 5 years of positive focusing, in wich sensitivity is given as the minimum of $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL ($\delta _{CP} = 0$). Second scenario is 2 years of positive focusing plus 8 years of negative focusing, in wich sensitivity is given as the minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta _{CP}$ case. A star $^{(*)}$ indicates the use of the the horn geometry producing a $350$\nobreakspace  {}MeV neutrino beam. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:thvsE_3545}{{9}{13}}
+\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV, and either a $260$\nobreakspace  {}MeV (default) neutrino beam or a $350$\nobreakspace  {}MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$\nobreakspace  {}m and $R_T = 2$\nobreakspace  {}m. The (\mbox {--- $\cdot $ ---}) curve corresponds to a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV (neutrino beam/SPL beam energy) setting; the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve corresponds to a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting; the (\mbox {- - - -}) curve corresponds to a $260$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting and the (\mbox {------}) curve corresponds to a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting.}}{13}}
+\newlabel{fig:comp5year}{{15}{13}}
+\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon _{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:thvseps}{{10}{13}}
+\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$\nobreakspace  {}GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta _{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
+\newlabel{tab:sign}{{11}{13}}
+\@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{13}}
+\citation{GEANT4}
+\citation{BIGICARUS}
+\citation{DONINI}
+\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces 90\% sensitivity contours obtained with SPL beam energy of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) at $90\%$ CL. Default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{14}}
+\newlabel{fig:compDeltaTheta}{{16}{14}}
+\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces 90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$\nobreakspace  {}m and $R_T=2$\nobreakspace  {}m and different SPL beam energies ($3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV) and different horn designs ($260$\nobreakspace  {}MeV or $350$\nobreakspace  {}MeV neutrino beams): (\mbox {------}) curve for a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve for a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting, (\mbox {- - - -}) curve for a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting. Other default parameters of table\nobreakspace  {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}}{14}}
+\newlabel{fig:sensiDeltaTheta}{{17}{14}}
+\@writefile{toc}{\contentsline {section}{\numberline {A}Decay probability computations}{14}}
+\newlabel{sec:decayprobcomp}{{A}{14}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}Pion neutrino probability computation}{14}}
+\newlabel{sec:Ppi}{{A.1}{14}}
+\newlabel{probaPi}{{1}{14}}
+\citation{donega}
+\citation{Gaisser}
+\citation{picasso}
+\citation{pdg}
+\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces 90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite  {CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite  {Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite  {MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite  {KOBAYASHI}. The BNL contour has been obtained from reference \cite  {BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta $ beam was analysed like a reactor experiment with 1\% systematic error \cite  {MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$\nobreakspace  {}GeV beam and a decay tunnel of $40$\nobreakspace  {}m length, and $2$\nobreakspace  {}m radius.}}{15}}
+\newlabel{fig:deltathetaFinal}{{18}{15}}
+\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha $ is needed.}}{15}}
+\newlabel{fig:pionDecay}{{19}{15}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Muon neutrino probability computation}{15}}
+\newlabel{sec:Pmu}{{A.2}{15}}
+\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Flux function in the muon rest frame \cite  {Gaisser}.}}{15}}
+\newlabel{tab:Function}{{12}{15}}
+\newlabel{probaMu}{{2}{15}}
+\newlabel{pola}{{3}{15}}
+\bibcite{SKNU04}{1}
+\bibcite{K2KNU04}{2}
+\bibcite{MINOS}{3}
+\bibcite{OPERA}{4}
+\bibcite{ICARUS}{5}
+\bibcite{CNGS}{6}
+\bibcite{LSND}{7}
+\bibcite{MINIBOONE}{8}
+\bibcite{PMNS}{9}
+\bibcite{CHOOZ}{10}
+\bibcite{Wpaper}{11}
+\bibcite{BETABEAM}{12}
+\bibcite{NOVA}{13}
+\bibcite{T2K}{14}
+\bibcite{BNLHS}{15}
+\bibcite{CERN}{16}
+\bibcite{DONINI}{17}
+\bibcite{DOUBLE-CHOOZ}{18}
+\bibcite{SPL}{19}
+\bibcite{UNO}{20}
+\bibcite{mosca}{21}
+\bibcite{Meer}{22}
+\bibcite{nuFact134}{23}
+\bibcite{MMWPSCazes}{24}
+\bibcite{JJG}{25}
+\@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces Charged and neutral kaon decay channels \cite  {pdg}.}}{16}}
+\newlabel{tab:BRKP0SL}{{13}{16}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {A.3}The treatment of the kaons}{16}}
+\newlabel{sec:kaons}{{A.3}{16}}
+\newlabel{probaL}{{4}{16}}
+\bibcite{Mezzetto}{26}
+\bibcite{nuFact138}{27}
+\bibcite{fluka}{28}
+\bibcite{MMWPSGaroby}{29}
+\bibcite{harp}{30}
+\bibcite{minerva}{31}
+\bibcite{MARS}{32}
+\bibcite{FLUKAprivate}{33}
+\bibcite{geant}{34}
+\bibcite{SIMONE1}{35}
+\bibcite{donega}{36}
+\bibcite{MEZZETTONUFACT060}{37}
+\bibcite{DONINI-2}{38}
+\bibcite{NUANCE}{39}
+\bibcite{KAMLAND}{40}
+\bibcite{MIGLIOZZITERANOVA}{41}
+\bibcite{KOBAYASHI}{42}
+\bibcite{BNL}{43}
+\bibcite{MAOROPRIVATE}{44}
+\bibcite{GEANT4}{45}
+\bibcite{BIGICARUS}{46}
+\bibcite{Gaisser}{47}
+\bibcite{picasso}{48}
+\bibcite{pdg}{49}
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r2.blg
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--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r2.blg	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r2.blg	(revision 392)
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Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r2.log
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r2.log	(revision 392)
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+LaTeX Info: Redefining \[ on input line 2666.
+LaTeX Info: Redefining \] on input line 2667.
+) (C:\Program Files\MikTex\tex\latex\base\latexsym.sty
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+\symlasy=\mathgroup6
+LaTeX Font Info:    Overwriting symbol font `lasy' in version `bold'
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+
+(C:\Program Files\MikTex\tex\latex\base\t1cmss.fd
+File: t1cmss.fd 1999/05/25 v2.5h Standard LaTeX font definitions
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+LaTeX Font Info:    Try loading font information for U+msb on input line 121.
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+(C:\Program Files\MikTex\tex\latex\amsfonts\umsb.fd
+File: umsb.fd 2002/01/19 v2.2g AMS font definitions
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+LaTeX Font Info:    Try loading font information for U+lasy on input line 121.
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+(C:\Program Files\MikTex\tex\latex\base\ulasy.fd
+File: ulasy.fd 1998/08/17 v2.2e LaTeX symbol font definitions
+)
+File: ../picts/cernSuperBeam_English.eps Graphic file (type eps)
+
+<../picts/cernSuperBeam_English.eps> [1
+
+
+]
+Overfull \hbox (1.68457pt too wide) in paragraph at lines 142--143
+\T1/cmr/m/n/10 [27], and in-tro-duced the kaon back-ground sim-u-la-tion which
+ []
+
+File: ../picts/compEner2.eps Graphic file (type eps)
+<../picts/compEner2.eps>
+File: ../picts/compMarsFlukav2.eps Graphic file (type eps)
+ <../picts/compMarsFlukav2.eps> [2] [3]
+File: ../picts/KaonPionProdFluka2003v2.eps Graphic file (type eps)
+
+<../picts/KaonPionProdFluka2003v2.eps>
+File: ../picts/corne350.eps Graphic file (type eps)
+ <../picts/corne350.eps> [4] [5]
+File: ../picts/flux22p.eps Graphic file (type eps)
+
+<../picts/flux22p.eps>
+File: ../picts/flux22m.eps Graphic file (type eps)
+ <../picts/flux22m.eps>
+File: ../picts/flux35p.eps Graphic file (type eps)
+ <../picts/flux35p.eps>
+File: ../picts/flux35m.eps Graphic file (type eps)
+
+<../picts/flux35m.eps>
+File: ../picts/flux8p.eps Graphic file (type eps)
+ <../picts/flux8p.eps>
+File: ../picts/flux8m.eps Graphic file (type eps)
+ <../picts/flux8m.eps>
+File: ../picts/compGeantDonega.eps Graphic file (type eps)
+
+<../picts/compGeantDonega.eps> [6] [7] [8] [9] [10]
+File: ../picts/sensi35.eps Graphic file (type eps)
+ <../picts/sensi35.eps>
+File: ../picts/compSensi.eps Graphic file (type eps)
+
+<../picts/compSensi.eps>
+File: ../picts/comp5year.eps Graphic file (type eps)
+ <../picts/comp5year.eps>
+Overfull \hbox (1.91864pt too wide) in paragraph at lines 649--651
+\T1/cmr/m/n/10 am-bi-gu-i-ties com-ing from the sign$\OT1/cmr/m/n/10 ([](2\OML/
+cmm/m/it/10 []\OT1/cmr/m/n/10 ))$ \T1/cmr/m/n/10 ig-no-rance also
+ []
+
+
+Underfull \vbox (badness 10000) has occurred while \output is active []
+
+ [11]
+File: ../picts/compDeltaTheta.eps Graphic file (type eps)
+
+<../picts/compDeltaTheta.eps>
+File: ../picts/sensiDeltaTheta.eps Graphic file (type eps)
+ <../picts/sensiDeltaTheta.eps>
+Underfull \vbox (badness 10000) has occurred while \output is active []
+
+ [12]
+Underfull \vbox (badness 3826) has occurred while \output is active []
+
+File: ../picts/comparaisonFinale.eps Graphic file (type eps)
+
+<../picts/comparaisonFinale.eps> [13] [14]
+File: ../picts/pionDecay.eps Graphic file (type eps)
+ <../picts/pionDecay.eps> [15]
+Overfull \hbox (1.72989pt too wide) in paragraph at lines 870--871
+[][]\T1/cmr/m/n/10 All the kaons daugh-ter par-ti-cles are tracked by GEANT
+ []
+
+
+Underfull \hbox (badness 2707) in paragraph at lines 1078--1080
+[][]\T1/cmr/m/n/9 K. An-der-son et al., \T1/cmr/m/sl/9 White pa-per re-port on 
+us-ing
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1078--1080
+\T1/cmr/m/n/9 http://www.hep.anl.gov/minos/reactor13/reactor13.pdf
+ []
+
+
+Underfull \hbox (badness 1831) in paragraph at lines 1088--1090
+[][]\T1/cmr/m/n/9 Y. Itow, KEK re-port 2001-4, ICRR-report-477-2001-
+ []
+
+
+Underfull \hbox (badness 3449) in paragraph at lines 1088--1090
+\T1/cmr/m/n/9 7, TRI-PP-01-05 (un-pub-lished), see also arXiv:hep-
+ []
+
+
+Underfull \hbox (badness 2119) in paragraph at lines 1108--1109
+[][]\T1/cmr/m/n/9 The UNO whitepa-per, \T1/cmr/m/sl/9 Physics Po-ten-tial and F
+ea-si-
+ []
+
+
+Underfull \hbox (badness 2990) in paragraph at lines 1108--1109
+\T1/cmr/m/sl/9 bil-ity of UNO\T1/cmr/m/n/9 , SBHEP01-3 (un-pub-lished), see als
+o
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1117--1119
+[][]\T1/cmr/m/n/9 J.E. Cam-pagne and A. Cazes, CERN-
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1117--1119
+\T1/cmr/m/n/9 NUFACT-Note-134, 2003 (un-pub-lished), see
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1121--1123
+[][]\T1/cmr/m/n/9 J.E. Cam-pagne and A. Cazes, Poster ses-sion
+ []
+
+
+Underfull \hbox (badness 7522) in paragraph at lines 1121--1123
+\T1/cmr/m/n/9 at the Physics with a Multi MegaWatt Pro-ton
+ []
+
+
+Underfull \hbox (badness 4229) in paragraph at lines 1121--1123
+\T1/cmr/m/n/9 Source Work-shop at CERN 25-27 May 2004, see
+ []
+
+[16]
+Underfull \hbox (badness 10000) in paragraph at lines 1163--1164
+[][]\T1/cmr/m/n/9 S. Gi-lar-doni, Talk at Nu-Fact03 (2003), see
+ []
+
+
+Underfull \hbox (badness 1163) in paragraph at lines 1170--1172
+[][]\T1/cmr/m/n/9 M. Mezzetto, CERN-NUFACT-Note-60, 2000 (un-pub-
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1182--1183
+[][]\T1/cmr/m/n/9 G. Gratta, talk at the In-ter-na-tional Con-
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1182--1183
+\T1/cmr/m/n/9 fer-ence NEU-TRINO 2004, 14-19 June 2004,
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1201--1202
+[][]\T1/cmr/m/n/9 A. Ered-i-tato and A. Ru-bia, Talk at the
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1201--1202
+\T1/cmr/m/n/9 Physics with a Multi MegaWatt Pro-ton Source
+ []
+
+
+Underfull \hbox (badness 10000) in paragraph at lines 1201--1202
+\T1/cmr/m/n/9 Work-shop at CERN 25-27 May 2004, see
+ []
+
+[17] (SPLFrejusv3r2.aux) ) 
+Here is how much of TeX's memory you used:
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+
+Output written on SPLFrejusv3r2.dvi (17 pages, 98228 bytes).
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/rephrasing.txt
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/rephrasing.txt	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/rephrasing.txt	(revision 392)
@@ -0,0 +1,15 @@
+
+%%%%%%%%% Avant
+
+The horns are designed to focus the $600$~MeV/c pions (see section~\ref{sec:horn}) and the variation of the number of such pion is rather smooth with respect to the beam energy considering a 4MW fixed beam power: $4.19\times10^{13}\pi$/s for the $2.2$~GeV beam, $4.91\times10^{13}\pi$/s for the $3.5$~GeV beam, $5.14\times10^{13}\pi$/s for the $4.5$~GeV beam, and $4.92\times10^{13}\pi$/s for the $6.5$~GeV beam. The main difference is made by the angular distribution. Figure~\ref{fig:compEner2}(b) shows this distribution for the $\pi^+$ exiting the target with a momentum between $500$~MeV/c and $700$~MeV/c. The acceptance of the horns is limited to the pion below $25^\circ$, and we see that more pions are accepted by the horns for the $3.5$~GeV and $4.5$~GeV proton beams compared to other beam energies.
+
+
+
+%%%%%%%%%%% Apres
+
+The variation of the number of $600$~MeV/c pions is rather smooth with respect to the beam energy (the horns are designed to focus such pions, see section~\ref{sec:horn}). Considering a 4MW fixed beam power, they are: $4.19\times10^{13}\pi$/s for the $2.2$~GeV beam, $4.91\times10^{13}\pi$/s for the $3.5$~GeV beam, $5.14\times10^{13}\pi$/s for the $4.5$~GeV beam, and $4.92\times10^{13}\pi$/s for the $6.5$~GeV beam. The main difference is made by the angular distribution. Figure~\ref{fig:compEner2}(b) shows this distribution for the $\pi^+$ exiting the target with a momentum between $500$~MeV/c and $700$~MeV/c. The acceptance of the horns is limited to the pion below $25^\circ$, and we see that more pions are accepted by the horns for the $3.5$~GeV and $4.5$~GeV proton beams compared to other beam energies.
+
+
+
+
+
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/svepj.clo
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/svepj.clo	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/svepj.clo	(revision 392)
@@ -0,0 +1,307 @@
+% SVJour DOCUMENT CLASS OPTION EPJ -- The European Physical Journal
+%
+% This is an enhancement for the
+% LaTeX document class for Springer journals (two column version)
+%
+%%
+%%
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
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+%%   Minus         \-     Point         \.     Solidus       \/
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+%%   Right brace   \}     Tilde         \~}
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+              [2002/03/11 v1.2
+      style option for The European Physical Journal]
+\typeout{SVJour Class option: svepj.clo for The European Physical Journal}
+\DeclareOption{leqno}{\input{leqno.clo}}
+\let\if@nopacs\iffalse
+\DeclareOption{nopacs}{\let\if@nopacs\iftrue}
+\ExecuteOptions{final,twocolumn,10pt}
+\newif\if@normhead \@normheadtrue
+\def\hugehead{\@normheadfalse
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+\onecolumn
+\let\thanks=\footnote
+\long\def\@makefntext##1{\parindent\bibindent
+     \columnwidth\textwidth
+     \advance\columnwidth -\columnsep
+     \divide\columnwidth\tw@
+     \hsize\columnwidth
+     \linewidth\columnwidth
+     \noindent\hbox to\parindent{\hss\@makefnmark\enspace}##1}%
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+   \belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@
+   \belowdisplayskip \abovedisplayskip
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+   \def\@listi{\leftmargin\leftmargini
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+               \topsep 8\p@ \@plus2\p@ \@minus4\p@
+               \itemsep0\p@}%
+   \belowdisplayskip \abovedisplayskip
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+\ch@ckobl{date}{the date of receipt and acceptance should be inserted
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+\ch@ckobl{title}{A title should be given}
+\ch@ckobl{author}{Name(s) and initial(s) of author(s) should be given}
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+    \footnotetext[0]{\kern-\bibindent\mailname\
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+    \ProcessRunnHead
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+ \setcounter{footnote}{0}
+ \global\let\thanks\relax
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+ \nointerlineskip
+ \makeheadbox\vss}\nointerlineskip
+ \if@normhead
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+ \lineskip .5em
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+ \protected@xdef\@thanks{\@thanks\protect\switch@fnmark}%
+ \setbox0=\vbox{\setcounter{auth}{1}\def\and{\stepcounter{auth} }%
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+ {\topsep=0pt\partopsep=0pt\parsep=0pt\itemsep=0pt\relax
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+  \@abstract
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+     \ch@ckobl{PACS}{{XX.XX.XX}{No PACS code given}}%
+     \@@PACS
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+  \endtrivlist}%
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+    \ifdim\@tempdima>0pt
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+    \fi
+    \unvbox\authrun
+    \global\@minipagetrue
+    \global\everypar{\global\@minipagefalse\global\everypar{}}
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+    \typeout{\the\c@auth\space author names and}
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+ \vskip22.47pt
+}
+%
+\def\PACS#1{\gdef\@PACS{#1}}
+\def\@@PACS{\par\addvspace\baselineskip\noindent{\sffamily\bfseries
+PACS.\enspace}\ignorespaces\expandafter\pacsstart\@PACS\par}
+%
+\def\epjabstract#1{\gdef\@abstract{#1}}
+%
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+    \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}%
+    \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}%
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+    \advance\instindent by-\headlineindent
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+      \edef\@title{\the\titlerunning}%
+    \fi
+    \global\setbox\titrun=\hbox{\small\rm\ignorespaces\@title}%
+    \ifdim\wd\titrun>\instindent
+       \typeout{^^JSVJour Warning: Title too long for running head.}%
+       \typeout{Please supply a shorter form with \string\titlerunning
+                \space prior to \string\maketitle}%
+       \global\setbox\titrun=\hbox{\small\rm
+       Title Suppressed Due to Excessive Length}%
+    \fi
+    \xdef\@title{\copy\titrun}%
+%
+    \if!\the\authorrunning!
+    \else
+      \setcounter{auth}{1}%
+      \edef\@author{\the\authorrunning}%
+    \fi
+    \ifnum\value{auth}>2
+       \def\stripauthor##1\and##2\endauthor{%
+       \protected@xdef\@author{##1\unskip\unskip\if!##2!\else\ et al.\fi}}%
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+       {\def\and{\noexpand\protect\noexpand\and}%
+       \protected@xdef\@author{\@author}}
+    \fi
+    \global\setbox\authrun=\hbox{\small\ignorespaces
+                                 \@author\unskip: \unhbox\titrun}%
+    \ifdim\wd\authrun>\instindent
+    \typeout{^^JSVJour Warning: The running head built automatically from
+             \string\author\space and \string\title
+             ^^Jexceeds the pagewidth, please supply a shorter form
+             ^^Jwith \string\authorrunning\space and
+             \string\titlerunning\space prior to \string\maketitle}%
+    \global\setbox\authrun=\hbox{\small\rm Please give a shorter version
+          with: {\tt\string\authorrunning\space and
+             \string\titlerunning\space prior to \string\maketitle}}%
+    \fi
+    \xdef\@author{\copy\authrun}%
+    \markboth{\@author}{\@author}%
+}
+%
+\AtEndOfClass{\let\ackname\@empty
+\let\if@runhead\iftrue
+\let\if@smartand\iftrue
+\let\@maketitle=\epj@@maketitle
+\let\maketitle=\epj@maketitle
+\let\ProcessRunnHead=\epjrunnhead
+\let\abstract=\epjabstract
+\def\@evenhead{\small\rlap{\thepage}\hfil\leftmark\hfil}%
+\def\@oddhead{\small\hfil\rightmark\hfil\llap{\thepage}}%
+\def\sectcounterend{}
+\setlength\columnsep{4mm}
+\def\section{\@startsection{section}{1}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\large\sffamily\bfseries}}
+\def\subsection{\@startsection{subsection}{2}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\normalsize\sffamily\bfseries}}
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\normalsize\sffamily}}
+\def\paragraph{\@startsection{subsubsection}{4}{\z@}%
+    {-21dd plus-4pt minus-4pt}{-1pt}{\normalsize\sffamily\bfseries}}
+\def\authorfont{\rmfamily}
+\def\leftlegendglue{\hfil}
+\journalname{EPJ}}
+%%
+%% End of copy of file `svepj.clo'.
+\endinput
Index: /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/svjour.cls
===================================================================
--- /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/svjour.cls	(revision 392)
+++ /Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/svjour.cls	(revision 392)
@@ -0,0 +1,1241 @@
+% SVJour DOCUMENT CLASS -- version 1.11 for LaTeX2e
+%
+% LaTeX document class for Springer journals
+%
+%%
+%%
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\ProvidesClass{svjour}[2003/04/15
+^^JLaTeX document class for Springer journals - version 1.11]
+\newcommand\@ptsize{}
+\newif\if@restonecol
+\newif\if@titlepage
+\@titlepagefalse
+\DeclareOption{a4paper}
+   {\setlength\paperheight {297mm}%
+    \setlength\paperwidth  {210mm}}
+\DeclareOption{10pt}{\renewcommand\@ptsize{0}}
+\DeclareOption{twoside}{\@twosidetrue  \@mparswitchtrue}
+\DeclareOption{draft}{\setlength\overfullrule{5pt}}
+\DeclareOption{final}{\setlength\overfullrule{0pt}}
+\DeclareOption{twocolumn}{\@twocolumntrue}
+\DeclareOption{fleqn}{\input{fleqn.clo}\AtEndOfClass{\mathindent\z@}}
+\let\if@mathematic\iftrue
+\let\if@numbook\iffalse
+\DeclareOption{numbook}{\let\if@envcntsect\iftrue
+  \AtEndOfPackage{%
+   \renewcommand\thefigure{\thesection.\@arabic\c@figure}%
+   \renewcommand\thetable{\thesection.\@arabic\c@table}%
+   \renewcommand\theequation{\thesection.\@arabic\c@equation}%
+   \@addtoreset{figure}{section}%
+   \@addtoreset{table}{section}%
+   \@addtoreset{equation}{section}%
+  }%
+}
+\DeclareOption{openbib}{%
+  \AtEndOfPackage{%
+   \renewcommand\@openbib@code{%
+      \advance\leftmargin\bibindent
+      \itemindent -\bibindent
+      \listparindent \itemindent
+      \parsep \z@
+      }%
+   \renewcommand\newblock{\par}}%
+}
+%
+\let\if@runhead\iffalse
+\DeclareOption{runningheads}{\let\if@runhead\iftrue}
+\let\if@smartrunh\iffalse
+\DeclareOption{smartrunhead}{\let\if@smartrunh\iftrue}
+\DeclareOption{nosmartrunhead}{\let\if@smartrunh\iffalse}
+\let\if@envcntreset\iffalse
+\DeclareOption{envcountreset}{\let\if@envcntreset\iftrue}
+\let\if@envcntsame\iffalse
+\DeclareOption{envcountsame}{\let\if@envcntsame\iftrue}
+\let\if@envcntsect\iffalse
+\DeclareOption{envcountsect}{\let\if@envcntsect\iftrue}
+\let\if@referee\iffalse
+\DeclareOption{referee}{\let\if@referee\iftrue}
+\def\makereferee{\def\baselinestretch{2}}
+\let\if@instindent\iffalse
+\DeclareOption{instindent}{\let\if@instindent\iftrue}
+\let\if@smartand\iffalse
+\DeclareOption{smartand}{\let\if@smartand\iftrue}
+\let\if@spthms\iftrue
+\DeclareOption{nospthms}{\let\if@spthms\iffalse}
+\let\switch@texts\relax
+\DeclareOption{deutsch}{\def\switch@texts{\ds@deutsch}}
+\DeclareOption{francais}{\def\switch@texts{\ds@francais}}
+%
+\let\journalopt\@empty
+\DeclareOption*{\InputIfFileExists{sv\CurrentOption.clo}{%
+\let\journalopt\CurrentOption}{%
+\ClassWarning{Springer-SVJour}{Specified option or subpackage
+"\CurrentOption" not found -}\OptionNotUsed}}
+\ExecuteOptions{a4paper,twoside,10pt,instindent}
+\ProcessOptions
+\ifx\journalopt\@empty
+\ClassError{Springer-SVJour}{No valid journal specified in option list}{}
+\expandafter\stop
+\fi
+%
+\if@smartrunh\AtEndDocument{\islastpageeven\getlastpagenumber}\fi
+%
+\DeclareMathSymbol{\Gamma}{\mathalpha}{letters}{"00}
+\DeclareMathSymbol{\Delta}{\mathalpha}{letters}{"01}
+\DeclareMathSymbol{\Theta}{\mathalpha}{letters}{"02}
+\DeclareMathSymbol{\Lambda}{\mathalpha}{letters}{"03}
+\DeclareMathSymbol{\Xi}{\mathalpha}{letters}{"04}
+\DeclareMathSymbol{\Pi}{\mathalpha}{letters}{"05}
+\DeclareMathSymbol{\Sigma}{\mathalpha}{letters}{"06}
+\DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07}
+\DeclareMathSymbol{\Phi}{\mathalpha}{letters}{"08}
+\DeclareMathSymbol{\Psi}{\mathalpha}{letters}{"09}
+\DeclareMathSymbol{\Omega}{\mathalpha}{letters}{"0A}
+%
+\setlength\parindent{15\p@}
+\setlength\smallskipamount{3\p@ \@plus 1\p@ \@minus 1\p@}
+\setlength\medskipamount{6\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\bigskipamount{12\p@ \@plus 4\p@ \@minus 4\p@}
+\setlength\headheight{12\p@}
+\setlength\headsep   {16.74dd}
+\setlength\topskip   {10\p@}
+\setlength\footskip{30\p@}
+\setlength\maxdepth{.5\topskip}
+%
+\@settopoint\textwidth
+\setlength\marginparsep {10\p@}
+\setlength\marginparpush{5\p@}
+\setlength\topmargin{-10pt}
+\if@twocolumn
+   \setlength\oddsidemargin {-30\p@}
+   \setlength\evensidemargin{-30\p@}
+\else
+   \setlength\oddsidemargin {\z@}
+   \setlength\evensidemargin{\z@}
+\fi
+\setlength\marginparwidth  {48\p@}
+\setlength\footnotesep{8\p@}
+\setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@}
+\setlength\floatsep    {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\textfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\intextsep   {20\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\dblfloatsep    {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\@fptop{0\p@}
+\setlength\@fpsep{12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\@fpbot{0\p@ \@plus 1fil}
+\setlength\@dblfptop{0\p@}
+\setlength\@dblfpsep{12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\@dblfpbot{0\p@ \@plus 1fil}
+\setlength\partopsep{2\p@ \@plus 1\p@ \@minus 1\p@}
+\def\@listi{\leftmargin\leftmargini
+            \parsep \z@
+            \topsep 6\p@ \@plus2\p@ \@minus4\p@
+            \itemsep\parsep}
+\let\@listI\@listi
+\@listi
+\def\@listii {\leftmargin\leftmarginii
+              \labelwidth\leftmarginii
+              \advance\labelwidth-\labelsep
+              \topsep    \z@
+              \parsep    \topsep
+              \itemsep   \parsep}
+\def\@listiii{\leftmargin\leftmarginiii
+              \labelwidth\leftmarginiii
+              \advance\labelwidth-\labelsep
+              \topsep    \z@
+              \parsep    \topsep
+              \itemsep   \parsep}
+\def\@listiv {\leftmargin\leftmarginiv
+              \labelwidth\leftmarginiv
+              \advance\labelwidth-\labelsep}
+\def\@listv  {\leftmargin\leftmarginv
+              \labelwidth\leftmarginv
+              \advance\labelwidth-\labelsep}
+\def\@listvi {\leftmargin\leftmarginvi
+              \labelwidth\leftmarginvi
+              \advance\labelwidth-\labelsep}
+%
+\setlength\lineskip{1\p@}
+\setlength\normallineskip{1\p@}
+\renewcommand\baselinestretch{}
+\setlength\parskip{0\p@ \@plus \p@}
+\@lowpenalty   51
+\@medpenalty  151
+\@highpenalty 301
+\setcounter{topnumber}{4}
+\renewcommand\topfraction{.9}
+\setcounter{bottomnumber}{2}
+\renewcommand\bottomfraction{.7}
+\setcounter{totalnumber}{6}
+\renewcommand\textfraction{.1}
+\renewcommand\floatpagefraction{.85}
+\setcounter{dbltopnumber}{3}
+\renewcommand\dbltopfraction{.85}
+\renewcommand\dblfloatpagefraction{.85}
+\def\ps@headings{%
+    \let\@oddfoot\@empty\let\@evenfoot\@empty
+    \def\@evenhead{\small\rlap{\thepage}\hfil\leftmark\unskip}%
+    \def\@oddhead{\small\rightmark\hfil\llap{\thepage}}%
+    \let\@mkboth\@gobbletwo
+    \let\sectionmark\@gobble
+    \let\subsectionmark\@gobble
+    }
+% make indentations changeable
+\def\setitemindent#1{\settowidth{\labelwidth}{#1}%
+        \leftmargini\labelwidth
+        \advance\leftmargini\labelsep
+   \def\@listi{\leftmargin\leftmargini
+        \labelwidth\leftmargini\advance\labelwidth by -\labelsep
+        \parsep=\parskip
+        \topsep=\medskipamount
+        \itemsep=\parskip \advance\itemsep by -\parsep}}
+\def\setitemitemindent#1{\settowidth{\labelwidth}{#1}%
+        \leftmarginii\labelwidth
+        \advance\leftmarginii\labelsep
+\def\@listii{\leftmargin\leftmarginii
+        \labelwidth\leftmarginii\advance\labelwidth by -\labelsep
+        \parsep=\parskip
+        \topsep=\z@
+        \itemsep=\parskip \advance\itemsep by -\parsep}}
+% labels of description
+\def\descriptionlabel#1{\hspace\labelsep #1\hfil}
+% adjusted environment "description"
+% if an optional parameter (at the first two levels of lists)
+% is present, its width is considered to be the widest mark
+% throughout the current list.
+\def\description{\@ifnextchar[{\@describe}{\list{}{\labelwidth\z@
+          \itemindent-\leftmargin \let\makelabel\descriptionlabel}}}
+\let\enddescription\endlist
+%
+\def\describelabel#1{#1\hfil}
+\def\@describe[#1]{\relax\ifnum\@listdepth=0
+\setitemindent{#1}\else\ifnum\@listdepth=1
+\setitemitemindent{#1}\fi\fi
+\list{--}{\let\makelabel\describelabel}}
+%
+\newdimen\logodepth
+\logodepth=2.2cm
+\newdimen\headerboxheight
+\headerboxheight=180pt % 18 10.5dd-lines - 2\baselineskip
+\newdimen\betweenumberspace          % dimension for space between
+\betweenumberspace=3.33pt            % number and text of titles.
+\newdimen\aftertext                  % dimension for space after
+\aftertext=5pt                       % text of title.
+\newdimen\headlineindent             % dimension for space between
+\headlineindent=1.166cm              % number and text of headings.
+\def\andname{and}
+\if@mathematic
+   \def\runinend{\enspace}
+   \def\floatcounterend{\enspace}
+   \def\sectcounterend{}
+\else
+   \def\runinend{.}
+   \def\floatcounterend{.\ }
+   \def\sectcounterend{.}
+\fi
+\def\keywordname{{\bfseries Key words\runinend}}
+\def\lastandname{, and}
+\def\mailname{{\itshape Correspondence to\/}:}
+\def\email#1{{e-mail: \tt#1}}
+\def\keywords#1{\par\addvspace\baselineskip\noindent\keywordname\enspace
+\ignorespaces#1}
+%
+\newcounter{inst}
+\newcounter{auth}
+\def\authdepth{2}
+\newdimen\instindent
+\newbox\authrun
+\newtoks\authorrunning
+\newbox\titrun
+\newtoks\titlerunning
+\def\authorfont{\bfseries}
+
+\def\combirunning#1{\gdef\@combi{#1}}
+\def\@combi{}
+\newbox\combirun
+%
+\def\ps@last{\def\@evenhead{\small\rlap{\thepage}\hfil
+\lastevenhead}}
+\newcounter{lastpage}
+\def\islastpageeven{\@ifundefined{lastpagenumber}
+{\setcounter{lastpage}{0}}{\setcounter{lastpage}{\lastpagenumber}}
+\ifnum\value{lastpage}>0
+   \ifodd\value{lastpage}%
+   \else
+      \if@smartrunh
+         \thispagestyle{last}%
+      \fi
+   \fi
+\fi}
+\def\getlastpagenumber{\clearpage
+\addtocounter{page}{-1}%
+   \immediate\write\@auxout{\string\gdef\string\lastpagenumber{\thepage}}%
+   \immediate\write\@auxout{\string\newlabel{LastPage}{{}{\thepage}}}%
+   \addtocounter{page}{1}}
+
+\def\journalname#1{\gdef\@journalname{#1}}
+
+\def\dedication#1{\gdef\@dedic{#1}}
+\def\@dedic{}
+
+\let\@date\undefined
+
+\def\institute#1{\gdef\@institute{#1}}
+
+\def\institutename{\par
+ \begingroup
+ \parindent=0pt
+ \parskip=0pt
+ \setcounter{inst}{1}%
+ \def\and{\par\stepcounter{inst}%
+ \if@instindent\hangindent\instindent\fi
+ \noindent
+ \hbox to\instindent{\hss\smash{$^{\theinst}$}\enspace}\ignorespaces}%
+ \setbox0=\vbox{\def\thanks##1{}\@institute}
+ \ifnum\value{inst}>9\relax\setbox0=\hbox{$^{88}$\enspace}%
+                 \else\setbox0=\hbox{$^{8}$\enspace}\fi
+ \instindent=\wd0\relax
+ \ifnum\value{inst}=1\relax
+ \else
+   \setcounter{inst}{1}%
+   \if@instindent\hangindent\instindent\fi
+   \noindent
+   \hbox to\instindent{\hss\smash{$^{\theinst}$}\enspace}\ignorespaces
+ \fi
+ \small
+ \ignorespaces
+ \@institute\par
+ \endgroup}
+
+\def\offprints#1{\begingroup
+\def\protect{\noexpand\protect\noexpand}\xdef\@thanks{\@thanks
+\protect\footnotetext[0]{\unskip\hskip-15pt{\itshape Send offprint requests
+to\/}: \ignorespaces#1}}\endgroup\ignorespaces}
+
+\def\mail#1{\gdef\@mail{#1}}
+\def\@mail{}
+
+\def\@thanks{}
+
+\def\@fnsymbol#1{\ifcase#1\or\star\or{\star\star}\or{\star\star\star}%
+   \or \dagger\or \ddagger\or
+   \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
+   \or \ddagger\ddagger \else\@ctrerr\fi\relax}
+
+\def\inst#1{\unskip$^{#1}$}
+\def\fnmsep{\unskip$^,$}
+
+\def\subtitle#1{\gdef\@subtitle{#1}}
+\def\@subtitle{}
+
+\def\headnote#1{\gdef\@headnote{#1}}
+\def\@headnote{}
+
+\def\ch@ckobl#1#2{\@ifundefined{@#1}
+ {\typeout{SVJour warning: Missing
+\expandafter\string\csname#1\endcsname}%
+  \csname #1\endcsname{#2}}
+ {}}
+%
+\def\ProcessRunnHead{%
+    \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}%
+    \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}%
+    \instindent=\textwidth
+    \advance\instindent by-\headlineindent
+    \if!\the\titlerunning!\else
+      \edef\@title{\the\titlerunning}%
+    \fi
+    \global\setbox\titrun=\hbox{\small\rmfamily\unboldmath\ignorespaces\@title
+                                \unskip}%
+    \ifdim\wd\titrun>\instindent
+       \typeout{^^JSVJour Warning: Title too long for running head.}%
+       \typeout{Please supply a shorter form with \string\titlerunning
+                \space prior to \string\maketitle}%
+       \global\setbox\titrun=\hbox{\small\rmfamily
+       Title Suppressed Due to Excessive Length}%
+    \fi
+    \xdef\@title{\copy\titrun}%
+%
+    \if!\the\authorrunning!
+    \else
+      \setcounter{auth}{1}%
+      \edef\@author{\the\authorrunning}%
+    \fi
+    \ifnum\value{auth}>\authdepth
+       \def\stripauthor##1\and##2\endauthor{%
+       \protected@xdef\@author{##1\unskip\unskip\if!##2!\else\ et al.\fi}}%
+       \expandafter\stripauthor\@author\and\endauthor
+    \else
+       \gdef\and{\unskip, \ignorespaces}%
+       {\def\and{\noexpand\protect\noexpand\and}%
+       \protected@xdef\@author{\@author}}
+    \fi
+    \global\setbox\authrun=\hbox{\small\rmfamily\unboldmath\ignorespaces
+                                 \@author\unskip}%
+    \ifdim\wd\authrun>\instindent
+    \typeout{^^JSVJour Warning: Author name(s) too long for running head.
+             ^^JPlease supply a shorter form with \string\authorrunning
+             \space prior to \string\maketitle}%
+    \global\setbox\authrun=\hbox{\small\rmfamily Please give a shorter version
+          with: {\tt\string\authorrunning\space and
+             \string\titlerunning\space prior to \string\maketitle}}%
+    \fi
+    \xdef\@author{\copy\authrun}%
+    \markboth{\@author}{\@title}%
+}
+%
+\def\maketitle{\par
+\ch@ckobl{journalname}{Noname}
+\ch@ckobl{date}{The date of receipt and acceptance will be inserted by
+the editor}
+\ch@ckobl{title}{A title should be given}
+\ch@ckobl{author}{Name(s) and initial(s) of author(s) should be given}
+\ch@ckobl{institute}{Address(es) of author(s) should be given}
+\begingroup
+%
+    \renewcommand\thefootnote{\@fnsymbol\c@footnote}%
+    \def\@makefnmark{$^{\@thefnmark}$}%
+%
+ \def\lastand{\ifnum\value{inst}=2\relax
+                 \unskip{} \andname\
+              \else
+                 \unskip, \andname\
+              \fi}%
+ \def\and{\stepcounter{auth}\relax
+          \if@smartand
+             \ifnum\value{auth}=\value{inst}%
+                \lastand
+             \else
+                \unskip,
+             \fi
+          \else
+             \unskip,
+          \fi}%
+ \ifnum \col@number=\@ne
+   \@maketitle
+ \else
+   \twocolumn[\@maketitle]%
+ \fi
+ \thispagestyle{empty}
+ \global\@topnum\z@
+ \@thanks
+ \if!\@mail!\else
+    \footnotetext[0]{\kern-\bibindent\mailname\
+    \ignorespaces\@mail}%
+ \fi
+%
+ \if@runhead
+    \ProcessRunnHead
+    \if@smartrunh
+       \instindent=\textwidth
+       \advance\instindent by-\headlineindent
+       \if!\@combi!%
+          \global\setbox\combirun=\hbox{\small\rmfamily\unboldmath\ignorespaces
+                                        \@author\unskip: \@title\unskip}%
+          \def\@tempa{Automatically generated running head}%
+       \else
+          \global\setbox\combirun=\hbox{\small\rmfamily\unboldmath\ignorespaces
+                                        \@combi\unskip}%
+          \def\@tempa{With \string\combirunning\space supplied running head}%
+       \fi
+       \ifdim\wd\combirun>\instindent
+          \typeout{^^JSVJour Warning: \@tempa}%
+          \typeout{for a possible last even numbered page is too long.}%
+          \typeout{Please supply a shorter form with \string\combirunning
+                   \space prior to \string\maketitle.}%
+          \global\setbox\combirun=\hbox{\small\rmfamily
+          Title Suppressed Due to Excessive Length --
+          supply \ttfamily\char92combirunning}%
+       \fi
+       \xdef\lastevenhead{\copy\combirun}%
+    \fi
+ \fi
+%
+ \endgroup
+ \setcounter{footnote}{0}
+ \global\let\thanks\relax
+ \global\let\maketitle\relax
+ \global\let\@maketitle\relax
+ \global\let\@thanks\@empty
+ \global\let\@author\@empty
+ \global\let\@date\@empty
+ \global\let\@title\@empty
+ \global\let\@subtitle\@empty
+ \global\let\title\relax
+ \global\let\author\relax
+ \global\let\date\relax
+ \global\let\and\relax}
+
+\def\makeheadbox{{%
+\hbox to0pt{\vbox{\baselineskip=10dd\hrule\hbox
+to\hsize{\vrule\kern3pt\vbox{\kern3pt
+\hbox{\bfseries\@journalname\ manuscript No.}
+\hbox{(will be inserted by the editor)}
+\kern3pt}\hfil\kern3pt\vrule}\hrule}%
+\hss}}}
+
+\def\@maketitle{\newpage
+ \normalfont
+ \vbox to0pt{\vskip-40pt
+ \nointerlineskip
+ \makeheadbox\vss}\nointerlineskip
+ \setbox\authrun=\vbox\bgroup
+ {\Large \bfseries\boldmath
+  \hrule\@height\logodepth\@width\z@
+  \pretolerance=10000
+  \rightskip=0pt plus 4cm
+ \if!\@headnote!\else
+   \noindent
+   {\normalfont\em\ignorespaces\@headnote\par}\vskip 3.5mm
+ \fi
+  \noindent\ignorespaces
+  \@title \par}\vskip 11.24pt\relax
+ \if!\@subtitle!\else
+   {\large\bfseries\boldmath
+   \pretolerance=10000
+   \rightskip=0pt plus 3cm
+   \noindent\ignorespaces\@subtitle \par}\vskip 11.24pt
+ \fi
+ \normalfont\authorfont
+ \lineskip .5em
+ \setbox0=\vbox{\setcounter{auth}{1}\def\and{\stepcounter{auth} }%
+                \hfuzz=2\textwidth\def\thanks##1{}\@author}%
+ \value{inst}=\value{auth}%
+ \setcounter{auth}{1}%
+ \rightskip=0pt plus 2cm
+ \noindent\ignorespaces\@author\vskip7.23pt
+ \rightskip=0pt\relax
+ \normalfont\small\rmfamily
+ \institutename
+ \vskip 12.85pt \noindent\@date
+ \if!\@dedic!\else
+    \par
+    \small\itshape
+    \addvspace\baselineskip
+    \noindent\@dedic
+ \fi
+ \egroup % end of header box
+ \@tempdima=\headerboxheight
+ \advance\@tempdima by-\ht\authrun
+ \ifdim\@tempdima>0pt
+    \vrule width0pt height\@tempdima
+ \fi
+ \unvbox\authrun
+ \global\@minipagetrue
+ \global\everypar{\global\@minipagefalse\global\everypar{}}
+ \vskip22.47pt
+}
+%
+\if@mathematic
+   \def\vec#1{\ensuremath{\mathchoice
+                     {\mbox{\boldmath$\displaystyle\mathbf{#1}$}}
+                     {\mbox{\boldmath$\textstyle\mathbf{#1}$}}
+                     {\mbox{\boldmath$\scriptstyle\mathbf{#1}$}}
+                     {\mbox{\boldmath$\scriptscriptstyle\mathbf{#1}$}}}}
+\else
+   \def\vec#1{\ensuremath{\mathchoice
+                     {\mbox{\boldmath$\displaystyle#1$}}
+                     {\mbox{\boldmath$\textstyle#1$}}
+                     {\mbox{\boldmath$\scriptstyle#1$}}
+                     {\mbox{\boldmath$\scriptscriptstyle#1$}}}}
+\fi
+%
+\def\tens#1{\ensuremath{\mathsf{#1}}}
+%
+\setcounter{secnumdepth}{3}
+\newcounter {section}
+\newcounter {subsection}[section]
+\newcounter {subsubsection}[subsection]
+\newcounter {paragraph}[subsubsection]
+\newcounter {subparagraph}[paragraph]
+\renewcommand\thesection      {\@arabic\c@section}
+\renewcommand\thesubsection   {\thesection.\@arabic\c@subsection}
+\renewcommand\thesubsubsection{\thesubsection.\@arabic\c@subsubsection}
+\renewcommand\theparagraph    {\thesubsubsection.\@arabic\c@paragraph}
+\renewcommand\thesubparagraph {\theparagraph.\@arabic\c@subparagraph}
+%
+\def\@hangfrom#1{\setbox\@tempboxa\hbox{#1}%
+      \hangindent \z@\noindent\box\@tempboxa}
+
+\def\@seccntformat#1{\csname the#1\endcsname\sectcounterend
+\hskip\betweenumberspace}
+
+\def\@sect#1#2#3#4#5#6[#7]#8{%
+  \ifnum #2>\c@secnumdepth
+    \let\@svsec\@empty
+  \else
+    \refstepcounter{#1}%
+    \protected@edef\@svsec{\@seccntformat{#1}\relax}%
+  \fi
+  \@tempskipa #5\relax
+  \ifdim \@tempskipa>\z@
+    \begingroup
+      #6{%
+        \@hangfrom{\hskip #3\relax\@svsec}%
+          \raggedright
+          \hyphenpenalty \@M%
+          \interlinepenalty \@M #8\@@par}%
+    \endgroup
+    \csname #1mark\endcsname{#7}%
+    \addcontentsline{toc}{#1}{%
+      \ifnum #2>\c@secnumdepth \else
+        \protect\numberline{\csname the#1\endcsname\sectcounterend}%
+      \fi
+      #7}%
+  \else
+    \def\@svsechd{%
+      #6{\hskip #3\relax
+      \@svsec #8\hskip\aftertext}%
+      \csname #1mark\endcsname{#7}%
+      \addcontentsline{toc}{#1}{%
+        \ifnum #2>\c@secnumdepth \else
+          \protect\numberline{\csname the#1\endcsname}%
+        \fi
+        #7}}%
+  \fi
+  \@xsect{#5}}
+
+%
+% measures and setting of sections
+%
+\def\section{\@startsection{section}{1}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\normalsize\bfseries\boldmath}}
+\def\subsection{\@startsection{subsection}{2}{\z@}%
+    {-21dd plus-4pt minus-4pt}{10.5dd plus 4pt
+     minus4pt}{\normalsize\itshape}}
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}%
+    {-13dd plus-4pt minus-4pt}{-5.5pt}{\normalsize\itshape}}
+\def\paragraph{\@startsection{paragraph}{4}{\z@}%
+    {-13pt plus-4pt minus-4pt}{-5.5pt}{\normalsize\itshape}}
+
+\setlength\leftmargini  {\parindent}
+\leftmargin  \leftmargini
+\setlength\leftmarginii {\parindent}
+\setlength\leftmarginiii {1.87em}
+\setlength\leftmarginiv  {1.7em}
+\setlength\leftmarginv  {.5em}
+\setlength\leftmarginvi {.5em}
+\setlength  \labelsep  {.5em}
+\setlength  \labelwidth{\leftmargini}
+\addtolength\labelwidth{-\labelsep}
+\@beginparpenalty -\@lowpenalty
+\@endparpenalty   -\@lowpenalty
+\@itempenalty     -\@lowpenalty
+\renewcommand\theenumi{\@arabic\c@enumi}
+\renewcommand\theenumii{\@alph\c@enumii}
+\renewcommand\theenumiii{\@roman\c@enumiii}
+\renewcommand\theenumiv{\@Alph\c@enumiv}
+\newcommand\labelenumi{\theenumi.}
+\newcommand\labelenumii{(\theenumii)}
+\newcommand\labelenumiii{\theenumiii.}
+\newcommand\labelenumiv{\theenumiv.}
+\renewcommand\p@enumii{\theenumi}
+\renewcommand\p@enumiii{\theenumi(\theenumii)}
+\renewcommand\p@enumiv{\p@enumiii\theenumiii}
+\newcommand\labelitemi{\normalfont\bfseries --}
+\newcommand\labelitemii{\normalfont\bfseries --}
+\newcommand\labelitemiii{$\m@th\bullet$}
+\newcommand\labelitemiv{$\m@th\cdot$}
+
+\if@spthms
+% definition of the "\spnewtheorem" command.
+%
+% Usage:
+%
+%     \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font}
+% or  \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font}
+% or  \spnewtheorem*{env_nam}{caption}{cap_font}{body_font}
+%
+% New is "cap_font" and "body_font". It stands for
+% fontdefinition of the caption and the text itself.
+%
+% "\spnewtheorem*" gives a theorem without number.
+%
+% A defined spnewthoerem environment is used as described
+% by Lamport.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\def\@thmcountersep{}
+\def\@thmcounterend{}
+\newdimen\spthmsep \spthmsep=3pt
+
+\def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}}
+
+% definition of \spnewtheorem with number
+
+\def\@spnthm#1#2{%
+  \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}}
+\def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}}
+
+\def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname
+   {\@definecounter{#1}\@addtoreset{#1}{#3}%
+   \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
+     \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}%
+   \expandafter\xdef\csname #1name\endcsname{#2}%
+   \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}%
+                              \global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
+   {\@definecounter{#1}%
+   \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
+   \expandafter\xdef\csname #1name\endcsname{#2}%
+   \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}%
+                               \global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@spothm#1[#2]#3#4#5{%
+  \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}%
+  {\expandafter\@ifdefinable\csname #1\endcsname
+  {\global\@namedef{the#1}{\@nameuse{the#2}}%
+  \expandafter\xdef\csname #1name\endcsname{#3}%
+  \global\@namedef{#1}{\@spthm{#2}{\csname #1name\endcsname}{#4}{#5}}%
+  \global\@namedef{end#1}{\@endtheorem}}}}
+
+\def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@
+\labelsep=\spthmsep\refstepcounter{#1}%
+\@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}}
+
+\def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}%
+                    \ignorespaces}
+
+\def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname
+       the#1\endcsname}{#5}{#3}{#4}\ignorespaces}
+
+\def\normalthmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist
+                 \item[\hskip\labelsep{##3##1\ ##2\@thmcounterend}]##4}
+\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
+      \item[\hskip\labelsep{##4##1\ ##2}]{##4(##3)\@thmcounterend\ }##5}}
+\normalthmheadings
+
+\def\reversethmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist
+                 \item[\hskip\labelsep{##3##2\ ##1\@thmcounterend}]##4}
+\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
+      \item[\hskip\labelsep{##4##2\ ##1}]{##4(##3)\@thmcounterend\ }##5}}
+
+% definition of \spnewtheorem* without number
+
+\def\@sthm#1#2{\@Ynthm{#1}{#2}}
+
+\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
+   {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}%
+    \expandafter\xdef\csname #1name\endcsname{#2}%
+    \global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@
+\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}}
+
+\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces}
+
+\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1}
+       {#4}{#2}{#3}\ignorespaces}
+
+\def\@Begintheorem#1#2#3{#3\trivlist
+                           \item[\hskip\labelsep{#2#1\@thmcounterend}]}
+
+\def\@Opargbegintheorem#1#2#3#4{#4\trivlist
+      \item[\hskip\labelsep{#3#1}]{#3(#2)\@thmcounterend\ }}
+
+\if@envcntsect
+   \def\@thmcountersep{.}
+   \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape}
+\else
+   \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape}
+   \if@envcntreset
+      \@addtoreset{theorem}{section}
+   \else
+      \@addtoreset{theorem}{chapter}
+   \fi
+\fi
+
+%definition of divers theorem environments
+\spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily}
+\spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily}
+\if@envcntsame % alle Umgebungen wie Theorem.
+   \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}}
+\else % alle Umgebungen mit eigenem Zaehler
+   \if@envcntsect % mit section numeriert
+      \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[section]{#3}{#4}}
+   \else % nicht mit section numeriert
+      \if@envcntreset
+         \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4}
+                                   \@addtoreset{#1}{section}}
+      \else
+         \let\spn@wtheorem=\@spynthm
+      \fi
+   \fi
+\fi
+\spn@wtheorem{case}{Case}{\itshape}{\rmfamily}
+\spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily}
+\spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape}
+\spn@wtheorem{definition}{Definition}{\bfseries}{\itshape}
+\spn@wtheorem{example}{Example}{\itshape}{\rmfamily}
+\spn@wtheorem{exercise}{Exercise}{\bfseries}{\rmfamily}
+\spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape}
+\spn@wtheorem{note}{Note}{\itshape}{\rmfamily}
+\spn@wtheorem{problem}{Problem}{\bfseries}{\rmfamily}
+\spn@wtheorem{property}{Property}{\itshape}{\rmfamily}
+\spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape}
+\spn@wtheorem{question}{Question}{\itshape}{\rmfamily}
+\spn@wtheorem{solution}{Solution}{\bfseries}{\rmfamily}
+\spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily}
+%
+\newenvironment{theopargself}
+    {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
+         \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5}
+     \def\@Opargbegintheorem##1##2##3##4{##4\trivlist
+         \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }}}{}
+\newenvironment{theopargself*}
+    {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
+         \item[\hskip\labelsep{##4##1\ ##2}]{\hspace*{-\labelsep}##4##3\@thmcounterend}##5}
+     \def\@Opargbegintheorem##1##2##3##4{##4\trivlist
+         \item[\hskip\labelsep{##3##1}]{\hspace*{-\labelsep}##3##2\@thmcounterend}}}{}
+\fi
+
+\def\@takefromreset#1#2{%
+    \def\@tempa{#1}%
+    \let\@tempd\@elt
+    \def\@elt##1{%
+        \def\@tempb{##1}%
+        \ifx\@tempa\@tempb\else
+            \@addtoreset{##1}{#2}%
+        \fi}%
+    \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname
+    \expandafter\def\csname cl@#2\endcsname{}%
+    \@tempc
+    \let\@elt\@tempd}
+
+\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}
+\def\qed{\ifmmode\else\unskip\quad\fi\squareforqed}
+\def\smartqed{\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil
+\penalty50\hskip1em\null\nobreak\hfil\squareforqed
+\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}}
+
+% Define `abstract' environment
+\def\abstract{\topsep=0pt\partopsep=0pt\parsep=0pt\itemsep=0pt\relax
+\trivlist\item[\hskip\labelsep
+{\bfseries\abstractname}]\if!\abstractname!\hskip-\labelsep\fi}
+\if@twocolumn
+   \def\endabstract{\endtrivlist\addvspace{5mm}\strich}
+   \def\strich{\hrule\vskip3ptplus12pt\null}
+\else
+   \def\endabstract{\endtrivlist\addvspace{3mm}}
+\fi
+%
+\newenvironment{verse}
+               {\let\\\@centercr
+                \list{}{\itemsep      \z@
+                        \itemindent   -1.5em%
+                        \listparindent\itemindent
+                        \rightmargin  \leftmargin
+                        \advance\leftmargin 1.5em}%
+                \item\relax}
+               {\endlist}
+\newenvironment{quotation}
+               {\list{}{\listparindent 1.5em%
+                        \itemindent    \listparindent
+                        \rightmargin   \leftmargin
+                        \parsep        \z@ \@plus\p@}%
+                \item\relax}
+               {\endlist}
+\newenvironment{quote}
+               {\list{}{\rightmargin\leftmargin}%
+                \item\relax}
+               {\endlist}
+\newcommand\appendix{\par
+  \setcounter{section}{0}%
+  \setcounter{subsection}{0}%
+  \renewcommand\thesection{\@Alph\c@section}}
+\setlength\arraycolsep{1.5\p@}
+\setlength\tabcolsep{6\p@}
+\setlength\arrayrulewidth{.4\p@}
+\setlength\doublerulesep{2\p@}
+\setlength\tabbingsep{\labelsep}
+\skip\@mpfootins = \skip\footins
+\setlength\fboxsep{3\p@}
+\setlength\fboxrule{.4\p@}
+\renewcommand\theequation{\@arabic\c@equation}
+\newcounter{figure}
+\renewcommand\thefigure{\@arabic\c@figure}
+\def\fps@figure{tbp}
+\def\ftype@figure{1}
+\def\ext@figure{lof}
+\def\fnum@figure{\figurename~\thefigure}
+\newenvironment{figure}
+               {\@float{figure}}
+               {\end@float}
+\newenvironment{figure*}
+               {\@dblfloat{figure}}
+               {\end@dblfloat}
+\newcounter{table}
+\renewcommand\thetable{\@arabic\c@table}
+\def\fps@table{tbp}
+\def\ftype@table{2}
+\def\ext@table{lot}
+\def\fnum@table{\tablename~\thetable}
+\newenvironment{table}
+               {\@float{table}}
+               {\end@float}
+\newenvironment{table*}
+               {\@dblfloat{table}}
+               {\end@dblfloat}
+
+\def \@floatboxreset {%
+        \reset@font
+        \small
+        \@setnobreak
+        \@setminipage
+}
+
+\newlength\abovecaptionskip
+\newlength\belowcaptionskip
+\setlength\abovecaptionskip{10\p@}
+\setlength\belowcaptionskip{0\p@}
+\newcommand\leftlegendglue{}
+
+\def\fig@type{figure}
+
+\newdimen\figcapgap\figcapgap=3pt
+\newdimen\tabcapgap\tabcapgap=5.5pt
+
+\@ifundefined{floatlegendstyle}{\def\floatlegendstyle{\bfseries}}{}
+
+\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname
+  ext@#1\endcsname}{#1}{\protect\numberline{\csname
+  the#1\endcsname}{\ignorespaces #2}}\begingroup
+    \@parboxrestore
+    \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
+  \endgroup}
+
+\def\capstrut{\vrule\@width\z@\@height\topskip}
+
+\@ifundefined{captionstyle}{\def\captionstyle{\normalfont\small}}{}
+
+\long\def\@makecaption#1#2{%
+ \captionstyle
+ \ifx\@captype\fig@type
+   \vskip\figcapgap
+ \fi
+ \setbox\@tempboxa\hbox{{\floatlegendstyle #1\floatcounterend}%
+ \capstrut #2}%
+ \ifdim \wd\@tempboxa >\hsize
+   {\floatlegendstyle #1\floatcounterend}\capstrut #2\par
+ \else
+   \hbox to\hsize{\leftlegendglue\unhbox\@tempboxa\hfil}%
+ \fi
+ \ifx\@captype\fig@type\else
+   \vskip\tabcapgap
+ \fi}
+
+\newdimen\figgap\figgap=1cc
+\long\def\@makesidecaption#1#2{%
+   \parbox[b]{\@tempdima}{\captionstyle{\floatlegendstyle
+                                         #1\floatcounterend}#2}}
+\def\sidecaption#1\caption{%
+\setbox\@tempboxa=\hbox{#1\unskip}%
+\if@twocolumn
+ \ifdim\hsize<\textwidth\else
+   \ifdim\wd\@tempboxa<\columnwidth
+      \typeout{Double column float fits into single column -
+            ^^Jyou'd better switch the environment. }%
+   \fi
+ \fi
+\fi
+\@tempdima=\hsize
+\advance\@tempdima by-\figgap
+\advance\@tempdima by-\wd\@tempboxa
+\ifdim\@tempdima<3cm
+    \typeout{\string\sidecaption: No sufficient room for the legend;
+             using normal \string\caption. }%
+   \unhbox\@tempboxa
+   \let\@capcommand=\@caption
+\else
+   \let\@capcommand=\@sidecaption
+   \leavevmode
+   \unhbox\@tempboxa
+   \hfill
+\fi
+\refstepcounter\@captype
+\@dblarg{\@capcommand\@captype}}
+
+\long\def\@sidecaption#1[#2]#3{\addcontentsline{\csname
+  ext@#1\endcsname}{#1}{\protect\numberline{\csname
+  the#1\endcsname}{\ignorespaces #2}}\begingroup
+    \@parboxrestore
+    \@makesidecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
+  \endgroup}
+
+% Define `acknowledgement' environment
+\def\acknowledgement{\par\addvspace{17pt}\small\rmfamily
+\trivlist\if!\ackname!\item[]\else
+\item[\hskip\labelsep
+{\it\ackname}]\fi}
+\def\endacknowledgement{\endtrivlist\addvspace{6pt}}
+% Define `noteadd' environment
+\def\noteadd{\par\addvspace{17pt}\small\rmfamily
+\trivlist\item[\hskip\labelsep
+{\itshape\noteaddname}]}
+\def\endnoteadd{\endtrivlist\addvspace{6pt}}
+
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
+\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
+\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}
+\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}
+\newcommand\@pnumwidth{1.55em}
+\newcommand\@tocrmarg{2.55em}
+\newcommand\@dotsep{4.5}
+\setcounter{tocdepth}{1}
+\newcommand\tableofcontents{%
+    \section*{\contentsname}%
+    \@starttoc{toc}%
+    \addtocontents{toc}{\begingroup\protect\small}%
+    \AtEndDocument{\addtocontents{toc}{\endgroup}}%
+    }
+\newcommand*\l@part[2]{%
+  \ifnum \c@tocdepth >-2\relax
+    \addpenalty\@secpenalty
+    \addvspace{2.25em \@plus\p@}%
+    \begingroup
+      \setlength\@tempdima{3em}%
+      \parindent \z@ \rightskip \@pnumwidth
+      \parfillskip -\@pnumwidth
+      {\leavevmode
+       \large \bfseries #1\hfil \hb@xt@\@pnumwidth{\hss #2}}\par
+       \nobreak
+       \if@compatibility
+         \global\@nobreaktrue
+         \everypar{\global\@nobreakfalse\everypar{}}%
+      \fi
+    \endgroup
+  \fi}
+\newcommand*\l@section{\@dottedtocline{1}{0pt}{1.5em}}
+\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
+\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
+\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
+\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
+\newcommand\listoffigures{%
+    \section*{\listfigurename
+      \@mkboth{\listfigurename}%
+              {\listfigurename}}%
+    \@starttoc{lof}%
+    }
+\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
+\newcommand\listoftables{%
+    \section*{\listtablename
+      \@mkboth{\listtablename}{\listtablename}}%
+    \@starttoc{lot}%
+    }
+\let\l@table\l@figure
+\newdimen\bibindent
+\setlength\bibindent{\parindent}
+\def\@biblabel#1{#1.}
+\def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw
+      {\let\protect\noexpand
+       \immediate
+       \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces}
+\newenvironment{thebibliography}[1]
+     {\section*{\refname
+        \@mkboth{\refname}{\refname}}\small
+      \list{\@biblabel{\@arabic\c@enumiv}}%
+           {\settowidth\labelwidth{\@biblabel{#1}}%
+            \leftmargin\labelwidth
+            \advance\leftmargin\labelsep
+            \@openbib@code
+            \usecounter{enumiv}%
+            \let\p@enumiv\@empty
+            \renewcommand\theenumiv{\@arabic\c@enumiv}}%
+      \sloppy\clubpenalty4000\widowpenalty4000%
+      \sfcode`\.\@m}
+     {\def\@noitemerr
+       {\@latex@warning{Empty `thebibliography' environment}}%
+      \endlist}
+%
+\newcount\@tempcntc
+\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
+  \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do
+    {\@ifundefined
+       {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries
+        ?}\@warning
+       {Citation `\@citeb' on page \thepage \space undefined}}%
+    {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}%
+     \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne
+       \@citea\def\@citea{,\hskip0.1em\ignorespaces}\hbox{\csname b@\@citeb\endcsname}%
+     \else
+      \advance\@tempcntb\@ne
+      \ifnum\@tempcntb=\@tempcntc
+      \else\advance\@tempcntb\m@ne\@citeo
+      \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}}
+\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else
+            \@citea\def\@citea{,\hskip0.1em\ignorespaces}%
+  \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else
+   {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else \def\@citea{--}\fi
+    \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi}
+%
+\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em}
+\let\@openbib@code\@empty
+\newenvironment{theindex}
+               {\if@twocolumn
+                  \@restonecolfalse
+                \else
+                  \@restonecoltrue
+                \fi
+                \columnseprule \z@
+                \columnsep 35\p@
+                \twocolumn[\section*{\indexname}]%
+                \@mkboth{\indexname}{\indexname}%
+                \thispagestyle{plain}\parindent\z@
+                \parskip\z@ \@plus .3\p@\relax
+                \let\item\@idxitem}
+               {\if@restonecol\onecolumn\else\clearpage\fi}
+\newcommand\@idxitem{\par\hangindent 40\p@}
+\newcommand\subitem{\@idxitem \hspace*{20\p@}}
+\newcommand\subsubitem{\@idxitem \hspace*{30\p@}}
+\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax}
+\renewcommand\footnoterule{%
+  \kern-3\p@
+  \hrule\@width.4\columnwidth
+  \kern2.6\p@}
+\newcommand\@makefntext[1]{%
+    \noindent
+    \hb@xt@\bibindent{\hss\@makefnmark\enspace}#1}
+%
+\newcommand\contentsname{Contents}
+\newcommand\listfigurename{List of Figures}
+\newcommand\listtablename{List of Tables}
+\newcommand\refname{References}
+\newcommand\indexname{Index}
+\newcommand\figurename{Fig.}
+\newcommand\tablename{Table}
+\newcommand\partname{Part}
+\newcommand\appendixname{Appendix}
+\newcommand\abstractname{Abstract\runinend}
+\newcommand\ackname{Acknowledgements\runinend}
+\newcommand\noteaddname{Note added in proof}
+% French section
+\def\ds@francais{%
+ \typeout{On parle francais.}%
+ \def\abstractname{R\'esum\'e\runinend}%
+ \def\ackname{Remerciements\runinend}%
+ \def\andname{et}%
+ \def\lastandname{ et}%
+ \def\appendixname{Appendice}
+ \def\chaptername{Chapitre}%
+ \def\claimname{Pr\'etention}%
+ \def\conjecturename{Hypoth\`ese}%
+ \def\contentsname{Table des mati\`eres}%
+ \def\corollaryname{Corollaire}%
+ \def\definitionname{D\'efinition}%
+ \def\examplename{Exemple}%
+ \def\exercisename{Exercice}%
+ \def\figurename{Fig.}%
+ \def\keywordname{{\bfseries Mots-cl\'e\runinend}}
+ \def\indexname{Index}
+ \def\lemmaname{Lemme}%
+ \def\contriblistname{Liste des contributeurs}
+ \def\listfigurename{Liste des figures}%
+ \def\listtablename{Liste des tables}%
+ \def\mailname{{\itshape Correspondence to\/}:}
+ \def\noteaddname{Note ajout\'ee \`a l'\'epreuve}%
+ \def\notename{Remarque}%
+ \def\partname{Partie}%
+ \def\problemname{Probl\`eme}%
+ \def\proofname{Preuve}%
+ \def\propertyname{Caract\'eristique}%
+%\def\propositionname{Proposition}%
+ \def\questionname{Question}%
+ \def\refname{Bibliographie}%
+ \def\remarkname{Remarque}%
+ \def\seename{voyez}
+ \def\solutionname{Solution}%
+%\def\subclassname{{\it Subject Classifications\/}:}
+ \def\tablename{Tableau}%
+ \def\theoremname{Th\'eor\`eme}%
+}
+%
+% German section
+\def\ds@deutsch{\typeout{Man spricht deutsch.}%
+ \def\abstractname{Zusammenfassung\runinend}%
+ \def\ackname{Danksagung\runinend}%
+ \def\andname{und}%
+ \def\lastandname{ und}%
+ \def\appendixname{Anhang}%
+ \def\chaptername{Kapitel}%
+ \def\claimname{Behauptung}%
+ \def\conjecturename{Hypothese}%
+ \def\contentsname{Inhaltsverzeichnis}%
+ \def\corollaryname{Korollar}%
+%\def\definitionname{Definition}%
+ \def\examplename{Beispiel}%
+ \def\exercisename{\"Ubung}%
+ \def\figurename{Abb.}%
+ \def\keywordname{{\bfseries Schl\"usselw\"orter\runinend}}
+ \def\indexname{Index}
+%\def\lemmaname{Lemma}%
+ \def\contriblistname{Mitarbeiter}
+ \def\listfigurename{Abbildungsverzeichnis}%
+ \def\listtablename{Tabellenverzeichnis}%
+ \def\mailname{{\itshape Correspondence to\/}:}
+ \def\noteaddname{Nachtrag}%
+ \def\notename{Anmerkung}%
+ \def\partname{Teil}%
+%\def\problemname{Problem}%
+ \def\proofname{Beweis}%
+ \def\propertyname{Eigenschaft}%
+%\def\propositionname{Proposition}%
+ \def\questionname{Frage}%
+ \def\refname{Literatur}%
+ \def\remarkname{Anmerkung}%
+ \def\seename{siehe}
+ \def\solutionname{L\"osung}%
+%\def\subclassname{{\it Subject Classifications\/}:}
+ \def\tablename{Tabelle}%
+%\def\theoremname{Theorem}%
+}
+\AtBeginDocument{\switch@texts}
+\newcommand\today{}
+\edef\today{\ifcase\month\or
+  January\or February\or March\or April\or May\or June\or
+  July\or August\or September\or October\or November\or December\fi
+  \space\number\day, \number\year}
+\setlength\columnsep{1.5cc}
+\setlength\columnseprule{0\p@}
+%
+\frenchspacing
+\clubpenalty=10000
+\widowpenalty=10000
+\def\thisbottomragged{\def\@textbottom{\vskip\z@ plus.0001fil
+\global\let\@textbottom\relax}}
+\pagestyle{headings}
+\pagenumbering{arabic}
+\if@twocolumn
+   \twocolumn
+\fi
+\if@referee
+   \makereferee
+\fi
+\flushbottom
+\endinput
+%%
+%% End of file `svjour.cls'.
