% --------------------------
\subsection{SPL SuperBeam}
% --------------------------
%In  the CERN-SPL SuperBeam project  \cite{SPL,SPL-Physics,nufact1}
% the planned 4MW SPL (Superconducting Proton Linac)  would deliver a 2.2  GeV/c
% proton beam,  on a Hg target to generate
% an intense $\pi^+$ ($\pi^-$) beam focused by a suitable
% magnetic horn in a short decay tunnel. As a result   an intense
% $\nu_{\mu}$ beam, will be produced
% mainly via the $\pi$-decay,  $\pi^+ \rightarrow \nu_{\mu} \; \mu^+$ providing a
% flux $\phi \sim 3.6 {\cdot} 10^{11} \nu_{\mu}$/year/m$^2$  at 130 Km
% of distance, and an average energy of 0.27 GeV.
% The $\nu_e$ contamination from $K$ will be suppressed by threshold effects
% and the resulting $\nu_e/\nu_{\mu}$ ratio ($ \sim 0.4 \%$) 
%  will be known within  $2\%$ error.
% The use of a near and far detector (the latter at $L = 130$ Km of distance
% in the Frejus area \cite{Mosca})
% will allow for both $\nu_{\mu}$-disappearance and
% $\nu_{\mu} \rightarrow \nu_e$ appearance studies.
% The physics potential of the 2.2 GeV SPL SuperBeam (SPL-SB)
% with a water Cerenkov far detector fiducial mass of 440 Kt \cite{UNO}  has been extensively
% studied \cite{SPL-Physics}. \\
%
% New developments show that the potential of the SPL-SB potential could be
% improved by rising the SPL energy to 3.5 GeV \cite{Cazes},
% to produce   more copious secondary mesons
% and to focus them more efficiently. This seems feasible if
% status of the art RF cavities would be used in place of the old foreseen LEP cavities
% \cite{Garoby-SPL}.
% In this upgraded configuration neutrino flux could be increased by a factor 3 with
% with respect to the 2.2 GeV configuration, reaching
% a sensitivity to $\sin^2{2 \thetaot}$ 8 times better than T2K and allowing
% to discovery CP violation (at 3 $\sigma$ level) if
% $\delCP \geq 25^\circ$  and
% $\theta_{13} \geq 1.4^\circ$ \cite{MMNufact04}. The expected
% performances are shown in Fig.~\ref{fig:th13}.
%
% \begin{figure}
%  \centerline{\epsfig{file=show_fluxes_new.eps,width=0.5\textwidth}}
%  \mycaption{Neutrino flux of $\beta$-Beam ($\gamma=100$)
%   and CERN-SPL SuperBeam, 3.5 GeV, at 130 Km of distance.}
%  \label{fig:fluxes}
% \end{figure}

An optimization of the energy as well as the secondary particle focusing and decay tunnel has been undertaken in the context of a Super Beam of 4~MW \cite{JECACLAL} using the CERN-SPL \cite{SPL} and searching for $\nu_\mu \rightarrow \nu_e$ ($\bar{\nu}_\mu \rightarrow \bar{\nu}_e$) appearance channels in an 500~kT  fiducial volume water Cerenkov detector, called MEMPHYS, and located in an possible new underground laboratory at the Fréjus tunnel, 130~km from the CERN complex. The use of a near detector will also enable the use of the disappearance channels. 

The secondary particles from the interaction of proton beam impinging a 30~cm long 1.5~cm diameter mercury target, have been obtained with the FLUKA generator (see Tab.~\ref{tab:nbPart}). At kinetic energy of 3.5 (2.2)~GeV, the number of p.o.t per year is 0.69 (1.10) $10^{23}$ while the numbers of $\pi^+/\pi^-/K^+/K^o$ per p.o.t are $0.41/0.37/35 10^{-4}/30 10^{-4}$ ($0.24/0.18/7 10^{-4}/6 10^{-4}$). At higher beam energy, the kaon rates grow rapidly compared to the pion rates, and needless to emphasize the need of an experimental confirmation \cite{HARP,MINERVA} of such numbers.

The focusing system (magnetic horns) optimized in the context of a Neutrino Factory \cite{SIMONE1,DONEGA} has been redesigned considering the specific requirements of a Super Beam. The most important points are the phase spaces that are covered by the two types of horns are different, and that for a Super Beam the pions to be focused should have an energy of the order of $p_\pi (\mathrm{MeV})/3 \approx E_\nu \gtrsim  2L(\mathrm{km})$ to obtain a maximum oscillation probability. In practice, this means that one should collect $800$~MeV/c pions to get a mean neutrino energy of $300$~MeV.

\begin{table}
\centering
\caption{\label{tab:nbPart}Average numbers of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA).}
\begin{tabular}{@{}l*{15}{l}}
\hline\noalign{\smallskip}
$E_k$ (GeV) &     p.o.t/y        & $\pi^+$ & $\pi^-$ & $K^+$ & $K^0$ \\
            & $\times 10^{23}$ &         &         & \multicolumn{2}{c}{$\times 10^{-4}$} \\
\noalign{\smallskip}\hline\noalign{\smallskip}
$2.2$ & $1.10$  &  $0.24$   &  $0.18$ &   $7$ &   $6$ \\
$3.5$ & $0.69$  &  $0.41$   &  $0.37$ &  $35$ &  $30$ \\
$4.5$ & $0.54$  &  $0.57$   &  $0.39$ &  $93$ &  $68$ \\
$8.0$ & $0.30$  &  $1.00$   &  $0.85$ & $413$ & $340$ \\
 \noalign{\smallskip}\hline
\end{tabular}
\end{table}

The resulting fluxes for the positive ($\nu_\mu$ beam) and the negative focusing ($\bar{\nu}_\mu$ beam) are show on figure \ref{fig:fluxComparison}. The total number of $\nu_\mu$ ($\bar{\nu}_\mu$) in positive (negative) focusing is about $1.18 (0.97) 10^{12}/\mathrm{m}^2/\mathrm{yr}$ with an average energy of $300$~MeV. The $\nu_e$ ($\bar{\nu}_\mu$) contamination in the $\nu_\mu$ beam is around $0.7\%$ ($6.0\%$) 
  and will be known within  $2\%$ error. Compared to  the fluxes used in references \cite{MEZZETTONF02,DONINI04} the gain is at least a factor $2.5$. Using neutrino cross-sections on water \cite{LIPARIxsec}, the number of expected $\nu_\mu$ charged current is about $95$ per kT.yr.
%
\begin{figure}
\centering
\includegraphics[height=60mm]{OptiVsOldFlux.eps}
\caption{\label{fig:fluxComparison}The $\nu_\mu$ and the $\bar{\nu}_\mu$ fluxes obtained by optimizing the SPL for a Super Beam case ("SB Opt.") are compared to those obtained with a focusing system designed for a Neutrino Factory ("NF Opt.").}
\end{figure}

The physics potential of the new optimized SPL may be determined using GLoBES software \cite{GLOBES}. Both the appearance and the disappearance channels have been used, and also five bins of 200~MeV each have been introduced. The $\pi^o$ background have been rejected using a tighter PID cut compared to standard SuperK analysis \cite{MEZZETTONF02}. The Michel electron has been required for the $\mu$ identification. As ultimate goal suggested by \cite{T2K} a 2\% systematical error is used both for signal and background.

The $90\%$ CL sensitivity contour in the ($\Delta m^2_{31}$,$\sin^22\theta_{13}$) plane after 5 years running with a positive focusing is shown on figure \ref{fig:SPLDmTheta13Comparison}. With the new optimized setup, one expects to reach a limit on $\theta_{13}$ of $0.7^o$.
%
\begin{figure}
\centering
\includegraphics[height=60mm]{compareOldNewthetaDm.eps}
\caption{\label{fig:SPLDmTheta13Comparison}Comparison of the sensitivity contours with the new optimized setup and the original SPL design after 5 years of running with positive focusing.}
\end{figure}
%
One may also appreciate on figure \ref{fig:SPLCPSensi} the improvement on the combined sensitivity of $\sin^22\theta_{13}$ and $\delta_{CP}$ with the new optimization compared for instance to the T2K project \cite{T2K}. 
%  
\begin{figure}
\centering
\includegraphics[height=60mm]{deltaThetaSens5yOldNew.eps}
\caption{\label{fig:SPLCPSensi}Comparison of the sensitivity on combined $\theta_{13}$ and $\delta_{CP}$ after 5 years of positive focusing. The T2K sensitivity contour has been derived from  reference \cite{T2K}. No mass hierarchy nor octant hierarchy ambiguity has been considered.}
\end{figure}
%

So, the optimized SPL beam line operating a Super Beam towards a megaton scale detector (called MEMPHYS) at the Fréjus tunnel has a great potential.


%%%%%%%%%%%%%%%%%%%% SPL Bibliography %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\bibitem{JECACLAL}
J.E Campagne and A. Cazes, LAL-04-102, arXiv:hep-ex/405002 submitted to \EJP

\bibitem{SPL}
SPL Conceptual Design, CERN 2000-012

\bibitem{HARP}
C. Catanesi \etal, CERN-SPSC 2002/019

\bibitem{MINERVA} 
D. Drakoulakos \etal, Fermilab P-938, arXiv:hep-ex/405002

\bibitem{SIMONE1}
S.~Gilardoni \etal, AIP Conf.\ Proc.\  {\bf 721} (2004) 334.

\bibitem{DONEGA}
A. Blondel \etal, CERN-NUFACT-Note-78 (2001)
 
\bibitem{MEZZETTONF02}
M. Mezzetto,  \jpg {\bf 29}, 1781-1784 (2003), arXiv:hep-ex/0302005

\bibitem{DONINI04}
A. Donini \etal, IFT-UAM/CSIC-04-30  (2004), arXiv:hep-ph/0406132
 
\bibitem{LIPARIxsec}
P.~Lipari, M.~Lusignoli and F.~Sartogo,
  %``The Neutrino cross-section and upward going muons,''
  \PRL {\bf 74} (1995) 4384, arXiv:hep-ph/9411341

\bibitem{GLOBES}
P. Hubert, M. Lindner and W. Winter, arXiv:hep-ph/0407333,
Comput.Phys.Commun. 167 (2005) 195. 

\bibitem{T2K}
T. Kobayashi, \NP B  143  (Proc. Supp.) (2005) 303

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