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| 53 | {\end{list}} |
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| 62 | \newcommand{\globallabel}[1]{\refstepcounter{equation}\label{#1}} |
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| 64 | \makeatletter |
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| 65 | \renewcommand{\section}{\@startsection{section}{1}{0em}{-\baselineskip}% |
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| 66 | {\baselineskip}{\normalfont\large\bfseries}} |
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| 67 | \renewcommand{\subsection}% |
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| 68 | {\@startsection{subsection}{2}{0em}{-0.7\baselineskip}% |
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| 69 | {0.7\baselineskip}{\normalfont\bfseries}} |
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| 70 | \makeatother |
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| 71 | |
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| 72 | |
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| 73 | %%%%%%%%%%%%%%%%%%%%%%%% |
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| 74 | % definitions |
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| 75 | %%%%%%%%%%%%%%%%%%%%%%%% |
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| 76 | \newcommand{\centre}[2]{\multispan{#1}{\hfill #2\hfill}} |
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| 77 | \newcommand{\etal}{\textit{et al.}} |
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| 78 | \newcommand{\stheta}{\ensuremath{\sin^22\theta_{13}}} |
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| 79 | \newcommand{\BB}{$\beta$B} |
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| 80 | \newcommand{\sigdm}{\ensuremath{{\rm sign}(\Delta m^2_{31})}} |
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| 81 | \newcommand{\delCP}{\ensuremath{\delta_{\rm CP}}} |
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| 82 | \newcommand{\thetatt}{\ensuremath{\theta_{23}}} |
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| 83 | |
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| 84 | \def\nubar{$\overline{\nu}\ $} |
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| 85 | \def\nue{\ensuremath{\nu_{e}}} |
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| 86 | \def\nubare{\ensuremath{\overline{\nu}_{e}}} |
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| 87 | \def\nubarecc{$\overline{\nu}_{e}^{CC}\ $} |
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| 88 | \def\numu{\ensuremath{\nu_{\mu}\ }} |
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| 89 | \def\nubarmu{\ensuremath{\overline{\nu}_{\mu}}} |
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| 90 | \def\nubarmucc{$\overline{\nu}_{\mu}^{CC}\ $} |
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| 91 | \def\nutau{\ensuremath{\nu_{\tau}\ }} |
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| 92 | \def\nubartau{\ensuremath{\overline{\nu}_{\tau}}} |
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| 93 | \newcommand{\nuenumu}{\ensuremath{\nue \rightarrow \numu\,}} |
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| 94 | \newcommand{\numunutau}{\ensuremath{\numu \rightarrow \nutau\,}} |
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| 95 | \newcommand{\nuenutau}{\ensuremath{\nue \rightarrow \nutau}} |
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| 96 | \newcommand{\nubarenubarmu}{\ensuremath{\overline{\nu}_e \rightarrow \overline{\nu}_\mu\,}} |
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| 97 | \newcommand{\nubarmunubare}{\ensuremath{\overline{\nu}_\mu \rightarrow \overline{\nu}_e\,}} |
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| 98 | \newcommand{\dmot}{\ensuremath{\Delta m^2_{12}\,}} |
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| 99 | |
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| 100 | \newcommand{\He}{\ensuremath{^6{\mathrm{He}}}} |
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| 101 | \newcommand{\Ne}{\ensuremath{^{18}{\mathrm{Ne}}}} |
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| 102 | \def\Li{^6{\mathrm{Li}}} |
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| 103 | \def\anue{\overline{{\mathrm\nu}}_{\mathrm e}} |
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| 104 | \def\anumu{\overline{{\mathrm\nu}}_{\mathrm \mu}} |
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| 105 | \newcommand{\thetaot}{\ensuremath{\theta_{13}}\,} |
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| 106 | \newcommand{\numunue}{\ensuremath{\nu_\mu \rightarrow \nu_e}} |
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| 107 | \newcommand{\nueovernumu}{\ensuremath{\nue/\numu}} |
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| 108 | |
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| 109 | |
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| 110 | |
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| 111 | \begin{document} |
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| 112 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 113 | %%%% Title-page %%%% |
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| 114 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 115 | |
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| 116 | %\begin{titlepage} |
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| 117 | |
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| 118 | % the footnote symbols are only redefined for the title page ! |
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| 119 | \renewcommand{\thefootnote}{\alph{footnote}} |
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| 120 | |
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| 121 | \begin{flushright} |
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| 122 | LAL-06-35\\ |
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| 123 | IC/2006/011\\ |
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| 124 | SISSA 16/2006/EP\\ |
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| 125 | \end{flushright} |
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| 126 | |
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| 127 | \vspace*{1cm} |
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| 128 | |
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| 129 | \renewcommand{\thefootnote}{\fnsymbol{footnote}} |
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| 130 | \setcounter{footnote}{-1} |
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| 131 | |
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| 132 | {\begin{center} |
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| 133 | {\Large\textbf{ |
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| 134 | Physics potential of the CERN--MEMPHYS\\[2mm] |
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| 135 | neutrino oscillation project} |
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| 136 | } |
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| 137 | \end{center}} |
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| 138 | |
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| 139 | \vspace*{.8cm} |
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| 140 | |
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| 141 | \begin{center} {\bf |
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| 142 | J.-E.\ Campagne$^a$, |
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| 143 | M.\ Maltoni$^b$, |
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| 144 | M.\ Mezzetto$^c$, and |
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| 145 | T.\ Schwetz$^d$} |
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| 146 | \end{center} |
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| 147 | |
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| 148 | {\it |
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| 149 | \begin{center} |
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| 150 | $^a$Laboratoire de l'Acc\'el\'erateur Lin\'eaire, |
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| 151 | IN2P3-CNRS and Universit\'e PARIS-SUD 11\\ |
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| 152 | Centre Scientifique d'Orsay-B\^at.\ 200-B.P.\ 34, |
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| 153 | 91898 Orsay Cedex, France\\[2mm] |
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| 154 | % |
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| 155 | $^b$International Centre for Theoretical Physics, |
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| 156 | Strada Costiera 11, 31014 Trieste, Italy\\[2mm] |
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| 157 | % |
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| 158 | $^c$Istituto Nazionale Fisica Nucleare, Sezione di Padova, |
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| 159 | Via Marzolo 8, 35100 Padova, Italy\\[2mm] |
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| 160 | % |
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| 161 | $^d$Scuola Internazionale Superiore di Studi Avanzati, |
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| 162 | Via Beirut 2--4, 34014 Trieste, Italy |
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| 163 | \end{center}} |
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| 164 | |
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| 165 | \vspace*{0.5cm} |
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| 166 | |
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| 167 | |
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| 168 | \begin{abstract} |
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| 169 | We consider the physics potential of CERN based neutrino oscillation |
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| 170 | experiments consisting of a Beta Beam (\BB) and a Super Beam (SPL) |
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| 171 | sending neutrinos to MEMPHYS, a 440~kt water \v{C}erenkov detector at |
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| 172 | Fr\'ejus, at a distance of 130~km from CERN. The $\theta_{13}$ |
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| 173 | discovery reach and the sensitivity to CP violation are investigated, |
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| 174 | including a detailed discussion of parameter degeneracies and |
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| 175 | systematical errors. For SPL sensitivities similar to the ones of the |
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| 176 | phase~II of the T2K experiment (T2HK) are obtained, whereas the \BB\ |
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| 177 | may reach significantly better sensitivities, depending on the |
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| 178 | achieved number of total ion decays. The results for the |
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| 179 | CERN--MEMPHYS experiments are less affected by systematical |
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| 180 | uncertainties than T2HK. |
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| 181 | % |
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| 182 | We point out that by a combination of data from \BB\ and SPL a |
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| 183 | measurement with antineutrinos is not necessary and hence the same |
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| 184 | physics results can be obtained within about half of the measurement time |
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| 185 | compared to one single experiment. |
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| 186 | % |
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| 187 | Furthermore, it is shown how including data from atmospheric neutrinos in |
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| 188 | the MEMPHYS detector allows to resolve parameter degeneracies and, in |
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| 189 | particular, provides sensitivity to the neutrino mass hierarchy and |
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| 190 | the octant of $\theta_{23}$. |
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| 191 | %\pacs{14.60.Pq, 14.60.Lm} |
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| 192 | \end{abstract} |
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| 193 | |
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| 194 | \renewcommand{\thefootnote}{\arabic{footnote}} |
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| 195 | \setcounter{footnote}{0} |
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| 196 | |
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| 197 | \newpage |
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| 198 | %\tableofcontents |
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| 199 | |
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| 200 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 201 | \section{Introduction} |
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| 202 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 203 | |
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| 204 | In recent years strong evidence for neutrino oscillations has been |
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| 205 | obtained in solar~\cite{solar}, atmospheric~\cite{sk-atm}, |
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| 206 | reactor~\cite{Araki:2004mb}, and accelerator~\cite{Aliu:2004sq} |
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| 207 | neutrino experiments. The very near future of long-baseline (LBL) |
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| 208 | neutrino experiments is devoted to the study of the oscillation |
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| 209 | mechanism in the range of $\Delta m^2_{31} \approx 2.4\times10^{-3} \: |
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| 210 | \mathrm{eV}^2$ indicated by atmospheric neutrinos using conventional |
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| 211 | $\nu_\mu$ beams. Similar as in the K2K experiment in |
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| 212 | Japan~\cite{Aliu:2004sq}, the presently running MINOS experiment in |
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| 213 | the USA~\cite{MINOS} uses a low energy beam to measure $\Delta m^2_{31}$ by |
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| 214 | observing the $\nu_\mu\rightarrow\nu_\mu$ disappearance probability, |
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| 215 | while the forthcoming OPERA~\cite{OPERA} experiment will be able to |
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| 216 | detect $\nu_\tau$ appearance within the high energy CERN--Gran Sasso |
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| 217 | beam~\cite{CNGS}. |
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| 218 | % |
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| 219 | If we do not consider the LSND anomaly~\cite{LSND} that will be |
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| 220 | further studied soon by the MiniBooNE experiment~\cite{MINIBOONE}, all |
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| 221 | data can be accommodated within the three flavor scenario (see |
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| 222 | Refs.~\cite{FOGLILISI05,Maltoni:2004ei} for recent global analyses), |
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| 223 | and neutrino oscillations are described by two neutrino mass-squared |
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| 224 | differences ($\Delta m^2_{21}$ and $\Delta m^2_{31}$) and the $3\times |
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| 225 | 3$ unitary Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton mixing |
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| 226 | matrix~\cite{PMNS} with three angles |
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| 227 | ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase |
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| 228 | $\delCP$. |
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| 229 | |
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| 230 | Future tasks of neutrino physics are an improved sensitivity to the |
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| 231 | last unknown mixing angle, $\theta_{13}$, to explore the CP violation |
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| 232 | mechanism in the leptonic sector, and to determine the sign of $\Delta |
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| 233 | m^2_{31}$ which describes the type of the neutrino mass hierarchy |
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| 234 | (normal, $\Delta m^2_{31} > 0$ or inverted, $\Delta m^2_{31} < 0$). |
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| 235 | % |
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| 236 | The present upper bound on $\theta_{13}$ is dominated by the |
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| 237 | constraint from the Chooz reactor experiment~\cite{CHOOZ}. A global |
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| 238 | analysis of all data yields $\sin^22\theta_{13}<0.082$ at |
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| 239 | 90\%~CL~\cite{Maltoni:2004ei}. A main purpose of upcoming reactor and |
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| 240 | accelerator experiments is to improve this bound or to reveal a finite |
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| 241 | value of $\theta_{13}$. In reactor experiments, one uses $\bar{\nu}_e$ |
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| 242 | in disappearance mode and the sensitivity is increased with respect to |
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| 243 | present experiments by the use of a near detector close to the |
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| 244 | reactor~\cite{Wpaper}. In accelerator experiments, the first |
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| 245 | generation of so-called Super Beams with sub-mega watt proton drivers |
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| 246 | such as T2K (phase-I)~\cite{T2K} and NO$\nu$A~\cite{Ayres:2004js}, the |
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| 247 | appearance channel $\nu_\mu\to\nu_e$ is explored. This next generation |
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| 248 | of reactor and Super Beam experiments will reach sensitivities of the |
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| 249 | order of $\sin^22\theta_{13} \lesssim 0.01$ ($90\%$~CL) within a time |
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| 250 | scale of several years~\cite{Huber:2003pm}. |
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| 251 | % |
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| 252 | Beyond this medium term program, there are several projects on how to |
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| 253 | enter the high precision age in neutrino oscillations and to attack |
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| 254 | the ultimate goals like the discovery of leptonic CP violation or the |
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| 255 | determination of the neutrino mass hierarchy. In accelerator |
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| 256 | experiments, one can extend the Super Beam concept by moving to |
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| 257 | multi-mega watt proton drivers~\cite{T2K,Albrow:2005kw,SPL,BNLHS} or |
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| 258 | apply novel technologies, such as neutrino beams from decaying ions |
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| 259 | (so-called Beta Beams)~\cite{zucchelli,Albright:2004iw} or from |
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| 260 | decaying muons (so-called Neutrino |
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| 261 | Factories)~\cite{Albright:2004iw,Blondel:2004ae}. |
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| 262 | |
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| 263 | In this work we focus on possible future neutrino oscillation |
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| 264 | facilities hosted at CERN, namely a multi-mega watt Super Beam |
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| 265 | experiment based on a Super Proton Linac (SPL)~\cite{Campagne:2004wt} |
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| 266 | and a $\gamma = 100$ Beta Beam |
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| 267 | (\BB)~\cite{Mezzetto:2003ub}. These experiments will search for |
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| 268 | $\stackrel{\scriptscriptstyle (-)}{\nu}_\mu \to |
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| 269 | \stackrel{\scriptscriptstyle(-)}{\nu}_e$ and |
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| 270 | $\stackrel{\scriptscriptstyle (-)}{\nu}_e \to |
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| 271 | \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$ appearance, respectively, |
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| 272 | by sending the neutrinos to a mega ton scale water \v{C}erenkov |
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| 273 | detector (MEMPHYS)~\cite{memphys}, located at a distance of 130~km from |
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| 274 | CERN under the Fr\'ejus mountain. Similar detectors are under |
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| 275 | consideration also in the US (UNO~\cite{UNO}) and in Japan |
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| 276 | (Hyper-K~\cite{T2K,Nakamura:2003hk}). |
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| 277 | % |
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| 278 | We perform a detailed analysis of the SPL and \BB\ physics |
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| 279 | potential, discussing the discovery reach for $\theta_{13}$ and |
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| 280 | leptonic CP violation. In addition we consider the possibility to |
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| 281 | resolve parameter degeneracies in the LBL data by using the |
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| 282 | atmospheric neutrinos available in the mega ton |
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| 283 | detector~\cite{Huber:2005ep}. This leads to a sensitivity to the |
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| 284 | neutrino mass hierarchy of the CERN--MEMPHYS experiments, despite the |
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| 285 | rather short baseline. |
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| 286 | % |
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| 287 | The physics performances of \BB\ and SPL are compared to the ones |
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| 288 | obtainable at the second phase of the T2K experiment in Japan, which |
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| 289 | is based on an upgraded version of the original T2K beam and the |
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| 290 | Hyper-K detector (T2HK)~\cite{T2K}. |
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| 291 | |
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| 292 | The outline of the paper is as follows. In Sec.~\ref{sec:analysis} we |
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| 293 | summarize the main characteristics of the \BB, SPL, and T2HK |
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| 294 | experiments and give general details of the physics analysis methods, |
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| 295 | whereas in Sec.~\ref{sec:experiments} we describe in some detail the |
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| 296 | MEMPHYS detector, the \BB, and the SPL Super Beam. In |
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| 297 | Sec.~\ref{sec:degeneracies} we review the problem of parameter |
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| 298 | degeneracies and discuss its implications for the experiments under |
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| 299 | consideration. In Sec.~\ref{sec:sensitivities} we present the |
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| 300 | sensitivities to the ``atmospheric parameters'' $\theta_{23}$ and |
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| 301 | $\Delta m^2_{31}$, the $\theta_{13}$ discovery potential, and the |
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| 302 | sensitivity to CP violation. We also investigate in some detail the |
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| 303 | impact of systematical errors. In Sec.~\ref{sec:synergies} we discuss |
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| 304 | synergies which are offered by the CERN--MEMPHYS facilities. We |
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| 305 | point out advantages of the case when \BB\ and SPL are available |
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| 306 | simultaneously, and we consider the use of atmospheric neutrino data in |
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| 307 | MEMPHYS in combination with the LBL experiments. Our results are |
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| 308 | summarized in Sec.~\ref{sec:conclusions}. |
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| 309 | |
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| 310 | |
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| 311 | |
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| 312 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 313 | \section{Experiments overview and analysis methods} |
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| 314 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 315 | \label{sec:analysis} |
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| 316 | |
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| 317 | In this section we give the most important experimental parameters |
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| 318 | which we adopt for the simulation of the CERN--MEMPHYS experiments |
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| 319 | \BB\ and SPL, as well as for the T2HK experiment in Japan. These |
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| 320 | parameters are summarized in Tab.~\ref{tab:setups}. For all |
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| 321 | experiments the detector mass is 440~kt, and the running time is 10 |
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| 322 | years, with a division in neutrino and antineutrino running time in |
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| 323 | such a way that roughly an equal number of events is obtained. We |
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| 324 | always use the total available information from appearance as well as |
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| 325 | disappearance channels including the energy spectrum. For all three |
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| 326 | experiments we adopt rather optimistic values for the systematical |
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| 327 | uncertainties of 2\% as default values, but we also consider the case |
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| 328 | when systematics are increased to 5\%. These errors are uncorrelated |
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| 329 | between the various signal channels (neutrinos and antineutrinos), and |
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| 330 | between signals and backgrounds. |
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| 331 | |
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| 332 | \begin{table} |
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| 333 | \centering |
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| 334 | \begin{tabular}{lcc@{\qquad\qquad}c} |
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| 335 | \hline\noalign{\smallskip} |
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| 336 | & \BB & SPL & T2HK \\ |
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| 337 | \noalign{\smallskip}\hline\noalign{\smallskip} |
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| 338 | Detector mass & 440~kt & 440~kt & 440~kt\\ |
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| 339 | Baseline & 130 km & 130 km & 295 km \\ |
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| 340 | Running time ($\nu + \bar\nu$) |
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| 341 | & 5 + 5 yr & 2 + 8 yr & 2 + 8 yr \\ |
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| 342 | Beam intensity & $5.8\,(2.2) \cdot 10^{18}$ He (Ne) dcys/yr & 4 MW & 4 MW\\ |
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| 343 | Systematics on signal & 2\% & 2\% & 2\%\\ |
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| 344 | Systematics on backgr. & 2\% & 2\% & 2\%\\ |
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| 345 | \noalign{\smallskip}\hline |
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| 346 | \end{tabular} |
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| 347 | \mycaption{Summary of default parameters used for the simulation of the |
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| 348 | \BB, SPL, and T2HK experiments.\label{tab:setups}} |
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| 349 | \end{table} |
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| 350 | |
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| 351 | A more detailed description of the CERN--MEMPHYS experiments is given |
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| 352 | in Sec.~\ref{sec:experiments}. For the T2HK simulation we use the |
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| 353 | setup provided by GLoBES~\cite{Globes} based on |
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| 354 | Ref.~\cite{Huber:2002mx}, which follows closely the LOI~\cite{T2K}. In |
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| 355 | order to allow a fair comparison we introduce the following changes |
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| 356 | with respect to the configuration used in Ref.~\cite{Huber:2002mx}: |
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| 357 | The fiducial mass is set to 440~kt, the systematical errors on the |
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| 358 | background and on the $\nu_e$ and $\bar\nu_e$ appearance signals is |
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| 359 | set to 2\%, and we use a total running time of 10 years, divided into |
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| 360 | 2 years of data taking with neutrinos and 8 years with |
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| 361 | antineutrinos. We include an additional background from the |
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| 362 | $\bar\nu_\mu \to \bar\nu_e$ ($\nu_\mu \to \nu_e$) channel in the |
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| 363 | neutrino (antineutrino) mode. Furthermore, we use |
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| 364 | the same CC detection cross section as for the \BB/SPL |
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| 365 | analysis~\cite{Nuance}. For more details see |
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| 366 | Refs.~\cite{T2K,Huber:2002mx}. |
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| 367 | |
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| 368 | \begin{table} |
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| 369 | \centering |
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| 370 | \begin{tabular}{lcccccc} |
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| 371 | \hline\noalign{\smallskip} |
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| 372 | & \centre{2}{\BB} & \centre{2}{SPL} & \centre{2}{T2HK} \\ |
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| 373 | \noalign{\smallskip}\hline\noalign{\smallskip} |
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| 374 | & $\delCP=0$ & $\delCP=\pi/2$ & $\delCP=0$ & $\delCP=\pi/2$ & $\delCP=0$ & $\delCP=\pi/2$\\ |
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| 375 | \noalign{\smallskip}\hline\noalign{\smallskip} |
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| 376 | % |
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| 377 | appearance $\nu$ & & & & & & \\ |
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| 378 | background & \centre{2}{143} &\centre{2}{622} &\centre{2}{898}\\ |
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| 379 | $\stheta=0$ & \centre{2}{28} &\centre{2}{51} &\centre{2}{83} \\ |
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| 380 | $\stheta=10^{-3}$& 76 & 88 & 105 & 14 & 178 & 17 \\ |
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| 381 | $\stheta=10^{-2}$& 326 & 365 & 423 & 137 & 746 & 238 \\ |
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| 382 | % |
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| 383 | \noalign{\smallskip}\hline\noalign{\smallskip} |
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| 384 | % |
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| 385 | appearance $\bar\nu$ & & & & & & \\ |
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| 386 | background & \centre{2}{157} &\centre{2}{640} &\centre{2}{1510}\\ |
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| 387 | $\stheta=0$ & \centre{2}{31} &\centre{2}{57} &\centre{2}{93} \\ |
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| 388 | $\stheta=10^{-3}$& 83 & 12 & 102 & 146 & 192 & 269 \\ |
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| 389 | $\stheta=10^{-2}$& 351 & 126 & 376 & 516 & 762 & 1007 \\ |
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| 390 | % |
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| 391 | \noalign{\smallskip}\hline\noalign{\smallskip} |
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| 392 | % |
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| 393 | disapp. $\nu$ &\centre{2}{100315}&\centre{2}{21653}&\centre{2}{24949}\\ |
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| 394 | background & \centre{2}{6} &\centre{2}{1} &\centre{2}{444}\\ |
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| 395 | disapp. $\bar\nu$&\centre{2}{84125}&\centre{2}{18321}&\centre{2}{34650}\\ |
---|
| 396 | background &\centre{2}{5} &\centre{2}{1} &\centre{2}{725}\\ |
---|
| 397 | \noalign{\smallskip}\hline |
---|
| 398 | % |
---|
| 399 | \end{tabular} |
---|
| 400 | \mycaption{Number of events for appearance and disappearance signals |
---|
| 401 | and backgrounds for the \BB, SPL, and T2HK experiments as |
---|
| 402 | defined in Tab.~\ref{tab:setups}. For the appearance signals the |
---|
| 403 | event numbers are given for several values of $\stheta$ and $\delCP |
---|
| 404 | = 0$ and $\pi/2$. The background as well as the disappearance event |
---|
| 405 | numbers correspond to $\theta_{13}=0$. For the other oscillation |
---|
| 406 | parameters the values of Eq.~(\ref{eq:default-params}) are |
---|
| 407 | used.\label{tab:events}} |
---|
| 408 | \end{table} |
---|
| 409 | |
---|
| 410 | In Tab.~\ref{tab:events} we give the number of signal and background |
---|
| 411 | events for the experiment setups as defined in Tab.~\ref{tab:setups}. |
---|
| 412 | For the appearance channels ($\stackrel{\scriptscriptstyle (-)}{\nu}_e |
---|
| 413 | \to \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$ for the \BB\ and |
---|
| 414 | $\stackrel{\scriptscriptstyle (-)}{\nu}_\mu \to |
---|
| 415 | \stackrel{\scriptscriptstyle(-)}{\nu}_e$ for SPL and T2HK) we give the |
---|
| 416 | signal events for various values of $\theta_{13}$ and $\delCP$. The |
---|
| 417 | ``signal'' events for $\theta_{13} = 0$ are appearance events induced by |
---|
| 418 | the oscillations with $\Delta m^2_{21}$. The value $\stheta = 10^{-3}$ |
---|
| 419 | corresponds roughly to the sensitivity limit for the considered |
---|
| 420 | experiments, whereas $\stheta = 10^{-2}$ gives a good sensitivity |
---|
| 421 | to CP violation. This can be appreciated by comparing the values of |
---|
| 422 | $\nu$ and $\bar\nu$ appearance events for $\delCP = 0$ and $\pi/2$. In |
---|
| 423 | the table the background to the appearance signal is given for |
---|
| 424 | $\theta_{13} = 0$. Note that in general the number of background |
---|
| 425 | events depends also on the oscillation parameters, since also the |
---|
| 426 | background neutrinos in the beam oscillate. This effect is |
---|
| 427 | consistently taken into account in the analysis, however, for the |
---|
| 428 | parameter values in the table the change in the background events due |
---|
| 429 | to oscillations is only of the order of a few events. |
---|
| 430 | |
---|
| 431 | The physics analysis is performed with the GLoBES open source |
---|
| 432 | software~\cite{Globes}, which provides a convenient tool to simulate |
---|
| 433 | long-baseline experiments and compare different facilities in a |
---|
| 434 | unified framework. The experiment definition (AEDL) files for the \BB\ |
---|
| 435 | and SPL simulation with GLoBES are available at Ref.~\cite{ISSpage} |
---|
| 436 | {\bf *** to be updated! ***}. In the analysis parameter degeneracies |
---|
| 437 | and correlations are fully taken into account and in general all |
---|
| 438 | oscillation parameters are varied in the fit. |
---|
| 439 | % |
---|
| 440 | To simulate the ``data'' we adopt the following |
---|
| 441 | set of ``true values'' for the oscillation parameters: |
---|
| 442 | % |
---|
| 443 | \begin{equation}\label{eq:default-params} |
---|
| 444 | \begin{array}{l@{\qquad}l} |
---|
| 445 | \Delta m^2_{31} = +2.4 \times 10^{-3}~\mathrm{eV}^2\,, & |
---|
| 446 | \sin^2\theta_{23} = 0.5\,,\\ |
---|
| 447 | \Delta m^2_{21} = 7.9 \times 10^{-5}~\mathrm{eV}^2 \,,& |
---|
| 448 | \sin^2\theta_{12} = 0.3 \,, |
---|
| 449 | \end{array} |
---|
| 450 | \end{equation} |
---|
| 451 | % |
---|
| 452 | and we include a prior knowledge of these values with an accuracy of |
---|
| 453 | 10\% for $\theta_{12}$, $\theta_{23}$, $\Delta m^2_{31}$, and 4\% for |
---|
| 454 | $\Delta m^2_{21}$ at 1$\sigma$. These values and accuracies are |
---|
| 455 | motivated by recent global fits to neutrino oscillation |
---|
| 456 | data~\cite{FOGLILISI05,Maltoni:2004ei}, and they are always used |
---|
| 457 | except where explicitly stated otherwise. |
---|
| 458 | |
---|
| 459 | |
---|
| 460 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 461 | \section{The CERN--MEMPHYS experiments} |
---|
| 462 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 463 | \label{sec:experiments} |
---|
| 464 | |
---|
| 465 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 466 | \subsection{The MEMPHYS detector} |
---|
| 467 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 468 | |
---|
| 469 | MEMPHYS (MEgaton Mass PHYSics)~\cite{memphys} is a mega ton class |
---|
| 470 | water \v{C}erenkov detector in the straight extrapolation of |
---|
| 471 | Super-Kamiokande, located at Fr\'ejus, at a distance of 130~km from |
---|
| 472 | CERN. It is an alternative design of the UNO~\cite{UNO} and |
---|
| 473 | Hyper-Kamiokande~\cite{Nakamura:2003hk} detectors and shares the same |
---|
| 474 | physics case, both from the non-accelerator domain (nucleon decay, |
---|
| 475 | super nova neutrino detection, solar neutrinos, atmospheric neutrinos) |
---|
| 476 | and from the accelerator domain which is the subject of this paper. A |
---|
| 477 | recent civil engineering pre-study to envisage the possibly of large |
---|
| 478 | cavity excavation located under the Fr\'ejus mountain (4800~m.e.w.) |
---|
| 479 | near the present Modane underground laboratory has been undertaken. |
---|
| 480 | The main result of this pre-study is that MEMPHYS may be built with |
---|
| 481 | present techniques as a modular detector consisting of several shafts, |
---|
| 482 | each with 65~m in diameter, 65~m in height for the total water |
---|
| 483 | containment. A schematic view of the layout is shown in |
---|
| 484 | Fig.~\ref{fig:MEMPHYS}. For the present study we have chosen a |
---|
| 485 | fiducial mass of 440~kt which means 3 shafts and an inner detector of |
---|
| 486 | 57~m in diameter and 57~m in height. Each inner detector may be |
---|
| 487 | equipped with photo detectors (81000 per shaft) with a 30\% |
---|
| 488 | geometrical coverage and the same photo-statistics of Super-Kamiokande |
---|
| 489 | (with a 40\% coverage). In principle up to 5 shafts are possible, |
---|
| 490 | corresponding to a fiducial mass of 730~kt. |
---|
| 491 | % |
---|
| 492 | The Fr\'ejus site offers a natural protection against cosmic rays by a |
---|
| 493 | factor $10^6$. If not mentioned otherwise, the event selection and |
---|
| 494 | particle identification are the Super-Kamiokande algorithms results. |
---|
| 495 | |
---|
| 496 | \begin{figure} |
---|
| 497 | \centering |
---|
| 498 | \includegraphics[width=0.65\textwidth]{./fig1.eps} |
---|
| 499 | \mycaption{\label{fig:MEMPHYS}Sketch of the MEMPHYS detector under the |
---|
| 500 | Fr\'ejus mountain.} |
---|
| 501 | \end{figure} |
---|
| 502 | |
---|
| 503 | |
---|
| 504 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 505 | \subsection{The $\gamma = 100\times100$ baseline Beta Beam} |
---|
| 506 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 507 | |
---|
| 508 | The concept of a Beta Beam (\BB) has been introduced by P.~Zucchelli |
---|
| 509 | in Ref.~\cite{zucchelli}. Neutrinos are produced by the decay of |
---|
| 510 | radioactive isotopes which are stored in a decay ring. An important |
---|
| 511 | parameter is the relativistic gamma factor of the ions, which |
---|
| 512 | determines the energy of the emitted neutrinos. \BB\ performances have |
---|
| 513 | been computed previously for $\gamma(\He)= 66$~\cite{Mezzetto:2003ub}, |
---|
| 514 | 100~\cite{MyNufact04,Donini:2004hu,JJHigh2}, 150~\cite{JJHigh2}, |
---|
| 515 | 200~\cite{LindnerBB}, 350~\cite{JJHigh2}, |
---|
| 516 | 500~\cite{JJHigh1,LindnerBB}, 1000~\cite{LindnerBB}, |
---|
| 517 | 2000~\cite{JJHigh1}, 2488~\cite{Terranova}. Reviews can be found in |
---|
| 518 | Ref.~\cite{BB-Reviews}, the physics potential of a very low gamma \BB\ |
---|
| 519 | has been studied in Ref.~\cite{Volpe}. Performances of a \BB\ with |
---|
| 520 | $\gamma > 150$ are extremely promising, however, they are neither |
---|
| 521 | based on an existing accelerator complex nor on a robust estimation of |
---|
| 522 | the ion decay rates. For a CERN based \BB, fluxes have been estimated |
---|
| 523 | in Ref.~\cite{Lindroos} and a design study is in progress for the |
---|
| 524 | facility \cite{Eurisol}. In this work we assume an integrated flux of |
---|
| 525 | neutrinos in 10 years, corresponding to $5.8\cdot 10^{19}$ useful \He\ |
---|
| 526 | decays and $2.2 \cdot 10^{19}$ useful \Ne\ decays. These fluxes have |
---|
| 527 | been assumed in all the physics papers quoted above, and they are two |
---|
| 528 | times higher than the baseline fluxes computed in |
---|
| 529 | Ref.~\cite{Lindroos}. These latter fluxes suffer for the known |
---|
| 530 | limitations of the PS and SPS synchrotrons at CERN, ways to improve |
---|
| 531 | them have been delineated in Ref.~\cite{Lindroos-Optimization}. |
---|
| 532 | |
---|
| 533 | The infrastructure available at CERN as well as the MEMPHYS |
---|
| 534 | location at a distance of 130~km suggest a $\gamma$-factor of about |
---|
| 535 | $100$. Such a value implies a mean neutrino energy of 400~MeV, which |
---|
| 536 | leads to the oscillation maximum at about 200~km for $\Delta m^2_{31} |
---|
| 537 | = 2.4\times 10^{-3}$~eV$^2$. We have checked that the performance at |
---|
| 538 | the somewhat shorter baseline of 130~km is rather similar to the one |
---|
| 539 | at the oscillation maximum. Moreover, the purpose of this paper is to |
---|
| 540 | estimate the physics potential for a realistic set-up and not to study |
---|
| 541 | the optimization of the \BB\ regardless of any logistic consideration |
---|
| 542 | (see, e.g., Refs.~\cite{LindnerBB,JJHigh2} for such optimization |
---|
| 543 | studies). |
---|
| 544 | |
---|
| 545 | \begin{figure}[!t] |
---|
| 546 | \centering |
---|
| 547 | \includegraphics[width=0.65\textwidth]{./fig2.eps} |
---|
| 548 | \mycaption{\label{fig:QE-Energy} Energy resolution for \nue\ |
---|
| 549 | interactions in the 200--300~MeV energy range. The quantitiy |
---|
| 550 | displayed is the difference between the reconstructed and the true |
---|
| 551 | neutrino energy.} |
---|
| 552 | \end{figure} |
---|
| 553 | |
---|
| 554 | The signal events from the $\nu_e \to \nu_\mu$ neutrino and |
---|
| 555 | antineutrino appearance channels in the \BB\ are \numu charged current |
---|
| 556 | (CC) events. The Nuance v3r503 Monte Carlo code~\cite{Nuance} is used |
---|
| 557 | to generate signal events. The selection for these events is based on |
---|
| 558 | standard Super-Kamiokande particle identification algorithms. The |
---|
| 559 | muon identification is reinforced by asking for the detection of the |
---|
| 560 | Michel decay electron. |
---|
| 561 | % |
---|
| 562 | The neutrino energy is reconstructed by smearing momentum and |
---|
| 563 | direction of the charged lepton with the Super-Kamiokande resolution |
---|
| 564 | functions, and applying quasi-elastic (QE) kinematics assuming the |
---|
| 565 | known incoming neutrino direction. Energy reconstruction in the \BB\ |
---|
| 566 | energy range is remarkably powerful, and the contamination of non-QE |
---|
| 567 | events very small, as shown in Fig.~\ref{fig:QE-Energy}. |
---|
| 568 | % |
---|
| 569 | As pointed out in Ref.~\cite{JJHigh2}, it is necessary to use a |
---|
| 570 | migration matrix for the neutrino energy reconstruction to properly |
---|
| 571 | handle Fermi motion smearing and the non-QE event contamination. We |
---|
| 572 | use 100 MeV bins for the reconstructed energy and 40 MeV bins for the |
---|
| 573 | true neutrino energy. Four migration matrices (for |
---|
| 574 | $\nu_e,\bar\nu_e,\nu_\mu,\bar\nu_\mu$) are applied to signal events as |
---|
| 575 | well as backgrounds. As shown in Ref.~\cite{MezzettoNuFact05} the |
---|
| 576 | migration matrix approximation has a visible (though small) effect for |
---|
| 577 | example in the leptonic CP violation discovery potential. |
---|
| 578 | |
---|
| 579 | \begin{table}[t] |
---|
| 580 | \centering |
---|
| 581 | \begin{tabular}{l@{\qquad}rrr@{\qquad}rrr} |
---|
| 582 | \hline\noalign{\smallskip} |
---|
| 583 | & \multicolumn{3}{ c }{\Ne} & \multicolumn{3}{c}{\He} \\ |
---|
| 584 | \hline\noalign{\smallskip} |
---|
| 585 | & \numu CC & $\pi^+$ & $\pi^-$ & \nubarmu CC & $\pi^+$ & $\pi^-$ \\ |
---|
| 586 | \hline\noalign{\smallskip} |
---|
| 587 | Generated ev.\ & 115367 & 557 & 341 & 101899 & 674 & 400 \\ |
---|
| 588 | Particle ID & 95717 & 204 & 100 & 85285 & 240 & 118 \\ |
---|
| 589 | Decay & 61347 & 107 & 8 & 69242 & 120 & 8 \\ |
---|
| 590 | \hline\noalign{\smallskip} |
---|
| 591 | \end{tabular} |
---|
| 592 | \mycaption{\label{tab:sigbck} Events for the \BB\ in a 4400~kt~yr |
---|
| 593 | exposure. \numu(\nubarmu) CC events are computed assuming full |
---|
| 594 | oscillations ($P_{\nu_e\to\nu_\mu} = 1$), and pion backgrounds are |
---|
| 595 | computed from \nue(\nubare) CC+NC events. In the rows we give the |
---|
| 596 | number events generated within the fiducial volume (``Generated |
---|
| 597 | ev.''), after muon particle identification (``Particle ID''), and |
---|
| 598 | after applying a further identification requiring the detection of |
---|
| 599 | the Michel electron (``Decay''). } |
---|
| 600 | \end{table} |
---|
| 601 | |
---|
| 602 | |
---|
| 603 | Backgrounds from charged pions and atmospheric neutrinos are computed |
---|
| 604 | with the identical analysis chain as signal events. |
---|
| 605 | Charged pions generated in NC events (or in NC-like events where the |
---|
| 606 | leading electron goes undetected) are the main source of background for |
---|
| 607 | the experiment. To compute this background inclusive NC and CC events |
---|
| 608 | have been generated with the \BB\ spectrum. Events have been selected |
---|
| 609 | where the only visible track is a charged pion above the \v{C}erenkov |
---|
| 610 | threshold. Particle identification efficiencies have been applied to |
---|
| 611 | those particles. The probability for a pion to survive in water until |
---|
| 612 | its decay has been computed with Geant~3.21 and cross-checked with a |
---|
| 613 | Fluka~2003 simulation. This probability is different for positive and |
---|
| 614 | negative pions, the latter having a higher probability to be absorbed |
---|
| 615 | before decaying. The surviving events are background, and the |
---|
| 616 | reconstructed neutrino energy is computed misidentifying these pions |
---|
| 617 | as muons. Event rates are reported in Tab.~\ref{tab:sigbck}. From |
---|
| 618 | these numbers it becomes evident that requiring the detection of the |
---|
| 619 | Michel electron provides an efficient cut to eliminate the pion |
---|
| 620 | background. |
---|
| 621 | % |
---|
| 622 | These background rates are significantly smaller than quoted in |
---|
| 623 | Ref.~\cite{MyNufact04}, where pion decays were computed with the |
---|
| 624 | same probabilities as for muons and they are slightly different |
---|
| 625 | from those quoted in Ref.~\cite{ MezzettoNuFact05}, where an |
---|
| 626 | older version of Nuance had been used. |
---|
| 627 | % |
---|
| 628 | The numbers of Tab.~\ref{tab:sigbck} have been cross-checked by |
---|
| 629 | comparing the Nuance and Neugen~\cite{Neugen} event |
---|
| 630 | generators, finding a fair agreement in background rates and energy shape. |
---|
| 631 | |
---|
| 632 | Also atmospheric neutrinos can constitute an important source of |
---|
| 633 | background~\cite{zucchelli,JJHigh2,JJHigh1,MezzettoNuFact05}. This |
---|
| 634 | background can be suppressed only by keeping a very short duty cycle |
---|
| 635 | ($2.2 \cdot 10^{-3}$ is the target value for the \BB\ design study), |
---|
| 636 | and this in turn is one of the most challenging bounds on the design |
---|
| 637 | of the Beta Beam complex. Following Ref.~\cite{MezzettoNuFact05} we |
---|
| 638 | include the atmospheric neutrino background based on a Monte Carlo |
---|
| 639 | simulation using Nuance. Events are reconstructed as if they were |
---|
| 640 | signal neutrino events. We estimate that 5 events/year would survive |
---|
| 641 | the analysis chain in a full solar year (the \BB\ should run for about |
---|
| 642 | 1/3 of this period) and include these events as backgrounds in the |
---|
| 643 | analysis. Under these circumstances, the present value of the \BB\ |
---|
| 644 | duty cycle seems to be an overkill, it could be reduced by a factor 5 |
---|
| 645 | at least, see also Ref.~\cite{MezzettoNuFact05} for a discussion of |
---|
| 646 | the effect of a higher duty cycle. |
---|
| 647 | |
---|
| 648 | |
---|
| 649 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 650 | \subsection{The $3.5$-GeV SPL Super Beam} |
---|
| 651 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 652 | |
---|
| 653 | In the Conceptual Design Report~1 (CDR1) the foreseen Super Proton |
---|
| 654 | Linac (SPL)~\cite{SPL} has been optimized to provide the protons |
---|
| 655 | for the muon production in the context of a Neutrino Factory. |
---|
| 656 | % |
---|
| 657 | Recently, in Ref.~\cite{Campagne:2004wt} a new optimization of the |
---|
| 658 | beam energy as well as the secondary particle focusing and decay has |
---|
| 659 | been undertaken considering a Super Beam searching for $\nu_\mu |
---|
| 660 | \rightarrow \nu_e$ and $\bar{\nu}_\mu \rightarrow \bar{\nu}_e$ |
---|
| 661 | appearance as well as $\nu_\mu$, $\bar\nu_\mu$ disappearance in a mega |
---|
| 662 | ton scale water \v{C}erenkov detector. In particular, a full |
---|
| 663 | simulation of the beam line from the proton on target interaction up |
---|
| 664 | to the secondary particle decay tunnel has been performed. The proton |
---|
| 665 | on a liquid mercury target (30~cm long, $7.5$~mm radius, 13.546 |
---|
| 666 | density) has been simulated with FLUKA~2002.4~\cite{FLUKA} while the |
---|
| 667 | horn focusing system and the decay tunnel simulation has been |
---|
| 668 | preformed with GEANT~3.21~\cite{GEANT}.\footnote{Although there are |
---|
| 669 | differences between the predicted pion and kaon productions as a |
---|
| 670 | function of proton kinetic energy with FLUKA~2002.4 and 2005.6, the |
---|
| 671 | results are consistent for the relevant energy of 3.5~GeV. We |
---|
| 672 | emphasize that the pion and the kaon production cross-sections are |
---|
| 673 | waiting for experimental confirmation~\cite{HARP-MINERVA} and a new |
---|
| 674 | optimization would be required if their is a disagreement with the |
---|
| 675 | present knowledge.} |
---|
| 676 | |
---|
| 677 | \begin{figure}[!t] |
---|
| 678 | \centering |
---|
| 679 | \includegraphics[width=0.65\textwidth]{./fig3.eps} |
---|
| 680 | \mycaption{\label{fig:fluxSPLContrib} Neutrino fluxes, at $130$~km |
---|
| 681 | from the target with the horns focusing the positive particles |
---|
| 682 | (top panel) or the negative particles (bottom panel). The fluxes are |
---|
| 683 | computed for a SPL proton beam of $3.5$~GeV (4~MW), a decay tunnel |
---|
| 684 | with a length of $40$~m and a radius of $2$~m.} |
---|
| 685 | \end{figure} |
---|
| 686 | |
---|
| 687 | Since the optimization requirements for a Neutrino Factory are rather |
---|
| 688 | different than for a Super Beam the new SPL configuration has a |
---|
| 689 | significant impact on the physics performance (see |
---|
| 690 | Ref.~\cite{Campagne:2004wt} for a detailed discussion). The SPL |
---|
| 691 | fluxes of the four neutrino species ($\nu_\mu$, $\nu_e$, |
---|
| 692 | $\bar{\nu}_\mu$, $\bar{\nu}_e$) for the positive ($\nu_\mu$ beam) and |
---|
| 693 | the negative focusing ($\bar{\nu}_\mu$ beam) are show in |
---|
| 694 | Fig.~\ref{fig:fluxSPLContrib}. The total number of $\nu_\mu$ |
---|
| 695 | ($\bar{\nu}_\mu$) in positive (negative) focusing is about |
---|
| 696 | $1.18\,(0.97) \times 10^{12}\:\mathrm{m}^{-2}\mathrm{y}^{-1}$ with an |
---|
| 697 | average energy of $300$~MeV. The $\nu_e$ ($\bar{\nu}_e$) contamination |
---|
| 698 | in the $\nu_\mu$ ($\bar\nu_\mu$) beam is around $0.7\%$ |
---|
| 699 | ($6.0\%$). Following Ref.~\cite{Mezzetto:2003mm}, the $\pi^o$ |
---|
| 700 | background is reduced using a tighter PID cut compared to standard |
---|
| 701 | Super-Kamiokande analysis. The Michel electron is required for the |
---|
| 702 | $\mu$ identification. |
---|
| 703 | % |
---|
| 704 | For the $\nu_\mu \rightarrow \nu_e$ channel the background consists |
---|
| 705 | roughly of 90\% $\nu_e \rightarrow \nu_e$ CC interactions, 6\% $\pi^o$ |
---|
| 706 | from NC interactions, 3\% miss identified muons from $\nu_\mu |
---|
| 707 | \rightarrow \nu_\mu$ CC, and 1\% $\bar{\nu}_e \rightarrow \bar{\nu}_e$ |
---|
| 708 | CC interactions. For the $\bar{\nu}_\mu \rightarrow \bar{\nu}_e$ |
---|
| 709 | channel the contributions to the background are 45\% $\bar{\nu}_e |
---|
| 710 | \rightarrow \bar{\nu}_e$ CC interactions, 35\% $\nu_e \rightarrow |
---|
| 711 | \nu_e$ CC interactions, 18\% $\pi^o$ from NC interactions and 2\% miss |
---|
| 712 | identified muons from $\bar{\nu}_\mu \rightarrow \bar{\nu}_\mu$ CC. |
---|
| 713 | In addition we include the events from the contamination of |
---|
| 714 | ``wrong sign'' muon-neutrinos due to $\bar\nu_\mu \to \bar\nu_e$ |
---|
| 715 | ($\nu_\mu \to \nu_e$) oscillations in the neutrino (antineutrino) |
---|
| 716 | mode. |
---|
| 717 | |
---|
| 718 | \begin{figure}[!t] |
---|
| 719 | \centering |
---|
| 720 | \includegraphics[width=0.5\textwidth]{./fig4.eps} |
---|
| 721 | % |
---|
| 722 | \mycaption{\label{fig:fluxComparison} |
---|
| 723 | Comparison of the fluxes from SPL and \BB.} |
---|
| 724 | \end{figure} |
---|
| 725 | |
---|
| 726 | Considering the signal over square-root of background |
---|
| 727 | ratio, the $3.5$~GeV beam energy is more favorable than the original |
---|
| 728 | $2.2$~GeV option. Compared to the fluxes used in |
---|
| 729 | Refs.~\cite{Mezzetto:2003mm,Donini:2004hu} the gain is at least a |
---|
| 730 | factor $2.5$ and this justifies to reconsider in detail the physics |
---|
| 731 | potential of the SPL Super Beam. |
---|
| 732 | % |
---|
| 733 | Both the appearance and the disappearance channels are used. For the |
---|
| 734 | spectral analysis we use 10 bins of 100~MeV in the interval $0 < E_\nu |
---|
| 735 | < 1$~GeV, applying the same migration matrices as for the \BB\ to take |
---|
| 736 | into account properly the neutrino energy reconstruction. As ultimate |
---|
| 737 | goal suggested in Ref.~\cite{T2K} a 2\% systematical error is used as |
---|
| 738 | default both for signal and background, this would be achieved by a |
---|
| 739 | special care of the design of the close position. However, we discuss |
---|
| 740 | also how a 5\% systematical error affects the sensitivities. |
---|
| 741 | % |
---|
| 742 | Using neutrino cross-sections on water from Ref.~\cite{Nuance}, the |
---|
| 743 | number of expected $\nu_\mu$ charged current is about $95$ per kt~yr |
---|
| 744 | {\bf *** does this number change using Nuance Xsects instead of |
---|
| 745 | Lipari? ***}. In Fig.~\ref{fig:fluxComparison} we compare the fluxes |
---|
| 746 | from the SPL to the one from the \BB. |
---|
| 747 | |
---|
| 748 | |
---|
| 749 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 750 | \section{Degeneracies} |
---|
| 751 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 752 | \label{sec:degeneracies} |
---|
| 753 | |
---|
| 754 | |
---|
| 755 | A characteristic feature in the analysis of future LBL experiments is |
---|
| 756 | the presence of {\it parameter degeneracies}. Due to the inherent |
---|
| 757 | three-flavor structure of the oscillation probabilities, for a given |
---|
| 758 | experiment in general several disconnected regions in the |
---|
| 759 | multi-dimensional space of oscillation parameters will be |
---|
| 760 | present. Traditionally these degeneracies are referred to in the |
---|
| 761 | following way: |
---|
| 762 | % |
---|
| 763 | \begin{itemize} |
---|
| 764 | \item |
---|
| 765 | The {\it intrinsic} or |
---|
| 766 | ($\delCP,\theta_{13}$)-degeneracy~\cite{Burguet-Castell:2001ez}: |
---|
| 767 | For a measurement based on the $\nu_\mu \to \nu_e$ oscillation probability for |
---|
| 768 | neutrinos and antineutrinos two disconnected solutions appear in the |
---|
| 769 | ($\delCP,\theta_{13}$) plane. |
---|
| 770 | \item |
---|
| 771 | The {\it hierarchy} or sign($\Delta |
---|
| 772 | m^2_{31}$)-degeneracy~\cite{Minakata:2001qm}: The two solutions |
---|
| 773 | corresponding to the two signs of $\Delta m^2_{31}$ appear in general |
---|
| 774 | at different values of $\delCP$ and $\theta_{13}$. |
---|
| 775 | \item |
---|
| 776 | The {\it octant} or $\theta_{23}$-degeneracy~\cite{Fogli:1996pv}: |
---|
| 777 | Since LBL experiments are sensitive mainly to $\sin^22\theta_{23}$ it |
---|
| 778 | is difficult to distinguish the two octants $\theta_{23} < \pi/4$ and |
---|
| 779 | $\theta_{23} > \pi/4$. Again, the solutions corresponding to |
---|
| 780 | $\theta_{23}$ and $\pi/2 - \theta_{23}$ appear in general at different |
---|
| 781 | values of $\delCP$ and $\theta_{13}$. |
---|
| 782 | \end{itemize} |
---|
| 783 | % |
---|
| 784 | This leads to an eight-fold ambiguity in $\theta_{13}$ and |
---|
| 785 | $\delCP$~\cite{Barger:2001yr}, and hence degeneracies provide a |
---|
| 786 | serious limitation for the determination of $\theta_{13}$, $\delCP$, |
---|
| 787 | and the sign of $\Delta m^2_{31}$. Recent discussions of degeneracies |
---|
| 788 | can be found for example in |
---|
| 789 | Refs.~\cite{Huber:2002mx,Huber:2005ep,Yasuda:2004gu,Ishitsuka:2005qi}; |
---|
| 790 | degeneracies in the context of CERN--Fr\'ejus \BB\ and SPL have been |
---|
| 791 | considered previously in Ref.~\cite{Donini:2004hu}. |
---|
| 792 | % |
---|
| 793 | In Fig.~\ref{fig:degeneracies} we illustrate the effect of |
---|
| 794 | degeneracies for the \BB, SPL, and T2HK experiments. Assuming the |
---|
| 795 | true parameter values $\delta_\mathrm{CP} = -0.85 \pi$, |
---|
| 796 | $\sin^22\theta_{13} = 0.03$, $\sin^2\theta_{23} = 0.6$ we show the |
---|
| 797 | allowed regions in the plane of $\stheta$ and $\delCP$ taking into |
---|
| 798 | account the solutions with the wrong hierarchy and the wrong octant of |
---|
| 799 | $\theta_{23}$. |
---|
| 800 | |
---|
| 801 | \begin{figure}[!t] |
---|
| 802 | \centering |
---|
| 803 | \includegraphics[width=0.95\textwidth]{./fig5.eps} |
---|
| 804 | % |
---|
| 805 | \mycaption{Allowed regions in $\sin^22\theta_{13}$ and |
---|
| 806 | $\delta_\mathrm{CP}$ for LBL data alone (contour lines) and LBL+ATM |
---|
| 807 | data combined (colored regions). $\mathrm{H^{tr/wr} (O^{tr/wr})}$ |
---|
| 808 | refers to solutions with the true/wrong mass hierarchy (octant of |
---|
| 809 | $\theta_{23}$). The true parameter values are $\delta_\mathrm{CP} = |
---|
| 810 | -0.85 \pi$, $\sin^22\theta_{13} = 0.03$, $\sin^2\theta_{23} = 0.6$, |
---|
| 811 | and the values from Eq.~(\ref{eq:default-params}) for the other |
---|
| 812 | parameters.} |
---|
| 813 | \label{fig:degeneracies} |
---|
| 814 | \end{figure} |
---|
| 815 | |
---|
| 816 | |
---|
| 817 | \begin{figure}[!t] |
---|
| 818 | \centering |
---|
| 819 | \includegraphics[width=0.9\textwidth]{./fig6.eps} |
---|
| 820 | % |
---|
| 821 | \mycaption{Resolving degeneracies in SPL by successively using the |
---|
| 822 | appearance rate measurement, disappearance channel rate and |
---|
| 823 | spectrum, spectral information in the appearance channel, and |
---|
| 824 | atmospheric neutrinos. Allowed regions in $\sin^22\theta_{13}$ and |
---|
| 825 | $\delta_\mathrm{CP}$ are shown at 95\%~CL, and $\mathrm{H^{tr/wr} |
---|
| 826 | (O^{tr/wr})}$ refers to solutions with the true/wrong mass hierarchy |
---|
| 827 | (octant of $\theta_{23}$). The true parameter values are |
---|
| 828 | $\delta_\mathrm{CP} = -0.85 \pi$, $\sin^22\theta_{13} = 0.03$, |
---|
| 829 | $\sin^2\theta_{23} = 0.6$, and the values from |
---|
| 830 | Eq.~(\ref{eq:default-params}) for the other parameters.} |
---|
| 831 | \label{fig:degeneracies_SPL} |
---|
| 832 | \end{figure} |
---|
| 833 | |
---|
| 834 | As visible in Fig.~\ref{fig:degeneracies} for the |
---|
| 835 | Super Beam experiments SPL and T2HK there is only a four-fold |
---|
| 836 | degeneracy related to sign($\Delta m^2_{31}$) and the octant of |
---|
| 837 | $\theta_{23}$, whereas the intrinsic degeneracy can be resolved. |
---|
| 838 | % |
---|
| 839 | Several pieces of information contribute to this effect, as we |
---|
| 840 | illustrate at the example of SPL in Fig.~\ref{fig:degeneracies_SPL}. |
---|
| 841 | The dashed curves in the left panel of this figure show the allowed |
---|
| 842 | regions for only the appearance measurement (for neutrinos and |
---|
| 843 | antineutrinos) without spectral information, i.e., just a counting |
---|
| 844 | experiment. In this case the eight-fold degeneracy is present in its |
---|
| 845 | full beauty, and one finds two solutions (corresponding to the |
---|
| 846 | intrinsic degeneracy) for each choice of sign($\Delta m^2_{31}$) and |
---|
| 847 | the octant of $\theta_{23}$. Moreover, the allowed regions are |
---|
| 848 | relatively large. For the thin solid curves the information from the |
---|
| 849 | disappearance rate is added. The main effect is to decrease the size |
---|
| 850 | of the allowed regions in $\stheta$. This is especially pronounced for |
---|
| 851 | the solutions involving the wrong octant of $\theta_{23}$, since these |
---|
| 852 | solutions are strongly affected by an uncertainty in $\theta_{23}$ |
---|
| 853 | which gets reduced by the disappearance information. Using in addition |
---|
| 854 | to the disappearance rate also the spectrum again decreases the size |
---|
| 855 | of the allowed regions, however, still all eight solutions are present |
---|
| 856 | (compare dashed curves in the right panel). |
---|
| 857 | % |
---|
| 858 | The most relevant effect comes from the inclusion of spectral |
---|
| 859 | information in the appearance channel, as visible from the comparison |
---|
| 860 | of the dashed and thick-solid curves in the right panel of |
---|
| 861 | Fig.~\ref{fig:degeneracies_SPL}. The intrinsic degeneracy gets |
---|
| 862 | resolved and only four solutions corresponding to the sign and octant |
---|
| 863 | degeneracies are left.\footnote{The inclusion of spectral information |
---|
| 864 | might be the source of possible differences to previous studies, see |
---|
| 865 | e.g.\ Ref.~\cite{Donini:2004hu}.} Note that the thick curves in the |
---|
| 866 | right panel of Fig.~\ref{fig:degeneracies_SPL} correspond to the |
---|
| 867 | regions show in Fig.~\ref{fig:degeneracies} for the SPL. |
---|
| 868 | % |
---|
| 869 | Finally, by the inclusion of information from atmospheric neutrinos |
---|
| 870 | all degeneracies can be resolved in this example, and the true |
---|
| 871 | solution is identified at 95\%~CL (see Sec.~\ref{sec:atmospherics} and |
---|
| 872 | Ref.~\cite{Huber:2005ep} for further discussions of atmospheric |
---|
| 873 | neutrinos). |
---|
| 874 | |
---|
| 875 | Concerning the \BB\ one observes from Fig.~\ref{fig:degeneracies} that |
---|
| 876 | in this case the ($\delCP,\theta_{13}$)-degeneracy cannot be resolved |
---|
| 877 | and one has to deal with eight distinct solutions. One reason for this |
---|
| 878 | is the absence of precise information on $|\Delta m^2_{31}|$ and |
---|
| 879 | $\sin^22\theta_{23}$ which is provided by the $\nu_\mu$ disappearance |
---|
| 880 | in Super Beam experiments but is not available from the \BB. If |
---|
| 881 | external information on these parameters at the level of 3\% is |
---|
| 882 | included the allowed regions in Fig.~\ref{fig:degeneracies} are |
---|
| 883 | significantly reduced. However, still all eight solutions are present, |
---|
| 884 | which indicates that for the \BB\ spectral information is not |
---|
| 885 | efficient enough to resolve the ($\delCP,\theta_{13}$)-degeneracy, and |
---|
| 886 | in this case only the inclusion of atmospheric neutrino data allows a |
---|
| 887 | nearly complete resolution of the degeneracies. |
---|
| 888 | |
---|
| 889 | An important observation from Fig.~\ref{fig:degeneracies} is that |
---|
| 890 | degeneracies have only a very small impact on the CP violation |
---|
| 891 | discovery, in the sense that if the true solution is CP violating also |
---|
| 892 | the fake solutions are located at CP violating values of |
---|
| 893 | $\delCP$. Indeed, since for the relatively short baselines in the |
---|
| 894 | experiments under consideration matter effects are very small, the |
---|
| 895 | sign($\Delta m^2_{31}$)-degenerate solution is located within good |
---|
| 896 | approximation at $\delCP' \approx \pi - |
---|
| 897 | \delCP$~\cite{Minakata:2001qm}. Therefore, although degeneracies |
---|
| 898 | strongly affect the determination of $\theta_{13}$ and $\delCP$ they |
---|
| 899 | have only a small impact on the CP violation discovery potential. |
---|
| 900 | Furthermore, as clear from Fig.~\ref{fig:degeneracies} the sign($\Delta |
---|
| 901 | m^2_{31}$) degeneracy has practically no effect on the $\theta_{13}$ |
---|
| 902 | measurement, whereas the octant degeneracy has very little impact on |
---|
| 903 | the determination of $\delCP$. |
---|
| 904 | |
---|
| 905 | \begin{figure}[!t] |
---|
| 906 | \centering |
---|
| 907 | \includegraphics[width=0.9\textwidth]{./fig7.eps} |
---|
| 908 | % |
---|
| 909 | \mycaption{Allowed regions in $\sin^22\theta_{13}$ and |
---|
| 910 | $\delta_\mathrm{CP}$ for 5~years data (neutrinos only) from \BB, |
---|
| 911 | SPL, and the combination. $\mathrm{H^{tr/wr} (O^{tr/wr})}$ refers to |
---|
| 912 | solutions with the true/wrong mass hierarchy (octant of |
---|
| 913 | $\theta_{23}$). For the colored regions in the left panel also |
---|
| 914 | 5~years of atmospheric data are included; the solution with the |
---|
| 915 | wrong hierarchy has $\Delta\chi^2 = 4$. The true parameter |
---|
| 916 | values are $\delta_\mathrm{CP} = -0.85 \pi$, $\sin^22\theta_{13} = |
---|
| 917 | 0.03$, $\sin^2\theta_{23} = 0.6$, and the values from |
---|
| 918 | Eq.~(\ref{eq:default-params}) for the other parameters. For the \BB\ |
---|
| 919 | only analysis (middle panel) an external accuracy of 2\% (3\%) for |
---|
| 920 | $|\Delta m^2_{31}|$ ($\theta_{23}$) has been assumed, whereas for |
---|
| 921 | the left and right panel the default value of 10\% has been used.} |
---|
| 922 | \label{fig:degeneracies_5yrs} |
---|
| 923 | \end{figure} |
---|
| 924 | |
---|
| 925 | Fig.~\ref{fig:degeneracies} shows also that the fake solutions occur |
---|
| 926 | at similar locations in the ($\stheta$, $\delCP$) plane for \BB\ and |
---|
| 927 | SPL. Therefore, as noted in Ref.~\cite{Donini:2004hu}, in this sense |
---|
| 928 | the two experiments are not complementary, and the combination of |
---|
| 929 | 10~years of \BB\ and SPL data is not very effective in resolving |
---|
| 930 | degeneracies. This is obvious since the baseline is the same and the |
---|
| 931 | neutrino energies are similar. |
---|
| 932 | % |
---|
| 933 | Note however, that the \BB\ looks for $\nu_e\to\nu_\mu$ appearance, |
---|
| 934 | whereas in SPL the T-conjugate channel $\nu_\mu\to\nu_e$ is observed. |
---|
| 935 | Assuming CPT invariance the relation $P_{\nu_\alpha\to\nu_\beta} = |
---|
| 936 | P_{\bar\nu_\beta\to\bar\nu_\alpha}$ holds, which implies that the |
---|
| 937 | antineutrino measurement can be replaced by a measurement in the |
---|
| 938 | T-conjugate channel. Hence, if \BB\ and SPL experiments are available |
---|
| 939 | simultaneously the full information can be obtained just from neutrino |
---|
| 940 | data, and in principle the (time consuming) antineutrino measurement |
---|
| 941 | is not necessary. As shown in Fig.~\ref{fig:degeneracies_5yrs} the |
---|
| 942 | combination of 5~yrs neutrino data from the \BB\ with 5~yrs of |
---|
| 943 | neutrino data from SPL leads to a result very close to the 10~yrs |
---|
| 944 | neutrino+antineutrino data from one experiment alone. Hence, if \BB\ |
---|
| 945 | and SPL experiments are available simultaneously the data taking |
---|
| 946 | period is reduced approximately by a factor of 2 with respect to a |
---|
| 947 | single experiment. This synergy is discussed later in |
---|
| 948 | Sec.~\ref{sec:synergies-beams} in the context of the $\theta_{13}$ and |
---|
| 949 | CP violation discovery potentials. |
---|
| 950 | |
---|
| 951 | |
---|
| 952 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 953 | \section{Physics potential} |
---|
| 954 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 955 | \label{sec:sensitivities} |
---|
| 956 | |
---|
| 957 | \subsection{Sensitivity to the atmospheric parameters} |
---|
| 958 | \label{sec:atm} |
---|
| 959 | |
---|
| 960 | The $\nu_\mu$ disappearance channel available in the Super Beam |
---|
| 961 | experiments SPL and T2HK allows a precise determination of the |
---|
| 962 | atmospheric parameters $|\Delta m^2_{31}|$ and $\sin^22\theta_{23}$, |
---|
| 963 | see, e.g., Refs.~\cite{Antusch:2004yx,Minakata:2004pg,Donini:2005db} |
---|
| 964 | for recent analyses). Fig.~\ref{fig:atm-params} illustrates the |
---|
| 965 | improvement on these parameters by Super Beam experiments with respect |
---|
| 966 | to the present knowledge from SK atmospheric and K2K data. We show the |
---|
| 967 | allowed regions at 99\%~CL for T2K-I, SPL, and T2HK, where in all |
---|
| 968 | three cases 5~years of neutrino data are assumed. T2K-I corresponds to |
---|
| 969 | the phase~I of the T2K experiment with a beam power of 0.77~MW and the |
---|
| 970 | Super-Kamiokande detector as target~\cite{T2K}. In Tab.~\ref{tab:atm-params} we |
---|
| 971 | give the corresponding relative accuracies at 3$\sigma$ for $|\Delta |
---|
| 972 | m^2_{31}|$ and $\sin^2\theta_{23}$. |
---|
| 973 | |
---|
| 974 | \begin{figure}[!t] |
---|
| 975 | \centering |
---|
| 976 | \includegraphics[width=0.55\textwidth]{./fig8.eps} |
---|
| 977 | \mycaption{\label{fig:atm-params} Allowed regions of $\Delta |
---|
| 978 | m^2_{31}$ and $\sin^2\theta_{23}$ at 99\%~CL (2 d.o.f.) after 5~yrs |
---|
| 979 | of neutrino data taking for SPL, T2K phase~I, T2HK, and the |
---|
| 980 | combination of SPL with 5~yrs of atmospheric neutrino data in the |
---|
| 981 | MEMPHYS detector. For the true parameter values we use $\Delta |
---|
| 982 | m^2_{31} = 2.2\, (2.6) \times 10^{-3}~\mathrm{eV}^2$ and |
---|
| 983 | $\sin^2\theta_{23} = 0.5 \, (0.37)$ for the test point 1 (2), and |
---|
| 984 | $\theta_{13} = 0$ and the solar parameters as given in |
---|
| 985 | Eq.~(\ref{eq:default-params}). The shaded region corresponds to the |
---|
| 986 | 99\%~CL region from present SK and K2K data~\cite{Maltoni:2004ei}.} |
---|
| 987 | \end{figure} |
---|
| 988 | |
---|
| 989 | |
---|
| 990 | \begin{table}[!t] |
---|
| 991 | \centering |
---|
| 992 | \begin{tabular}{lcrrr} |
---|
| 993 | \hline\noalign{\smallskip} |
---|
| 994 | & True values & T2K-I & SPL & T2HK \\ |
---|
| 995 | \noalign{\smallskip}\hline\noalign{\smallskip} |
---|
| 996 | $\Delta m^2_{31}$ & $2.2\cdot 10^{-3}$ eV$^2$ & 4.7\% & 3.2\% & 1.1\% \\ |
---|
| 997 | $\sin^2\theta_{23}$ & $0.5$ & 20\% & 20\% & 6\% \\ |
---|
| 998 | \noalign{\smallskip}\hline\noalign{\smallskip} |
---|
| 999 | $\Delta m^2_{31}$ & $2.6\cdot 10^{-3}$ eV$^2$ & 4.4\% & 2.5\% & 0.7\% \\ |
---|
| 1000 | $\sin^2\theta_{23}$ & $0.37$ & 8.9\% & 3.1\% & 0.8\% \\ |
---|
| 1001 | \noalign{\smallskip}\hline |
---|
| 1002 | \end{tabular} |
---|
| 1003 | \mycaption{Accuracies at $3\sigma$ on the atmospheric parameters |
---|
| 1004 | $|\Delta m^2_{31}|$ and $\sin^2\theta_{23}$ for 5 years of neutrino |
---|
| 1005 | data from T2K-I, SPL, and T2HK for the two test points shown in |
---|
| 1006 | Fig.~\ref{fig:atm-params} ($\theta^\mathrm{true}_{13} = 0$). The |
---|
| 1007 | accuracy for a parameter $x$ is defined as $(x^\mathrm{upper} - |
---|
| 1008 | x^\mathrm{lower})/(2 x^\mathrm{true})$, where $x^\mathrm{upper}$ |
---|
| 1009 | ($x^\mathrm{lower}$) is the upper (lower) bound at 3$\sigma$ for |
---|
| 1010 | 1~d.o.f.\ obtained by projecting the contour $\Delta \chi^2 = 9$ |
---|
| 1011 | onto the $x$-axis. For the accuracies for test point~2 the octant |
---|
| 1012 | degenerate solution is neglected.\label{tab:atm-params}} |
---|
| 1013 | \end{table} |
---|
| 1014 | |
---|
| 1015 | From the figure and the table it becomes evident that the T2K setups |
---|
| 1016 | are very good in measuring the atmospheric parameters, and only a |
---|
| 1017 | modest improvement is possible with SPL with respect to T2K phase~I. |
---|
| 1018 | T2HK provides an excellent sensitivity for these parameters, and for |
---|
| 1019 | the example of the test point~2 sub-percent accuracies are obtained at |
---|
| 1020 | 3$\sigma$. The disadvantage of SPL with respect to T2HK is the |
---|
| 1021 | limited spectral information. Because of the lower beam energy |
---|
| 1022 | nuclear Fermi motion is a severe limitation for energy reconstruction |
---|
| 1023 | in SPL, whereas in T2K the somewhat higher energy allows an efficient |
---|
| 1024 | use of spectral information of quasi-elastic events. Indeed, due to |
---|
| 1025 | the large number of events in the disappearance channel (cf.\ |
---|
| 1026 | Tab.~\ref{tab:events}) the measurement is completely dominated by the |
---|
| 1027 | spectrum, and even increasing the normalization uncertainty up to |
---|
| 1028 | 100\% has very little impact on the allowed regions. The effect of |
---|
| 1029 | spectral information on the disappearance measurement is |
---|
| 1030 | discussed in some detail in Ref.~\cite{Donini:2005db}. |
---|
| 1031 | |
---|
| 1032 | For the test point~1, with maximal mixing for $\theta_{23}$, rather |
---|
| 1033 | poor accuracies of $\sim20\%$ for T2K-I and SPL, and $6\%$ for T2HK |
---|
| 1034 | are obtained for $\sin^2\theta_{23}$. The reason is that in the |
---|
| 1035 | disappearance channel $\sin^22\theta_{23}$ is measured with high |
---|
| 1036 | precision, which translates to rather large errors for |
---|
| 1037 | $\sin^2\theta_{23}$ if $\theta_{23} = \pi/4$~\cite{Minakata:2004pg}. |
---|
| 1038 | % |
---|
| 1039 | For the same reason it is difficult to resolve the octant degeneracy, |
---|
| 1040 | and for the test point~2, with a non-maximal value of |
---|
| 1041 | $\sin^2\theta_{23} = 0.37$, for all three LBL experiments the |
---|
| 1042 | degenerate solution is present around $\sin^2\theta_{23} = 0.63$. |
---|
| 1043 | % |
---|
| 1044 | As pointed out in Refs.~\cite{Peres:2003wd,Gonzalez-Garcia:2004cu} |
---|
| 1045 | atmospheric neutrino data may allow to distinguish between the two |
---|
| 1046 | octants of $\theta_{23}$. If 5~years of atmospheric neutrino data in |
---|
| 1047 | MEMPHYS are added to the SPL data, the degenerate solution for the |
---|
| 1048 | test point~2 can be excluded at more than $5\sigma$ and hence the |
---|
| 1049 | octant degeneracy is resolved in this example, see |
---|
| 1050 | Sec.~\ref{sec:atmospherics} for a more detailed discussion. |
---|
| 1051 | |
---|
| 1052 | |
---|
| 1053 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1054 | \subsection{The $\theta_{13}$ discovery potential} |
---|
| 1055 | \label{sec:th13} |
---|
| 1056 | |
---|
| 1057 | If no finite value of $\theta_{13}$ is discovered by the next round of |
---|
| 1058 | experiments an important task of the experiments under consideration |
---|
| 1059 | here is to push further the sensitivity to this parameter. In this |
---|
| 1060 | section we address this problem, where we use to following definition |
---|
| 1061 | of the $\theta_{13}$ discovery potential: Data are simulated for a |
---|
| 1062 | finite true value of $\stheta$ and a given true value for $\delCP$. If |
---|
| 1063 | the $\Delta\chi^2$ of the fit to these data with $\theta_{13} = 0$ is |
---|
| 1064 | larger than 9 the corresponding true value of $\theta_{13}$ ``is |
---|
| 1065 | discovered at 3$\sigma$''. In other words, the $3\sigma$ discovery |
---|
| 1066 | limit as a function of the true $\delCP$ is given by the true value of |
---|
| 1067 | $\stheta$ for which $\Delta\chi^2(\theta_{13}=0) = 9$. In the fitting |
---|
| 1068 | process we minimize the $\Delta\chi^2$ with respect to $\theta_{12}$, |
---|
| 1069 | $\theta_{23}$, $\Delta m^2_{12}$, and $\Delta m^2_{31}$, and in |
---|
| 1070 | general one has to test also for degenerate solutions in sign($\Delta |
---|
| 1071 | m^2_{31}$) and the octant of $\theta_{23}$. |
---|
| 1072 | |
---|
| 1073 | \begin{figure} |
---|
| 1074 | \centering \includegraphics[width=0.9\textwidth]{./fig9.eps} |
---|
| 1075 | \mycaption{$3\sigma$ discovery sensitivity to $\stheta$ for \BB, |
---|
| 1076 | SPL, and T2HK as a function of the true value of \delCP\ (left |
---|
| 1077 | panel) and as a function of the fraction of all possible values of |
---|
| 1078 | \delCP\ (right panel). The width of the bands corresponds to values |
---|
| 1079 | for the systematical errors between 2\% and 5\%. The black curves |
---|
| 1080 | correspond to the combination of \BB\ and SPL with 10~yrs of total |
---|
| 1081 | data taking each for a systematical error of 2\%, and the dashed |
---|
| 1082 | curves show the sensitivity of the \BB\ when the number of ion |
---|
| 1083 | decays/yr are reduced by a factor of two with respect to the values |
---|
| 1084 | given in Tab.~\ref{tab:setups}.\label{fig:th13}} |
---|
| 1085 | \end{figure} |
---|
| 1086 | |
---|
| 1087 | The discovery limits are shown for \BB, SPL, and T2HK in |
---|
| 1088 | Fig.~\ref{fig:th13}. One observes that SPL and T2HK are rather similar |
---|
| 1089 | in performance, whereas the \BB\ with our standard fluxes performs |
---|
| 1090 | significantly better. For all three facilities a guaranteed discovery |
---|
| 1091 | reach of $\stheta \simeq 5\times 10^{-3}$ is obtained, irrespective of |
---|
| 1092 | the actual value of \delCP, however, for certain values of \delCP\ the |
---|
| 1093 | sensitivity is significantly improved. For SPL and T2HK discovery |
---|
| 1094 | limits around $\stheta \simeq 10^{-3}$ are possible for a large |
---|
| 1095 | fraction of all possible values of \delCP, whereas for our standard |
---|
| 1096 | \BB\ a sensitivity below $\stheta = 4\times 10^{-4}$ is reached for |
---|
| 1097 | 80\% of all possible values of \delCP. If 10~years of data from \BB\ |
---|
| 1098 | and SPL are combined the discovery limit is dominated by the \BB. |
---|
| 1099 | % |
---|
| 1100 | Let us stress that the \BB\ performance depends crucially on the |
---|
| 1101 | neutrino flux intensity, as can be seen from the dashed curves in |
---|
| 1102 | Fig.~\ref{fig:th13}, which has been obtained by reducing the number of |
---|
| 1103 | ion decays/yr by a factor of two with respect to our standard values |
---|
| 1104 | given in Tab.~\ref{tab:setups}. In this case the sensitivity decreases |
---|
| 1105 | significantly, but still values slightly better than from the |
---|
| 1106 | Super Beam experiments are reached. |
---|
| 1107 | |
---|
| 1108 | In Fig.~\ref{fig:th13} we illustrate also the effect of systematical |
---|
| 1109 | errors on the $\theta_{13}$ discovery reach. The lower boundary of the |
---|
| 1110 | band for each experiment corresponds to a systematical error of 2\%, |
---|
| 1111 | whereas the upper boundary is obtained for 5\%. These errors include |
---|
| 1112 | the (uncorrelated) normalization uncertainties on the signal as well |
---|
| 1113 | as on the background, where the crucial uncertainty is the error on |
---|
| 1114 | the background. We find that the \BB\ is basically not affected by |
---|
| 1115 | these errors, since the background has a rather different spectral |
---|
| 1116 | shape (strongly peaked at low energies) than the signal. The fact |
---|
| 1117 | that T2HK is relatively strongly affected by the actual value of the |
---|
| 1118 | systematics can by understood by considering the ratio of signal to |
---|
| 1119 | the square-root of the background using the numbers of |
---|
| 1120 | Tab.~\ref{tab:events}. We shall discuss this issue in more detail in |
---|
| 1121 | the next section in the context of the CP violation discovery reach. |
---|
| 1122 | |
---|
| 1123 | Let us remark that the $\theta_{13}$ sensitivities are practically not |
---|
| 1124 | affected by the sign($\Delta m^2_{31}$)-degeneracy. This is easy to |
---|
| 1125 | understand, since the data is fitted with $\theta_{13} = 0$, and in |
---|
| 1126 | this case both mass hierarchies lead to very similar event rates. If |
---|
| 1127 | the inverted hierarchy is used as the true hierarchy, the peak in the |
---|
| 1128 | discovery limit visible in the left panel of Fig.~\ref{fig:th13} |
---|
| 1129 | around $\delCP \sim \pi$ moves to $\delCP \sim 0$. However, the |
---|
| 1130 | characteristic shape of the curves, and in particular, the sensitivity |
---|
| 1131 | as a function of the \delCP-fraction shown in the right panel are |
---|
| 1132 | hardly affected by the sign of the true $\Delta m^2_{31}$. |
---|
| 1133 | % |
---|
| 1134 | In case of a non-maximal value of $\theta_{23}$ the octant-degeneracy |
---|
| 1135 | has a minor impact on the $\theta_{13}$ discovery potential, as |
---|
| 1136 | illustrated in Fig.~\ref{fig:SPLTheta13Disco} for the SPL. We show the |
---|
| 1137 | discovery limit obtained with the true and the fake octant of |
---|
| 1138 | $\theta_{23}$ for a true value of $\sin^2\theta_{23}= 0.6$. Let us |
---|
| 1139 | note that for true values of $\sin^2\theta_{23} > 0.5$ the |
---|
| 1140 | octant-degenerate solution leads to a worse sensitivity to |
---|
| 1141 | $\theta_{13}$ (see figure), whereas for $\sin^2\theta_{23} < 0.5$ the |
---|
| 1142 | fake solution does not affect the $\theta_{13}$ discovery, since in |
---|
| 1143 | this case the sensitivity is increased. |
---|
| 1144 | |
---|
| 1145 | \begin{figure} |
---|
| 1146 | \centering |
---|
| 1147 | \includegraphics[width=0.9\textwidth]{./fig10.eps} |
---|
| 1148 | \mycaption{\label{fig:SPLTheta13Disco} $3\sigma$ discovery |
---|
| 1149 | sensitivity to $\stheta$ for the SPL as a function of the true value |
---|
| 1150 | of \delCP\ for $\sin^2\theta_{23}^\mathrm{true} = 0.6$ and true values for |
---|
| 1151 | the other parameters as given in Eq.~(\ref{eq:default-params}).} |
---|
| 1152 | \end{figure} |
---|
| 1153 | |
---|
| 1154 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1155 | \subsection{Sensitivity to CP violation} |
---|
| 1156 | \label{sec:CPV} |
---|
| 1157 | |
---|
| 1158 | In case a finite value of $\theta_{13}$ is established it is important |
---|
| 1159 | to quantitatively assess the discovery potential for leptonic CP |
---|
| 1160 | violation (CPV). The CP symmetry is violated if the complex phase |
---|
| 1161 | \delCP\ is different from $0$ and $\pi$. Therefore, CPV is discovered |
---|
| 1162 | if these values for \delCP\ can be excluded. |
---|
| 1163 | % |
---|
| 1164 | We evaluate the discovery potential for CPV in the following way: |
---|
| 1165 | Data are calculated by scanning the true values of $\stheta$ and |
---|
| 1166 | $\delCP$. Then these data are fitted with the CP conserving values |
---|
| 1167 | $\delCP = 0$ and $\delCP = \pi$, where all parameters except \delCP\ |
---|
| 1168 | are varied and the sign and octant degeneracies are taken into |
---|
| 1169 | account. If no fit with $\Delta \chi^2 < 9$ is found CP conserving |
---|
| 1170 | values of \delCP\ can be excluded at $3\sigma$ for the chosen values |
---|
| 1171 | of $\delta_\mathrm{CP}^\mathrm{true}$ and $\stheta^\mathrm{true}$. |
---|
| 1172 | |
---|
| 1173 | \begin{figure}[!t] |
---|
| 1174 | \centering |
---|
| 1175 | \includegraphics[width=0.65\textwidth]{./fig11.eps} |
---|
| 1176 | % |
---|
| 1177 | \mycaption{CPV discovery potential for \BB, SPL, and T2HK: For |
---|
| 1178 | parameter values inside the ellipse-shaped curves CP conserving |
---|
| 1179 | values of \delCP\ can be excluded at $3\sigma$ $(\Delta\chi^2>9)$. |
---|
| 1180 | The width of the bands corresponds to values for the systematical |
---|
| 1181 | errors from 2\% to 5\%. The dashed curves show the sensitivity of |
---|
| 1182 | the \BB\ when the number of ion decays/yr are reduced by a factor |
---|
| 1183 | of two with respect to the values given in Tab.~\ref{tab:setups} |
---|
| 1184 | for 2\% systematics.\label{fig:CPV}} |
---|
| 1185 | \end{figure} |
---|
| 1186 | |
---|
| 1187 | The CPV discovery potential for \BB, SPL, and T2HK is shown in |
---|
| 1188 | Fig.~\ref{fig:CPV}. As in the case of the $\theta_{13}$ sensitivity we |
---|
| 1189 | find that SPL and T2HK perform rather similar, whereas the \BB\ has |
---|
| 1190 | significantly better sensitivity if our adopted numbers of ion decays |
---|
| 1191 | per year can be achieved. For systematical errors of 2\% maximal CPV |
---|
| 1192 | (for $\delCP^\mathrm{true} = \pi/2, \, 3\pi/2$) can be discovered at |
---|
| 1193 | $3\sigma$ down to $\stheta \simeq 8.8 \,(6.6)\times 10^{-4}$ for SPL |
---|
| 1194 | (T2HK), and $\stheta \simeq 2\times 10^{-4}$ for the \BB. This number |
---|
| 1195 | for the \BB\ is increased by a factor 3 if the fluxes are reduced to |
---|
| 1196 | half of our nominal values. The best sensitivity to CPV is obtained |
---|
| 1197 | for all three facilities around $\stheta \sim 10^{-2}$. For this value |
---|
| 1198 | CPV can be established for 78\%, 73\%, 75\% of all values of \delCP\ |
---|
| 1199 | for \BB, SPL, T2HK, respectively (again for systematics of 2\%). |
---|
| 1200 | |
---|
| 1201 | The widths of the bands in Fig.~\ref{fig:CPV} corresponds to different |
---|
| 1202 | values for systematical errors. The curves which give the best |
---|
| 1203 | sensitivities are obtained for systematics of 2\%, the curves |
---|
| 1204 | corresponding to the worst sensitivity have been computed for |
---|
| 1205 | systematics of 5\%. We change the uncertainty on the signal as well as |
---|
| 1206 | on the background, however, it turns out that the most relevant |
---|
| 1207 | uncertainty is the background normalization. We find that the impact |
---|
| 1208 | of systematics is very small for the \BB. The reason for this is that |
---|
| 1209 | the spectral shape of the background in the \BB\ (from pions and |
---|
| 1210 | atmospheric neutrinos) is very different from the signal, and |
---|
| 1211 | therefore they can be disentangled by the fit of the energy spectrum. |
---|
| 1212 | For the Super Beams the background spectrum is more similar to the |
---|
| 1213 | signal, and therefore an uncertainty on the backgound normalization |
---|
| 1214 | might have a strong impact on the sensitivity, as visible from the SPL |
---|
| 1215 | and T2HK curves in Fig.~\ref{fig:CPV}. In particular T2HK is strongly |
---|
| 1216 | affected, and moving from 2\% to 5\% uncertainy decreases the |
---|
| 1217 | sensitivity to maximal CPV by a factor 3. |
---|
| 1218 | |
---|
| 1219 | This interesting feature can be understood in the following way. A |
---|
| 1220 | rough measure to estimate the sensitivity is given by the signal |
---|
| 1221 | compared to the error on the background. The latter receives |
---|
| 1222 | contributions from the statistical error $\sqrt{B}$ and from the |
---|
| 1223 | systematical uncertainty $\sigma_\mathrm{bkgr}B$, where $B$ is the |
---|
| 1224 | number of background events and $\sigma_\mathrm{bkgr}$ is the |
---|
| 1225 | (relative) systematical error. Hence the importance of the systematics |
---|
| 1226 | can be estimated by the ratio of systematical and statistical errors |
---|
| 1227 | $\sigma_\mathrm{bkgr} B / \sqrt{B} = \sigma_\mathrm{bkgr} \sqrt{B}$. |
---|
| 1228 | Summing the numbers for background events in the neutrino and |
---|
| 1229 | antineutrino channels given in Tab.~\ref{tab:events} one finds that |
---|
| 1230 | systematical errors dominate ($\sigma_\mathrm{bkgr} \sqrt{B} > 1$) if |
---|
| 1231 | $\sigma_\mathrm{bkgr} \gtrsim 6\%,\, 3\%, \, 2\%$ for \BB, SPL, T2HK, |
---|
| 1232 | respectively. |
---|
| 1233 | % |
---|
| 1234 | In the right panel Fig.~\ref{fig:systematics} we show the sensitivity |
---|
| 1235 | to maximal CPV (as defined in the figure caption) as a function of |
---|
| 1236 | $\sigma_\mathrm{bkgr}$. Indeed, the worsening of the sensitivity due |
---|
| 1237 | to systematics occurs roughly at the values of $\sigma_\mathrm{bkgr}$ |
---|
| 1238 | as estimated above. For a more quantitative understanding of these |
---|
| 1239 | curves it is necessary to consider the number of signal and background |
---|
| 1240 | events for neutrinos and antineutrinos separately, as well as to take |
---|
| 1241 | into account spectral information. |
---|
| 1242 | |
---|
| 1243 | |
---|
| 1244 | \begin{figure}[!t] |
---|
| 1245 | \centering |
---|
| 1246 | \includegraphics[width=0.9\textwidth]{./fig12.eps} |
---|
| 1247 | % |
---|
| 1248 | \mycaption{Impact of total exposure and systematical errors on the |
---|
| 1249 | CPV discovery potential of \BB, SPL, and T2HK. We show the |
---|
| 1250 | smallest true value of $\stheta$ for which $\delCP = \pi/2$ can be |
---|
| 1251 | distinguished from $\delCP = 0$ or $\delCP = \pi$ at $3\sigma$ |
---|
| 1252 | $(\Delta\chi^2>9)$ as a function of the exposure in kt~yrs (left) |
---|
| 1253 | and as a function of the systematical error on the background |
---|
| 1254 | $\sigma_\mathrm{bkgr}$ (right). The widths of the curves in the |
---|
| 1255 | left panel corresponds to values of $\sigma_\mathrm{bkgr}$ from 2\% |
---|
| 1256 | to 5\%. The thin solid curves in the left panel corresponds to no |
---|
| 1257 | systematical errors. The right plot is calculated for the standard |
---|
| 1258 | exposure of 4400~kt~yrs. No systematical error on the signal has |
---|
| 1259 | been assumed. \label{fig:systematics}} |
---|
| 1260 | \end{figure} |
---|
| 1261 | |
---|
| 1262 | The left panel of Fig.~\ref{fig:systematics} shows the sensitivity to |
---|
| 1263 | maximal CPV as a function of the exposure\footnote{Note that the CPV |
---|
| 1264 | sensitivity for the \BB\ with reduced fluxes from Fig.~\ref{fig:CPV} |
---|
| 1265 | is worse than the value which follows from Fig.~\ref{fig:systematics}. |
---|
| 1266 | The reason is that in Fig.~\ref{fig:systematics} the total exposure is |
---|
| 1267 | scaled (mass~$\times$~time), i.e., signal and background are scaled in |
---|
| 1268 | the same way, whereas for the dashed curve in Fig.~\ref{fig:CPV} only |
---|
| 1269 | the fluxes are reduced but backgrounds are kept constant.} for values |
---|
| 1270 | of $\sigma_\mathrm{bkgr}$ from 2\% to 5\%. One can observe clearly |
---|
| 1271 | that for the standard exposure of 4400~kt~yrs T2HK is dominated by |
---|
| 1272 | systematics and changing $\sigma_\mathrm{bkgr}$ from 2\% to 5\% has a |
---|
| 1273 | big impact on the sensitivity. In contrast the CERN--MEMPHYS |
---|
| 1274 | experiments (especially the \BB) are rather stable with respect to |
---|
| 1275 | systematics and for the standard exposure they are still statistics |
---|
| 1276 | dominated. We conclude that in T2HK systematics have to be under very |
---|
| 1277 | good control\footnote{As a possible solution to this problem for T2HK |
---|
| 1278 | it has been proposed in Ref.~\cite{Ishitsuka:2005qi} to place one half |
---|
| 1279 | of the Hyper-K detector mass at Kamioka and the second half at the |
---|
| 1280 | same off-axis angle in Korea.}, whereas this issue is less important |
---|
| 1281 | for \BB\ and SPL. |
---|
| 1282 | % |
---|
| 1283 | We have checked explicitly that the systematical error on the signal |
---|
| 1284 | has negligible impact on these results. Therefore, we have set this |
---|
| 1285 | error to zero for calculating Fig.~\ref{fig:systematics} to highlight |
---|
| 1286 | the importance of the background error. In all other calculations also |
---|
| 1287 | the signal error is included, in particular also in Fig.~\ref{fig:CPV}. |
---|
| 1288 | |
---|
| 1289 | |
---|
| 1290 | \begin{figure}[!t] |
---|
| 1291 | \centering |
---|
| 1292 | \includegraphics[width=0.8\textwidth]{./fig13.eps} |
---|
| 1293 | % |
---|
| 1294 | \mycaption{Impact of degeneracies on the CPV discovery potential |
---|
| 1295 | for the \BB. We show the sensitivity to CPV at $3\sigma$ |
---|
| 1296 | $(\Delta\chi^2>9)$ computed for 4 different combinations of the |
---|
| 1297 | true values of the hierarchy (NH or IH) and $\theta_{23}$ |
---|
| 1298 | ($\sin^2\theta_{23} = 0.4$ or $0.6$). Dashed curves are computed |
---|
| 1299 | neglecting degeneracies in the fit.\label{fig:deltacp}} |
---|
| 1300 | \end{figure} |
---|
| 1301 | |
---|
| 1302 | Finally, in Fig.~\ref{fig:deltacp} we illustrate the impact of |
---|
| 1303 | degeneracies, as well as the true hierarchy and \thetatt-octant on the |
---|
| 1304 | CPV sensitivity. Curves of different colors correspond to the four |
---|
| 1305 | different choices for \sigdm\ and the \thetatt-octant of the true |
---|
| 1306 | parameters. For the solid curves the simulated data for each choice of |
---|
| 1307 | true \sigdm\ and \thetatt-octant are fitted by taking into account all |
---|
| 1308 | four degenerate solutions, i.e., also for the fit all four |
---|
| 1309 | combinations of \sigdm\ and \thetatt-octant are used. One observes |
---|
| 1310 | from the figure that the true hierarchy and octant have a rather small |
---|
| 1311 | impact on the \BB\ CPV sensitivity, in particular the sensitivity to |
---|
| 1312 | maximal CPV is completely independent. The main effect of changing the |
---|
| 1313 | true hierarchy is to exchange the behavior between $0 < \delCP < |
---|
| 1314 | 180^\circ$ and $180^\circ < \delCP < 360^\circ$. For $\stheta \lesssim |
---|
| 1315 | 10^{-2}$ the sensitivity gets slightly worse if |
---|
| 1316 | $\thetatt^\mathrm{true} > \pi/4$ compared to $\thetatt^\mathrm{true} < |
---|
| 1317 | \pi/4$. |
---|
| 1318 | |
---|
| 1319 | The dashed curves in Fig.~\ref{fig:deltacp} are computed without |
---|
| 1320 | taking into account the degeneracies, i.e., for each choice of true |
---|
| 1321 | \sigdm\ and \thetatt-octant the data are fitted only with this |
---|
| 1322 | particular choice. The effect of the degeneracies becomes visible for |
---|
| 1323 | large values of \thetaot. Note that this is just the region where they |
---|
| 1324 | can be reduced by a combined analysis with atmospheric neutrinos (see |
---|
| 1325 | Sec.~\ref{sec:atmospherics} or Ref.~\cite{Huber:2005ep}). |
---|
| 1326 | |
---|
| 1327 | |
---|
| 1328 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1329 | \section{Synergies provided by the CERN--MEMPHYS facilities} |
---|
| 1330 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1331 | \label{sec:synergies} |
---|
| 1332 | |
---|
| 1333 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1334 | \subsection{Combining Beta Beam and Super Beam} |
---|
| 1335 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1336 | \label{sec:synergies-beams} |
---|
| 1337 | |
---|
| 1338 | In this section we discuss synergies which emerge if both \BB\ and SPL |
---|
| 1339 | are available. The main difference between these two beams is the |
---|
| 1340 | different initial neutrino flavor, |
---|
| 1341 | $\stackrel{\scriptscriptstyle(-)}{\nu}_e$ for \BB\ and |
---|
| 1342 | $\stackrel{\scriptscriptstyle (-)}{\nu}_\mu$ for SPL. This implies |
---|
| 1343 | that at near detectors all relevant cross sections can be measured. In |
---|
| 1344 | particular, the near detector of the \BB\ will measure the cross |
---|
| 1345 | section for the SPL appearance search, and vice versa. |
---|
| 1346 | % |
---|
| 1347 | If both experiments run with neutrinos and antineutrinos all possible |
---|
| 1348 | transition probabilities are covered: $P_{\nu_e\to\nu_\mu}$, |
---|
| 1349 | $P_{\bar\nu_e\to\bar\nu_\mu}$, $P_{\nu_\mu\to\nu_e}$, and |
---|
| 1350 | $P_{\bar\nu_\mu\to\bar\nu_e}$. Together with the fact that matter |
---|
| 1351 | effects are very small because of the relatively short baseline, this |
---|
| 1352 | means that in addition to CP also direct tests of the T and CPT |
---|
| 1353 | symmetries are possible. |
---|
| 1354 | |
---|
| 1355 | \begin{figure}[!t] |
---|
| 1356 | \centering |
---|
| 1357 | \includegraphics[width=0.9\textwidth]{./fig14.eps} |
---|
| 1358 | % |
---|
| 1359 | \mycaption{Discovery potential of a finite value of $\stheta$ at |
---|
| 1360 | $3\sigma$ $(\Delta\chi^2>9)$ for 5~yrs neutrino data from |
---|
| 1361 | \BB, SPL, and the combination of \BB\ + SPL compared to |
---|
| 1362 | 10~yrs data from T2HK (2~yrs neutrinos + 8~yrs antineutrinos). |
---|
| 1363 | \label{fig:th13-5yrs}} |
---|
| 1364 | \end{figure} |
---|
| 1365 | |
---|
| 1366 | \begin{figure}[!t] |
---|
| 1367 | \centering |
---|
| 1368 | \includegraphics[width=0.6\textwidth]{./fig15.eps} |
---|
| 1369 | % |
---|
| 1370 | \mycaption{Sensitivity to CPV at $3\sigma$ $(\Delta\chi^2>9)$ for |
---|
| 1371 | combining 5~yrs neutrino data from \BB\ and SPL compared to |
---|
| 1372 | 10~yrs data from T2HK (2~yrs neutrinos + 8~yrs antineutrinos). |
---|
| 1373 | \label{fig:CP-5yrs}} |
---|
| 1374 | \end{figure} |
---|
| 1375 | |
---|
| 1376 | However, if the CPT symmetry is assumed in principle all information |
---|
| 1377 | can be obtained just from neutrino data because of the relations |
---|
| 1378 | $P_{\bar\nu_e\to\bar\nu_\mu} = P_{\nu_\mu\to\nu_e}$ and |
---|
| 1379 | $P_{\bar\nu_\mu\to\bar\nu_e} = P_{\nu_e\to\nu_\mu}$. As mentioned |
---|
| 1380 | already in Sec.~\ref{sec:degeneracies} this implies that (time |
---|
| 1381 | consuming) antineutrino running can be avoided. We illustrate this |
---|
| 1382 | synergy in Figs.~\ref{fig:th13-5yrs} and \ref{fig:CP-5yrs}. In |
---|
| 1383 | Fig.~\ref{fig:th13-5yrs} we show the $\theta_{13}$ discovery potential |
---|
| 1384 | of 5 years of neutrino data from \BB\ and SPL. From the left panel the |
---|
| 1385 | complementarity of the two experiments is obvious, since each of them |
---|
| 1386 | is most sensitive in a different region of \delCP. (As expected from |
---|
| 1387 | general properties of the oscillation probabilities the sensitivity |
---|
| 1388 | curves of \BB\ and SPL are approximately related by the transformation |
---|
| 1389 | $\delCP \to 2\pi - \delCP$.) Combining these two data sets results in |
---|
| 1390 | a sensitivity slightly better than from 10 years (2$\nu$+8$\bar\nu$) |
---|
| 1391 | of T2HK data. |
---|
| 1392 | % |
---|
| 1393 | As visible in Fig.~\ref{fig:CP-5yrs} also for the CPV discovery this |
---|
| 1394 | synergy works and 5 years of neutrino data from \BB\ and SPL lead to a |
---|
| 1395 | similar sensitivity as 10 years of T2HK. |
---|
| 1396 | |
---|
| 1397 | |
---|
| 1398 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1399 | \subsection{Resolving degeneracies with atmospheric neutrinos} |
---|
| 1400 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1401 | \label{sec:atmospherics} |
---|
| 1402 | |
---|
| 1403 | It was pointed out in Ref.~\cite{Huber:2005ep} that for LBL |
---|
| 1404 | experiments based on mega ton scale water \v{C}erenkov detectors data |
---|
| 1405 | from atmospheric neutrinos (ATM) provide an attractive method to |
---|
| 1406 | resolve degeneracies. Atmospheric neutrinos are sensitive to the |
---|
| 1407 | neutrino mass hierarchy if $\theta_{13}$ is sufficiently large due to |
---|
| 1408 | Earth matter effects, mainly in multi-GeV $e$-like |
---|
| 1409 | events~\cite{Petcov:1998su,Akhmedov:1998ui,Bernabeu:2003yp}. Moreover, |
---|
| 1410 | sub-GeV $e$-like events provide sensitivity to the octant of |
---|
| 1411 | $\theta_{23}$~\cite{Kim:1998bv,Peres:2003wd,Gonzalez-Garcia:2004cu} |
---|
| 1412 | due to oscillations with $\Delta m^2_{21}$ (see also |
---|
| 1413 | Ref.~\cite{Kajita} for a discussion of atmospheric neutrinos in the |
---|
| 1414 | context of Hyper-K). |
---|
| 1415 | % |
---|
| 1416 | Following Ref.~\cite{Huber:2005ep} we investigate here the synergy |
---|
| 1417 | from a combination of LBL data from \BB\ and SPL with ATM data in the |
---|
| 1418 | MEMPHYS detector. A general three-flavor analysis of ATM data is |
---|
| 1419 | performed based on Ref.~\cite{Gonzalez-Garcia:2004cu} and references |
---|
| 1420 | therein. |
---|
| 1421 | % |
---|
| 1422 | We include fully-contained $e$-like and $\mu$-like events (further |
---|
| 1423 | divided into sub-GeV $p_l<400$~MeV, sub-GeV $p_l > 400$~MeV, and |
---|
| 1424 | Multi-GeV events), partially-contained $\mu$-like events, stopping |
---|
| 1425 | muons, and through-going muons. Each of these data samples is divided |
---|
| 1426 | into 10 zenith bins, so we have a total of 90 data points. The |
---|
| 1427 | simulation of the atmospheric event rates has been adapted to the |
---|
| 1428 | actual geometry of the MEMPHYS detector proposal (see |
---|
| 1429 | Fig.~\ref{fig:MEMPHYS}). Details of the statistical analysis can be |
---|
| 1430 | found in Ref.~\cite{Gonzalez-Garcia:2004wg}. Note that our analysis of |
---|
| 1431 | atmospheric data is conservative, since there is room for improvement |
---|
| 1432 | by including multi-ring events as well as by optimizing the energy |
---|
| 1433 | binning.\footnote{The impact of energy binning on the hierarchy |
---|
| 1434 | determination with atmospheric neutrinos has been discussed recently |
---|
| 1435 | in Ref.~\cite{Petcov:2005rv} in the context of magnetized iron |
---|
| 1436 | detectors.} |
---|
| 1437 | |
---|
| 1438 | \begin{figure}[!t] |
---|
| 1439 | \centering |
---|
| 1440 | \includegraphics[width=0.9\textwidth]{./fig16.eps} |
---|
| 1441 | % |
---|
| 1442 | \mycaption{Sensitivity to the mass hierarchy at $2\sigma$ |
---|
| 1443 | $(\Delta\chi^2 = 4)$ as a function of the true values of |
---|
| 1444 | $\sin^22\theta_{13}$ and $\delta_\mathrm{CP}$ (left), and the |
---|
| 1445 | fraction of true values of $\delCP$ (right). The solid curves are |
---|
| 1446 | the sensitivities from the combination of long-baseline and |
---|
| 1447 | atmospheric neutrino data, the dashed curves correspond to |
---|
| 1448 | long-baseline data only. For comparison we show in the right panel |
---|
| 1449 | also the sensitivities of NO$\nu$A and NO$\nu$A+T2K extracted from |
---|
| 1450 | Fig.~13.14 of Ref.~\cite{Ayres:2004js}. For the curve labeled |
---|
| 1451 | ``NO$\nu$A (p.dr.)+T2K@4~MW'' a proton driver has been assumed for |
---|
| 1452 | NO$\nu$A and the T2K beam has been up-graded to 4~MW, see |
---|
| 1453 | Ref.~\cite{Ayres:2004js} for details.} |
---|
| 1454 | \label{fig:hierarchy} |
---|
| 1455 | \end{figure} |
---|
| 1456 | |
---|
| 1457 | The effect of degeneracies in LBL data has been discussed in |
---|
| 1458 | Sec.~\ref{sec:degeneracies}, see Figs.~\ref{fig:degeneracies} and |
---|
| 1459 | \ref{fig:degeneracies_SPL}. As discussed there, for given true |
---|
| 1460 | parameter values the data can be fitted with the wrong hierarchy |
---|
| 1461 | and/or with the wrong octant of $\theta_{23}$. Hence, from LBL data |
---|
| 1462 | alone the hierarchy and the octant cannot be determined and |
---|
| 1463 | ambiguities exist in the determination of $\theta_{13}$ and |
---|
| 1464 | $\delta_\mathrm{CP}$. |
---|
| 1465 | % |
---|
| 1466 | If the LBL data are combined with ATM data only the colored regions in |
---|
| 1467 | Fig.~\ref{fig:degeneracies} survive, i.e., in this particular example |
---|
| 1468 | for SPL and T2HK the degeneracies are completely lifted at 95\%~CL, |
---|
| 1469 | the mass hierarchy and the octant of $\theta_{23}$ can be identified, |
---|
| 1470 | and the ambiguities in $\theta_{13}$ and $\delta_\mathrm{CP}$ are |
---|
| 1471 | resolved. For the \BB\ an island corresponding to the wrong hierarchy |
---|
| 1472 | does survive at the 95\%~CL for 2~dof. Still, the solution with the |
---|
| 1473 | wrong sign of $\Delta m^2_{31}$ is disfavored with $\Delta\chi^2 = |
---|
| 1474 | 5.1$ with respect to the true solution, which corresponds to |
---|
| 1475 | 2.4$\sigma$ for 1~dof. |
---|
| 1476 | % |
---|
| 1477 | Let us note that in Fig.~\ref{fig:degeneracies} we have chosen a |
---|
| 1478 | favorable value of $\sin^2\theta_{23} = 0.6$; for values |
---|
| 1479 | $\sin^2\theta_{23} < 0.5$ in general the sensitivity of ATM data is |
---|
| 1480 | weaker~\cite{Huber:2005ep}. |
---|
| 1481 | |
---|
| 1482 | In Fig.~\ref{fig:hierarchy} we show how the combination of ATM+LBL |
---|
| 1483 | data leads to a non-trivial sensitivity to the neutrino mass |
---|
| 1484 | hierarchy, i.e.\ to the sign of $\Delta m^2_{31}$. For LBL data alone |
---|
| 1485 | (dashed curves) there is practically no sensitivity for the |
---|
| 1486 | CERN--MEMPHYS experiments (because of the very small matter effects |
---|
| 1487 | due to the relatively short baseline), and the sensitivity of T2HK |
---|
| 1488 | depends strongly on the true value of $\delta_\mathrm{CP}$. However, |
---|
| 1489 | by including data from atmospheric neutrinos (solid curves) the mass |
---|
| 1490 | hierarchy can be identified at $2\sigma$~CL provided |
---|
| 1491 | $\sin^22\theta_{13} \gtrsim 0.03-0.05$ for \BB\ and SPL, and |
---|
| 1492 | $\sin^22\theta_{13} \gtrsim 0.02-0.03$ for T2HK, where for the CERN |
---|
| 1493 | experiments the sensitivity shows somewhat more dependence on the true |
---|
| 1494 | value of $\delta_\mathrm{CP}$. As an example we have chosen in that |
---|
| 1495 | figure a true value of $\theta_{23} = \pi/4$. Generically the |
---|
| 1496 | hierarchy sensitivity increases with increasing $\theta_{23}$, see |
---|
| 1497 | Ref.~\cite{Huber:2005ep} for a detailed discussion. |
---|
| 1498 | |
---|
| 1499 | Although \BB\ and SPL alone have no sensitivity to the hierarchy at |
---|
| 1500 | all, we find that the combination of them does provide rather good |
---|
| 1501 | sensitivity even without atmosheric data. The reason for this |
---|
| 1502 | interesting effect is the following. Because of the rather short |
---|
| 1503 | baseline the matter effect is too small to distinguish between NH and |
---|
| 1504 | IH given only neutrino and antineutrino information in one channel. |
---|
| 1505 | However, the tiny matter effect suffices to move the hierarchy |
---|
| 1506 | degenerate solution to slightly different locations in the ($\stheta$, |
---|
| 1507 | $\delCP$) plane for the $\stackrel{\scriptscriptstyle(-)}{\nu}_e \to |
---|
| 1508 | \stackrel{\scriptscriptstyle (-)}{\nu}_\mu$ (\BB) and |
---|
| 1509 | $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu \to |
---|
| 1510 | \stackrel{\scriptscriptstyle (-)}{\nu}_e$ (SPL) channels (compare |
---|
| 1511 | Fig.~\ref{fig:degeneracies}). Hence, if all four CP and T conjugate |
---|
| 1512 | channels are available (as it is the case for the \BB+SPL combination) |
---|
| 1513 | already the small matter effect picked up allong the 130~km |
---|
| 1514 | CERN--MEMPHYS distance provides sensitivity to the mass hierarchy for |
---|
| 1515 | $\sin^22\theta_{13} \gtrsim 0.03$, or $\sin^22\theta_{13} \gtrsim 0.02$ |
---|
| 1516 | if also atmospheric neutrino data is included. |
---|
| 1517 | |
---|
| 1518 | For comparison we show in the right panel of Fig.~\ref{fig:hierarchy} |
---|
| 1519 | also the sensitivity of the NO$\nu$A~\cite{Ayres:2004js} experiment, |
---|
| 1520 | and of NO$\nu$A+T2K, where in the second case a beam upgrade by a |
---|
| 1521 | proton driver has been assumed for NO$\nu$A, and for T2K the |
---|
| 1522 | Super-Kamiokande detector has been used but the beam intensity has |
---|
| 1523 | been increased by assuming 4~MW power. More details on these |
---|
| 1524 | sensitivities can be found in Ref.~\cite{Ayres:2004js}. |
---|
| 1525 | % |
---|
| 1526 | Let us note that in general LBL experiments with two detectors (or the |
---|
| 1527 | combination of two different LBL experiments) are a competitive method |
---|
| 1528 | to atmospheric neutrinos for the hierarchy determination, see, e.g., |
---|
| 1529 | Refs.~\cite{Ishitsuka:2005qi,MenaRequejo:2005hn,Hagiwara:2005pe} for |
---|
| 1530 | recent analyses. |
---|
| 1531 | % |
---|
| 1532 | We mention also the possibility to determine the neutrino mass |
---|
| 1533 | hierarchy by using neutrino events from a galactic Super Nova |
---|
| 1534 | explosion in mega ton \v{C}erenkov detectors such as MEMPHYS, see, |
---|
| 1535 | e.g., Ref.~\cite{Kachelriess:2004vs}. |
---|
| 1536 | |
---|
| 1537 | \begin{figure}[!t] |
---|
| 1538 | \centering |
---|
| 1539 | \includegraphics[width=0.55\textwidth]{./fig17.eps} |
---|
| 1540 | % |
---|
| 1541 | \mycaption{$\Delta\chi^2$ of the solution with the wrong octant of |
---|
| 1542 | $\theta_{23}$ as a function of the true value of |
---|
| 1543 | $\sin^2\theta_{23}$. We have assumed a true value of $\theta_{13} = |
---|
| 1544 | 0$.} |
---|
| 1545 | \label{fig:octant} |
---|
| 1546 | \end{figure} |
---|
| 1547 | |
---|
| 1548 | Fig.~\ref{fig:octant} shows the potential of ATM+LBL data to exclude |
---|
| 1549 | the octant degenerate solution. Since this effect is based mainly on |
---|
| 1550 | oscillations with $\Delta m^2_{21}$ there is very good sensitivity |
---|
| 1551 | even for $\theta_{13} = 0$; a finite value of $\theta_{13}$ in general |
---|
| 1552 | improves the sensitivity~\cite{Huber:2005ep}. From the figure one can |
---|
| 1553 | read off that atmospheric data alone can can resolve the correct |
---|
| 1554 | octant at $3\sigma$ if $|\sin^2\theta_{23} - 0.5| \gtrsim 0.085$. If |
---|
| 1555 | atmospheric data is combined with the LBL data from SPL or T2HK there |
---|
| 1556 | is sensitivity to the octant for $|\sin^2\theta_{23} - 0.5| \gtrsim |
---|
| 1557 | 0.05$. The improvement of the octant sensitivity with respect to |
---|
| 1558 | previous analyses~\cite{Huber:2005ep,Gonzalez-Garcia:2004cu} follows |
---|
| 1559 | from changes in the analysis of sub-GeV atmospheric events, where now |
---|
| 1560 | three bins {\bf *** to be confirmed ***} in lepton momentum are used |
---|
| 1561 | instead of one. Note that since in Fig.~\ref{fig:octant} we have |
---|
| 1562 | assumed a true value of $\theta_{13} = 0$, combining the \BB\ with ATM |
---|
| 1563 | does not improve the sensitivity with respect to atmospheric data |
---|
| 1564 | alone. |
---|
| 1565 | |
---|
| 1566 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1567 | \section{Summary} |
---|
| 1568 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
| 1569 | \label{sec:conclusions} |
---|
| 1570 | |
---|
| 1571 | In this work we have studied the physics potential of the |
---|
| 1572 | CERN--MEMPHYS neutrino oscillation project. We consider a Beta Beam |
---|
| 1573 | (\BB) with $\gamma = 100$ for the stored ions, where existing |
---|
| 1574 | facilities at CERN can be used optimally, and a Super Beam based on an |
---|
| 1575 | optimized Super Proton Linac (SPL) with a beam energy of 3.5~GeV and |
---|
| 1576 | 4~MW power. As target we assume the MEMPHYS detector, a 440~kt water |
---|
| 1577 | \v{C}erenkov detector at Fr\'ejus, at a distance of 130~km from |
---|
| 1578 | CERN. The main characteristics of the experiments are summarized in |
---|
| 1579 | Tab.~\ref{tab:setups}. |
---|
| 1580 | % |
---|
| 1581 | The adopted neutrino fluxes are based on realistic calculations of ion |
---|
| 1582 | production and storage for the \BB, and a full simulation of the beam |
---|
| 1583 | line (particle production and decay of secondaries) for SPL. Special |
---|
| 1584 | care has be given to the issue of backgrounds, which we include by |
---|
| 1585 | means of detailed event simulations and applying Super-Kamiokande particle |
---|
| 1586 | identification algorithms. |
---|
| 1587 | |
---|
| 1588 | The physics potential of the \BB\ and SPL experiments in terms of |
---|
| 1589 | $\theta_{13}$ discovery reach and sensitivity to CP violation has been |
---|
| 1590 | addressed where parameter degeneracies are fully taken into account. |
---|
| 1591 | The main results on these performance indicators are summarized in |
---|
| 1592 | Figs.~\ref{fig:th13} and \ref{fig:CPV}. |
---|
| 1593 | % |
---|
| 1594 | We obtain a guaranteed discovery reach of $\stheta \simeq 5\times |
---|
| 1595 | 10^{-3}$ at $3\sigma$, irrespective of the actual value of \delCP. For |
---|
| 1596 | certain values of \delCP\ the sensitivity is significantly improved, |
---|
| 1597 | and for \BB\ (SPL) discovery limits arround $\stheta \simeq 3\,(10) |
---|
| 1598 | \times 10^{-4}$ are possible for a large fraction of all possible |
---|
| 1599 | values of \delCP. |
---|
| 1600 | % |
---|
| 1601 | Maximal CP violation (for $\delCP^\mathrm{true} = \pi/2, \, 3\pi/2$) |
---|
| 1602 | can be discovered at $3\sigma$ down to $\stheta \simeq 2\, (9)\times |
---|
| 1603 | 10^{-4}$ for \BB\ (SPL), whereas the best sensitivity to CP violation |
---|
| 1604 | is obtained for $\stheta \sim 10^{-2}$: For $\stheta = 10^{-2}$ CP |
---|
| 1605 | violation can be established at $3\sigma$ for 78\% (73\%) of all |
---|
| 1606 | possible true values of \delCP\ for \BB\ (SPL). |
---|
| 1607 | % |
---|
| 1608 | We stress that the \BB\ performance in general depends crucially on |
---|
| 1609 | the number of ion decays per year. |
---|
| 1610 | % |
---|
| 1611 | The impact of the value of systematical uncertainties on signal and |
---|
| 1612 | background on our results is discussed. |
---|
| 1613 | % |
---|
| 1614 | The \BB\ and SPL sensitivities are compared to the ones of the |
---|
| 1615 | phase~II of the T2K experiment in Japan (T2HK), which is a competing |
---|
| 1616 | proposal of similar size and timescale. In general we obtain rather |
---|
| 1617 | similar sensitivities for T2HK and SPL, and hence the CERN--MEMPHYS |
---|
| 1618 | experiments provide a viable alternative to T2HK. We find that \BB\ |
---|
| 1619 | and SPL are less sensitive to systematical errors, whereas the |
---|
| 1620 | sensitivity of T2HK crucially depends on the systematical error on the |
---|
| 1621 | background.\footnote{Let us note that in the present study we have not |
---|
| 1622 | considered the recent ``T2KK'' proposal~\cite{Ishitsuka:2005qi}, where |
---|
| 1623 | one half of the Hyper-K detector mass is at Kamioka and the second |
---|
| 1624 | half in Korea. For such a setup our results do not apply and |
---|
| 1625 | especially the conclusion on systematical errors may be different.} |
---|
| 1626 | |
---|
| 1627 | Assuming that both \BB\ and SPL experiments are available, we point |
---|
| 1628 | out that one can benefit from the different oscillation channels |
---|
| 1629 | $\nu_e\to\nu_\mu$ for \BB\ and $\nu_\mu\to\nu_e$ for SPL, since by the |
---|
| 1630 | combination of these channels the time intensive antineutrino |
---|
| 1631 | measurements can be avoided. We show that 5 years of neutrino data from |
---|
| 1632 | \BB\ and SPL lead to similar results as 2 years of neutrino plus 8 |
---|
| 1633 | years of antineutrino data from T2HK. |
---|
| 1634 | % |
---|
| 1635 | Furthermore, we discuss the use of atmospheric neutrinos in the |
---|
| 1636 | MEMPHYS detector to resolve parameter degeneracies in the |
---|
| 1637 | long-baseline data. This effect leads to a sensitivity to the neutrino |
---|
| 1638 | mass hierarchy at $2\sigma$~CL for $\sin^22\theta_{13} \gtrsim |
---|
| 1639 | 0.03-0.05$ for \BB\ and SPL, although these experiments alone (without |
---|
| 1640 | atmospheric data) have no sensitivity at all. The optimal hierarchy |
---|
| 1641 | sensitivity is obtained from combining \BB+SPL+atmospheric data. |
---|
| 1642 | Furthermore, the combination of atmospheric data with a Super Beam |
---|
| 1643 | provides a possibility to determine the octant of $\theta_{23}$. |
---|
| 1644 | |
---|
| 1645 | To conclude, we have shown that the CERN--MEMPHYS neutrino oscillation |
---|
| 1646 | project based on a Beta Beam and/or a Super Beam plus a mega ton scale |
---|
| 1647 | water \v{C}erenkov detector offers interesting and competitive physics |
---|
| 1648 | possibilities and is worth to be considered as a serious option in |
---|
| 1649 | the worldwide process of identifying future high precision neutrino |
---|
| 1650 | oscillation facilities~\cite{ISSpage}. |
---|
| 1651 | |
---|
| 1652 | \subsection*{Acknowledgment} |
---|
| 1653 | |
---|
| 1654 | We thank J.~Argyriades for communication on the Super-K atmospheric |
---|
| 1655 | neutrino analysis, A.~Cazes for his work on the SPL simulation, and |
---|
| 1656 | P.~Huber for his patience in answering questions concerning the use of |
---|
| 1657 | GLoBES. T.S.\ is supported by the $6^\mathrm{th}$~Framework Program |
---|
| 1658 | of the European Community under a Marie Curie Intra-European |
---|
| 1659 | Fellowship. |
---|
| 1660 | |
---|
| 1661 | |
---|
| 1662 | %\newpage |
---|
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| 1809 | %``Super beams,'' |
---|
| 1810 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 143} (2005) 303. |
---|
| 1811 | %%CITATION = NUPHZ,143,303;%% |
---|
| 1812 | |
---|
| 1813 | \bibitem{Ayres:2004js} |
---|
| 1814 | D.~S.~Ayres {\it et al.} [NOvA Coll.], |
---|
| 1815 | %``NOvA proposal to build a 30-kiloton off-axis detector to study neutrino |
---|
| 1816 | %oscillations in the Fermilab NuMI beamline,'' |
---|
| 1817 | hep-ex/0503053. |
---|
| 1818 | %%CITATION = HEP-EX 0503053;%% |
---|
| 1819 | |
---|
| 1820 | \bibitem{Huber:2003pm} |
---|
| 1821 | P.~Huber, M.~Lindner, T.~Schwetz and W.~Winter, |
---|
| 1822 | %``Reactor neutrino experiments compared to superbeams,'' |
---|
| 1823 | Nucl.\ Phys.\ B {\bf 665} (2003) 487 |
---|
| 1824 | [hep-ph/0303232]; |
---|
| 1825 | %%CITATION = HEP-PH 0303232;%% |
---|
| 1826 | % |
---|
| 1827 | %\bibitem{Huber:2004ug} |
---|
| 1828 | P.~Huber, M.~Lindner, M.~Rolinec, T.~Schwetz and W.~Winter, |
---|
| 1829 | %``Prospects of accelerator and reactor neutrino oscillation experiments for |
---|
| 1830 | %the coming ten years,'' |
---|
| 1831 | Phys.\ Rev.\ D {\bf 70} (2004) 073014 |
---|
| 1832 | [hep-ph/0403068]. |
---|
| 1833 | %%CITATION = HEP-PH 0403068;%% |
---|
| 1834 | |
---|
| 1835 | \bibitem{Albrow:2005kw} |
---|
| 1836 | M.~G.~Albrow {\it et al.}, |
---|
| 1837 | Physics at a Fermilab proton driver, |
---|
| 1838 | hep-ex/0509019. |
---|
| 1839 | %%CITATION = HEP-EX 0509019;%% |
---|
| 1840 | |
---|
| 1841 | \bibitem{SPL} |
---|
| 1842 | %\bibitem{Autin:2000mn} |
---|
| 1843 | B.~Autin {\it et al.}, |
---|
| 1844 | Conceptual design of the SPL, a high-power superconducting H- linac at |
---|
| 1845 | CERN, CERN-2000-012. |
---|
| 1846 | |
---|
| 1847 | \bibitem{BNLHS} |
---|
| 1848 | %\bibitem{Diwan:2003bp} |
---|
| 1849 | M.~V.~Diwan {\it et al.}, |
---|
| 1850 | %``Very long baseline neutrino oscillation experiments for precise |
---|
| 1851 | %measurements of mixing parameters and CP violating effects,'' |
---|
| 1852 | Phys.\ Rev.\ D {\bf 68} (2003) 012002 |
---|
| 1853 | [hep-ph/0303081]. |
---|
| 1854 | %%CITATION = HEP-PH 0303081;%% |
---|
| 1855 | |
---|
| 1856 | \bibitem{zucchelli} |
---|
| 1857 | %\bibitem{Zucchelli:2002sa} |
---|
| 1858 | P.~Zucchelli, |
---|
| 1859 | %``A novel concept for a anti-nu/e / nu/e neutrino factory: The Beta Beam,'' |
---|
| 1860 | Phys.\ Lett.\ B {\bf 532} (2002) 166. |
---|
| 1861 | %%CITATION = PHLTA,B532,166;%% |
---|
| 1862 | |
---|
| 1863 | \bibitem{Albright:2004iw} |
---|
| 1864 | C.~Albright {\it et al.} [Neutrino Factory/Muon Collider Coll.], |
---|
| 1865 | %``The neutrino factory and Beta Beam experiments and development,'' |
---|
| 1866 | physics/0411123. |
---|
| 1867 | %%CITATION = PHYS-ICS 0411123;%% |
---|
| 1868 | |
---|
| 1869 | \bibitem{Blondel:2004ae} |
---|
| 1870 | A.~Blondel {\it et al.}, |
---|
| 1871 | ECFA/CERN studies of a European neutrino factory complex, |
---|
| 1872 | CERN-2004-002 |
---|
| 1873 | |
---|
| 1874 | \bibitem{Campagne:2004wt} |
---|
| 1875 | J.~E.~Campagne and A.~Cazes, |
---|
| 1876 | %``The theta(13) and delta(CP) sensitivities of the SPL-Frejus project |
---|
| 1877 | %revisited,'' |
---|
| 1878 | Eur.\ Phys.\ J.\ C {\bf 45} (2006) 643 |
---|
| 1879 | [hep-ex/0411062]. |
---|
| 1880 | %%CITATION = HEP-EX 0411062;%% |
---|
| 1881 | |
---|
| 1882 | \bibitem{Mezzetto:2003ub} |
---|
| 1883 | M.~Mezzetto, |
---|
| 1884 | %``Physics reach of the beta beam,'' |
---|
| 1885 | J.\ Phys.\ G {\bf 29} (2003) 1771 |
---|
| 1886 | [hep-ex/0302007]; |
---|
| 1887 | %%CITATION = HEP-EX 0302007;%% |
---|
| 1888 | % |
---|
| 1889 | J.~Bouchez, M.~Lindroos, M.~Mezzetto, |
---|
| 1890 | %``Beta Beams: Present design and expected performances,'' |
---|
| 1891 | AIP Conf.\ Proc.\ {\bf 721} (2004) 37 |
---|
| 1892 | [hep-ex/0310059]. |
---|
| 1893 | %%CITATION = HEP-EX 0310059;%% |
---|
| 1894 | |
---|
| 1895 | \bibitem{memphys} |
---|
| 1896 | A.~de Bellefon {\it et al.}, |
---|
| 1897 | MEMPHYS: A large scale water \v{C}erenkov detector |
---|
| 1898 | at Fr\'ejus, Contribution to the CERN strategic committee,\\ |
---|
| 1899 | \verb!http://apc-p7.org/APC_CS/Experiences/MEMPHYS/! |
---|
| 1900 | |
---|
| 1901 | \bibitem{UNO} |
---|
| 1902 | C.~K.~Jung, |
---|
| 1903 | Feasibility of a next generation underground water Cherenkov detector: |
---|
| 1904 | UNO, hep-ex/0005046. |
---|
| 1905 | %%CITATION = HEP-EX 0005046;%% |
---|
| 1906 | |
---|
| 1907 | \bibitem{Nakamura:2003hk} |
---|
| 1908 | K.~Nakamura, |
---|
| 1909 | %``Hyper-Kamiokande: A next generation water Cherenkov detector,'' |
---|
| 1910 | Int.\ J.\ Mod.\ Phys.\ A {\bf 18} (2003) 4053. |
---|
| 1911 | %%CITATION = IMPAE,A18,4053;%% |
---|
| 1912 | |
---|
| 1913 | \bibitem{Huber:2005ep} |
---|
| 1914 | P.~Huber, M.~Maltoni, T.~Schwetz, |
---|
| 1915 | %``Resolving parameter degeneracies in long-baseline experiments by |
---|
| 1916 | %atmospheric neutrino data,'' |
---|
| 1917 | Phys.\ Rev.\ D {\bf 71} (2005) 053006 |
---|
| 1918 | [hep-ph/0501037]. |
---|
| 1919 | %%CITATION = HEP-PH 0501037;%% |
---|
| 1920 | |
---|
| 1921 | \bibitem{Globes} |
---|
| 1922 | P.~Huber, M.~Lindner and W.~Winter, |
---|
| 1923 | %``Simulation of long-baseline neutrino oscillation experiments with |
---|
| 1924 | %GLoBES,'' |
---|
| 1925 | Comput.\ Phys.\ Commun.\ {\bf 167} (2005) 195 |
---|
| 1926 | [hep-ph/0407333], |
---|
| 1927 | \verb!http://www.ph.tum.de/~globes! |
---|
| 1928 | |
---|
| 1929 | \bibitem{Huber:2002mx} |
---|
| 1930 | P.~Huber, M.~Lindner and W.~Winter, |
---|
| 1931 | %``Superbeams versus neutrino factories,'' |
---|
| 1932 | Nucl.\ Phys.\ B {\bf 645} (2002) 3 |
---|
| 1933 | [hep-ph/0204352]. |
---|
| 1934 | %%CITATION = HEP-PH 0204352;%% |
---|
| 1935 | |
---|
| 1936 | \bibitem{Nuance} |
---|
| 1937 | NUANCE event generator (v3), |
---|
| 1938 | \verb!http://nuint.ps.uci.edu/nuance/!, |
---|
| 1939 | D.~Casper, |
---|
| 1940 | %``The nuance neutrino physics simulation, and the future,'' |
---|
| 1941 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 112} (2002) 161 |
---|
| 1942 | [hep-ph/0208030]. |
---|
| 1943 | |
---|
| 1944 | \bibitem{ISSpage} |
---|
| 1945 | Webpage of the International Scoping Study physics working group:\\ |
---|
| 1946 | \verb!http://www.hep.ph.ic.ac.uk/iss/wg1-phys-phen/index.html! |
---|
| 1947 | |
---|
| 1948 | \bibitem{MyNufact04} |
---|
| 1949 | M.~Mezzetto, |
---|
| 1950 | %``SPL and Beta Beams to the Frejus,'' |
---|
| 1951 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 149} (2005) 179. |
---|
| 1952 | |
---|
| 1953 | \bibitem{Donini:2004hu} |
---|
| 1954 | A.~Donini, E.~Fernandez-Martinez, P.~Migliozzi, S.~Rigolin and L.~Scotto Lavina, |
---|
| 1955 | %``Study of the eightfold degeneracy with a standard beta-beam and a |
---|
| 1956 | %super-beam facility,'' |
---|
| 1957 | Nucl.\ Phys.\ B {\bf 710}, 402 (2005) |
---|
| 1958 | [hep-ph/0406132]. |
---|
| 1959 | %%CITATION = HEP-PH 0406132;%% |
---|
| 1960 | |
---|
| 1961 | \bibitem{JJHigh2} |
---|
| 1962 | %\bibitem{Burguet-Castell:2005pa} |
---|
| 1963 | J.~Burguet-Castell, D.~Casper, E.~Couce, J.~J.~Gomez-Cadenas and P.~Hernandez, |
---|
| 1964 | %``Optimal beta-beam at the CERN-SPS,'' |
---|
| 1965 | Nucl.\ Phys.\ B {\bf 725} (2005) 306 |
---|
| 1966 | [hep-ph/0503021]. |
---|
| 1967 | %%CITATION = HEP-PH 0503021;%% |
---|
| 1968 | |
---|
| 1969 | \bibitem{LindnerBB} |
---|
| 1970 | %\bibitem{Huber:2005jk} |
---|
| 1971 | P.~Huber, M.~Lindner, M.~Rolinec and W.~Winter, |
---|
| 1972 | %``Physics and optimization of beta-beams: From low to very high gamma,'' |
---|
| 1973 | hep-ph/0506237. |
---|
| 1974 | %%CITATION = HEP-PH 0506237;%% |
---|
| 1975 | |
---|
| 1976 | \bibitem{JJHigh1} |
---|
| 1977 | J.~Burguet-Castell, D.~Casper, J.~J.~Gomez-Cadenas, P.~Hernandez and F.~Sanchez, |
---|
| 1978 | Nucl.\ Phys.\ B {\bf 695} (2004) 217 |
---|
| 1979 | [hep-ph/0312068]. |
---|
| 1980 | |
---|
| 1981 | \bibitem{Terranova} |
---|
| 1982 | F.~Terranova, A.~Marotta, P.~Migliozzi and M.~Spinetti, |
---|
| 1983 | %``High energy beta beams without massive detectors,'' |
---|
| 1984 | Eur.\ Phys.\ J.\ C {\bf 38}, 69 (2004) |
---|
| 1985 | [hep-ph/0405081]. |
---|
| 1986 | %%CITATION = HEP-PH 0405081;%% |
---|
| 1987 | |
---|
| 1988 | \bibitem{BB-Reviews} |
---|
| 1989 | M.~Mezzetto, %``Beta Beams,'' |
---|
| 1990 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 143} (2005) 309 |
---|
| 1991 | [hep-ex/0410083]; |
---|
| 1992 | % |
---|
| 1993 | C.~Volpe, |
---|
| 1994 | %``Topical review on 'beta-beams','' |
---|
| 1995 | hep-ph/0605033. |
---|
| 1996 | |
---|
| 1997 | \bibitem{Volpe} |
---|
| 1998 | C.~Volpe, |
---|
| 1999 | %``What about a Beta Beam facility for low energy neutrinos?,'' |
---|
| 2000 | J.\ Phys.\ G {\bf 30} (2004) L1 |
---|
| 2001 | [hep-ph/0303222]. |
---|
| 2002 | |
---|
| 2003 | \bibitem{Lindroos} |
---|
| 2004 | %\bibitem{Autin:2002ms} |
---|
| 2005 | B.~Autin {\it et al.}, |
---|
| 2006 | %``The acceleration and storage of radioactive ions for a neutrino factory,'' |
---|
| 2007 | J.\ Phys.\ G {\bf 29}, 1785 (2003) |
---|
| 2008 | [physics/0306106]; |
---|
| 2009 | %%CITATION = PHYS-ICS 0306106;%% |
---|
| 2010 | % |
---|
| 2011 | M.~Benedikt, S.~Hancock and M.~Lindroos, |
---|
| 2012 | % ``Baseline Design for a Beta-Beam Neutrino Factory'', |
---|
| 2013 | Proceedings of EPAC, 2004, |
---|
| 2014 | \verb!http://accelconf.web.cern.ch/AccelConf/e04!; |
---|
| 2015 | % |
---|
| 2016 | M.~Lindroos, EURISOL DS/TASK12/TN-05-02. |
---|
| 2017 | |
---|
| 2018 | \bibitem{Eurisol} |
---|
| 2019 | Eurisol Beta Beam webpage: \verb!http://beta-beam.web.cern.ch/beta-beam/!. |
---|
| 2020 | |
---|
| 2021 | \bibitem{Lindroos-Optimization} |
---|
| 2022 | M.~Benedikt, A.~Fabich, S.~Hancock and M.~Lindroos, |
---|
| 2023 | %``Optimization Of The Beta-Beam Baseline,'' |
---|
| 2024 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 155} (2006) 211. |
---|
| 2025 | |
---|
| 2026 | \bibitem{Neugen} |
---|
| 2027 | The NEUGEN neutrino event generator, |
---|
| 2028 | \verb!http://minos.phy.tufts.edu/gallag/neugen/!. |
---|
| 2029 | |
---|
| 2030 | \bibitem{MezzettoNuFact05} |
---|
| 2031 | M.~Mezzetto, |
---|
| 2032 | %``Physics potential of the gamma = 100,100 beta beam,'' |
---|
| 2033 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 155} (2006) 214 |
---|
| 2034 | [hep-ex/0511005]. |
---|
| 2035 | |
---|
| 2036 | \bibitem{FLUKA} |
---|
| 2037 | A.~Fasso \etal, Proceedings of the MonteCarlo 2000 conference, |
---|
| 2038 | Lisbon, October 26 2000, |
---|
| 2039 | A.~Kling \etal\ (eds.), Springer-Verlag Berlin (2001), 159-164 and 955-960. |
---|
| 2040 | |
---|
| 2041 | \bibitem{GEANT} |
---|
| 2042 | Application Software group, Computing and Network Division \etal, |
---|
| 2043 | GEANT Description and Simulation Tool, CERN Geneva, Switzerland |
---|
| 2044 | |
---|
| 2045 | \bibitem{HARP-MINERVA} |
---|
| 2046 | C. Catanesi \etal\ [HARP Coll.], CERN-SPSC 2002/019; |
---|
| 2047 | % |
---|
| 2048 | %\bibitem{Drakoulakos:2004gn} |
---|
| 2049 | D.~Drakoulakos {\it et al.} [Minerva Coll.], |
---|
| 2050 | %``Proposal to perform a high-statistics neutrino scattering experiment using |
---|
| 2051 | %a fine-grained detector in the NuMI beam,'' |
---|
| 2052 | hep-ex/0405002. |
---|
| 2053 | %%CITATION = HEP-EX 0405002;%% |
---|
| 2054 | |
---|
| 2055 | \bibitem{Mezzetto:2003mm} |
---|
| 2056 | M.~Mezzetto, |
---|
| 2057 | %``Physics potential of the SPL super beam,'' |
---|
| 2058 | J.\ Phys.\ G {\bf 29}, 1781 (2003) |
---|
| 2059 | [hep-ex/0302005]. |
---|
| 2060 | %%CITATION = HEP-EX 0302005;%% |
---|
| 2061 | |
---|
| 2062 | \bibitem{Burguet-Castell:2001ez} |
---|
| 2063 | J.~Burguet-Castell, M.~B.~Gavela, J.~J.~Gomez-Cadenas, P.~Hernandez and O.~Mena, |
---|
| 2064 | %``On the measurement of leptonic CP violation,'' |
---|
| 2065 | Nucl.\ Phys.\ B {\bf 608} (2001) 301 |
---|
| 2066 | [hep-ph/0103258]. |
---|
| 2067 | %%CITATION = HEP-PH 0103258;%% |
---|
| 2068 | |
---|
| 2069 | \bibitem{Minakata:2001qm} |
---|
| 2070 | H.~Minakata and H.~Nunokawa, |
---|
| 2071 | %``Exploring neutrino mixing with low energy superbeams,'' |
---|
| 2072 | JHEP {\bf 0110}, 001 (2001) |
---|
| 2073 | [hep-ph/0108085]. |
---|
| 2074 | %%CITATION = HEP-PH 0108085;%% |
---|
| 2075 | |
---|
| 2076 | \bibitem{Fogli:1996pv} |
---|
| 2077 | G.~L.~Fogli and E.~Lisi, |
---|
| 2078 | %``Tests of three-flavor mixing in long-baseline neutrino oscillation |
---|
| 2079 | %experiments,'' |
---|
| 2080 | Phys.\ Rev.\ D {\bf 54}, 3667 (1996) |
---|
| 2081 | [hep-ph/9604415]. |
---|
| 2082 | %%CITATION = HEP-PH 9604415;%% |
---|
| 2083 | |
---|
| 2084 | \bibitem{Barger:2001yr} |
---|
| 2085 | V.~Barger, D.~Marfatia and K.~Whisnant, |
---|
| 2086 | %``Breaking eight-fold degeneracies in neutrino CP violation, mixing, and |
---|
| 2087 | %mass hierarchy,'' |
---|
| 2088 | Phys.\ Rev.\ D {\bf 65}, 073023 (2002) |
---|
| 2089 | [hep-ph/0112119]. |
---|
| 2090 | %%CITATION = HEP-PH 0112119;%% |
---|
| 2091 | |
---|
| 2092 | \bibitem{Yasuda:2004gu} |
---|
| 2093 | O.~Yasuda, |
---|
| 2094 | %``New plots and parameter degeneracies in neutrino oscillations,'' |
---|
| 2095 | New J.\ Phys.\ {\bf 6}, 83 (2004) |
---|
| 2096 | [hep-ph/0405005]. |
---|
| 2097 | %%CITATION = HEP-PH 0405005;%% |
---|
| 2098 | |
---|
| 2099 | \bibitem{Ishitsuka:2005qi} |
---|
| 2100 | M.~Ishitsuka, T.~Kajita, H.~Minakata and H.~Nunokawa, |
---|
| 2101 | %``Resolving neutrino mass hierarchy and CP degeneracy by two identical |
---|
| 2102 | %detectors with different baselines,'' |
---|
| 2103 | Phys.\ Rev.\ D {\bf 72} (2005) 033003 |
---|
| 2104 | [hep-ph/0504026]. |
---|
| 2105 | %%CITATION = HEP-PH 0504026;%% |
---|
| 2106 | |
---|
| 2107 | \bibitem{Antusch:2004yx} |
---|
| 2108 | S.~Antusch, P.~Huber, J.~Kersten, T.~Schwetz and W.~Winter, |
---|
| 2109 | %``Is there maximal mixing in the lepton sector?,'' |
---|
| 2110 | Phys.\ Rev.\ D {\bf 70}, 097302 (2004) |
---|
| 2111 | [hep-ph/0404268]. |
---|
| 2112 | %%CITATION = HEP-PH 0404268;%% |
---|
| 2113 | |
---|
| 2114 | \bibitem{Minakata:2004pg} |
---|
| 2115 | H.~Minakata, M.~Sonoyama and H.~Sugiyama, |
---|
| 2116 | %``Determination of theta(23) in long-baseline neutrino oscillation |
---|
| 2117 | %experiments with three-flavor mixing effects,'' |
---|
| 2118 | Phys.\ Rev.\ D {\bf 70} (2004) 113012 |
---|
| 2119 | [hep-ph/0406073]. |
---|
| 2120 | %%CITATION = HEP-PH 0406073;%% |
---|
| 2121 | |
---|
| 2122 | \bibitem{Donini:2005db} |
---|
| 2123 | A.~Donini, E.~Fernandez-Martinez, D.~Meloni and S.~Rigolin, |
---|
| 2124 | %``nu/mu disappearance at the SPL, T2K-I, NOnuA and the neutrino factory,'' |
---|
| 2125 | hep-ph/0512038. |
---|
| 2126 | %%CITATION = HEP-PH 0512038;%% |
---|
| 2127 | |
---|
| 2128 | \bibitem{Peres:2003wd} |
---|
| 2129 | O.L.G.~Peres, A.Y.~Smirnov, |
---|
| 2130 | %``Atmospheric neutrinos: LMA oscillations, U(e3) induced interference and |
---|
| 2131 | %CP-violation,'' |
---|
| 2132 | Nucl.\ Phys.\ B {\bf 680} (2004) 479 |
---|
| 2133 | [hep-ph/0309312]. |
---|
| 2134 | %%CITATION = HEP-PH 0309312;%% |
---|
| 2135 | |
---|
| 2136 | \bibitem{Gonzalez-Garcia:2004cu} |
---|
| 2137 | M.C.~Gonzalez-Garcia, M.~Maltoni, A.Y. Smirnov, |
---|
| 2138 | %``Measuring the deviation of the 2-3 lepton mixing from maximal with |
---|
| 2139 | %atmospheric neutrinos,'' |
---|
| 2140 | Phys.\ Rev.\ D {\bf 70} (2004) 093005 |
---|
| 2141 | [hep-ph/0408170]. |
---|
| 2142 | %%CITATION = HEP-PH 0408170;%% |
---|
| 2143 | |
---|
| 2144 | \bibitem{Petcov:1998su} |
---|
| 2145 | S.~T.~Petcov, |
---|
| 2146 | %``Diffractive-like (or parametric-resonance-like?) enhancement of the earth |
---|
| 2147 | %(day-night) effect for solar neutrinos crossing the earth core,'' |
---|
| 2148 | Phys.\ Lett.\ B {\bf 434} (1998) 321 |
---|
| 2149 | [hep-ph/9805262]; |
---|
| 2150 | %%CITATION = HEP-PH 9805262;%% |
---|
| 2151 | % |
---|
| 2152 | %\bibitem{Chizhov:1998ug} |
---|
| 2153 | M.~Chizhov, M.~Maris and S.~T.~Petcov, |
---|
| 2154 | %``On the oscillation length resonance in the transitions of solar and |
---|
| 2155 | %atmospheric neutrinos crossing the earth core,'' |
---|
| 2156 | hep-ph/9810501; |
---|
| 2157 | %%CITATION = HEP-PH 9810501;%% |
---|
| 2158 | % |
---|
| 2159 | %\bibitem{Chizhov:1999az} |
---|
| 2160 | M.~V.~Chizhov and S.~T.~Petcov, |
---|
| 2161 | %``New conditions for a total neutrino conversion in a medium,'' |
---|
| 2162 | Phys.\ Rev.\ Lett.\ {\bf 83} (1999) 1096 |
---|
| 2163 | [hep-ph/9903399]. |
---|
| 2164 | %%CITATION = HEP-PH 9903399;%% |
---|
| 2165 | |
---|
| 2166 | \bibitem{Akhmedov:1998ui} |
---|
| 2167 | E.~K.~Akhmedov, |
---|
| 2168 | %``Parametric resonance of neutrino oscillations and passage of solar and |
---|
| 2169 | %atmospheric neutrinos through the earth,'' |
---|
| 2170 | Nucl.\ Phys.\ B {\bf 538}, 25 (1999) |
---|
| 2171 | [hep-ph/9805272]; |
---|
| 2172 | %%CITATION = HEP-PH 9805272;%% |
---|
| 2173 | % |
---|
| 2174 | %\bibitem{Akhmedov:1998xq} |
---|
| 2175 | E.~K.~Akhmedov, A.~Dighe, P.~Lipari and A.~Y.~Smirnov, |
---|
| 2176 | %``Atmospheric neutrinos at Super-Kamiokande and parametric resonance in |
---|
| 2177 | %neutrino oscillations,'' |
---|
| 2178 | Nucl.\ Phys.\ B {\bf 542}, 3 (1999) |
---|
| 2179 | [hep-ph/9808270]. |
---|
| 2180 | %%CITATION = HEP-PH 9808270;%% |
---|
| 2181 | |
---|
| 2182 | \bibitem{Bernabeu:2003yp} |
---|
| 2183 | J.~Bernabeu, S.~Palomares-Ruiz and S.~T.~Petcov, |
---|
| 2184 | %``Atmospheric neutrino oscillations, theta(13) and neutrino mass |
---|
| 2185 | %hierarchy,'' |
---|
| 2186 | Nucl.\ Phys.\ B {\bf 669}, 255 (2003) |
---|
| 2187 | [hep-ph/0305152]. |
---|
| 2188 | %%CITATION = HEP-PH 0305152;%% |
---|
| 2189 | |
---|
| 2190 | \bibitem{Kim:1998bv} |
---|
| 2191 | C.~W.~Kim and U.~W.~Lee, |
---|
| 2192 | %``Comment on the possible electron-neutrino excess in the Super-Kamiokande |
---|
| 2193 | %atmospheric neutrino experiment,'' |
---|
| 2194 | Phys.\ Lett.\ B {\bf 444}, 204 (1998) |
---|
| 2195 | [hep-ph/9809491]. |
---|
| 2196 | %%CITATION = HEP-PH 9809491;%% |
---|
| 2197 | |
---|
| 2198 | \bibitem{Kajita} |
---|
| 2199 | T.~Kajita, Talk at NNN05, 7--9 April 2005, Aussois, Savoie, France,\\ |
---|
| 2200 | \verb!http://nnn05.in2p3.fr/! |
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| 2201 | |
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| 2202 | \bibitem{Gonzalez-Garcia:2004wg} |
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| 2203 | M.~C.~Gonzalez-Garcia and M.~Maltoni, |
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| 2204 | %``Atmospheric neutrino oscillations and new physics,'' |
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| 2205 | Phys.\ Rev.\ D {\bf 70} (2004) 033010 |
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| 2206 | [hep-ph/0404085]. |
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| 2207 | %%CITATION = HEP-PH 0404085;%% |
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| 2208 | |
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| 2209 | \bibitem{Petcov:2005rv} |
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| 2210 | S.~T.~Petcov and T.~Schwetz, |
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| 2211 | %``Determining the neutrino mass hierarchy with atmospheric neutrinos,'' |
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| 2212 | Nucl.\ Phys.\ B {\bf 740}, 1 (2006) |
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| 2213 | [hep-ph/0511277]. |
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| 2214 | %%CITATION = HEP-PH 0511277;%% |
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| 2215 | |
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| 2216 | \bibitem{MenaRequejo:2005hn} |
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| 2217 | O.~Mena-Requejo, S.~Palomares-Ruiz and S.~Pascoli, |
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| 2218 | %``Super-NOvA: A long-baseline neutrino experiment with two off-axis |
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| 2219 | %detectors,'' |
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| 2221 | [hep-ph/0504015]; |
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| 2222 | %%CITATION = HEP-PH 0504015;%% |
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| 2223 | % |
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| 2224 | %\bibitem{Mena:2005ri} |
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| 2225 | %O.~Mena, S.~Palomares-Ruiz and S.~Pascoli, |
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| 2226 | %``Determining the neutrino mass hierarchy and CP violation in NOnuA with a |
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| 2227 | %second off-axis detector,'' |
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| 2228 | hep-ph/0510182. |
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| 2229 | %%CITATION = HEP-PH 0510182;%% |
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| 2230 | |
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| 2231 | \bibitem{Hagiwara:2005pe} |
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| 2232 | K.~Hagiwara, N.~Okamura and K.~Senda, |
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| 2233 | %``Solving the neutrino parameter degeneracy by measuring the T2K off-axis |
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| 2234 | %beam in Korea,'' |
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| 2235 | hep-ph/0504061. |
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| 2236 | %%CITATION = HEP-PH 0504061;%% |
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| 2237 | |
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| 2238 | \bibitem{Kachelriess:2004vs} |
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| 2239 | M.~Kachelriess and R.~Tomas, |
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| 2240 | %``Identifying the neutrino mass hierarchy with supernova neutrinos,'' |
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| 2241 | hep-ph/0412100. |
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| 2242 | %%CITATION = HEP-PH 0412100;%% |
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| 2243 | |
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| 2244 | \end{thebibliography} |
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| 2245 | \end{document} |
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| 2246 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 2247 | |
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| 2248 | |
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