%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%JEC 27/4/06 change the name of the section for symmetry with reactor neutrinos which also provide oscillation
%parameters measurements
\section{Neutrinos from beams}
\label{sec:oscillation}
%\REDBLA{updated by A. Bueno 23/3/06}
%\REDBLA{updated by T. Marrodan Undagoitia  10/4/06}
%\REDBLA{updated by JEC 27/4/06-> 3/5/06
%%(nb. the name of the file itself has been changed to acc_det.tex instead of osc_det.tex)
%}
%\REDBLA{updated by J. Bouchez 11/5/06}
%\REDBLA{update by A. Bueno 19/5/06}
%\REDBLA{updated by J. Campagne 24/7/06}
%\REDBLA{updated by J. Campagne 26/9/06}
%\REDBLA{updated by J. Campagne 16/10/06 this is a section now}
%\REDBLA{updated by T. Marrodan Undagoitia  01/11/06}
%JEC 27/4/06 START
\subsection{Introduction}
%
%JEC 2/5/06 START
In this section, we review the physics program offered by the proposed detectors using different accelerator based neutrino beams to push the search for a tiny non-zero $\theta_{13}$ or the measurement in case of previous discovery for instance at reactor based experiment such Double-CHOOZ; the search for possible leptonic CP violation ($\delCP$); the determination of the mass hierarchy (i.e. the sign of $\Delta m^2_{31}$) and the $\theta_{23}$ octant (i.e. $\theta_{23}>45^\circ$ or $\theta_{23}<45^\circ$). We cover the potentiality of Liquid Argon detectors in an upgraded version of the existing CERN to Gran Sasso (CNGS) neutrino beam, and the MEMPHYS detector at the Fréjus site using a possible new CERN proton driver (SPL) to upgrade to 4MW the conventional neutrino beams (so-called Super Beams) and/or a possible new scheme of pure electron (anti)neutrino production by using radioactive ion decays (so-called \BB\ Beam). Note that LENA is considered also as a candidate detector for the latter beam. Finally, as an ultimate tool, one thinks of producing very intense neutrino beams by mean of muon decays (so-called Neutrino Factory) that may be detected with a Liquid Argon detector as large as GLACIER.  
%JEC 2/5/06 END
%
%A. Bueno 3/11/06 START new section
\subsection{CNGS upgraded beam} 
%
The determination of the missing $U_{e3}$ element (magnitude and phase)
of the PMNS neutrino mixing matrix is possible via the detection of
$\nu_\mu\rightarrow\nu_e$ oscillations at a baseline $L$ and energy $E$ given by the atmospheric
observations, corresponding to a mass squared difference
$E/L \sim \Delta m^2\simeq 2.5\times 10^{-3}\ eV^2$.  
While the current optimization of the CNGS beam provides limited
sensitivity to this reaction, we discuss the physics potential 
of an intensity-upgraded and 
energy-reoptimized CNGS neutrino beam coupled to an off-axis GLACIER
detector \cite{Meregaglia:2006du}. This idea is based on the possible upgrade of the
CERN PS or on a new machine (PS+) to deliver protons around 50~GeV/c
with a power of 200~kW. Post acceleration to SPS energies followed 
by extraction to the CNGS target region should allow to reach MW
power, with neutrino energies peaked around 2 GeV.

To evaluate the physics potential we have assumed five years of
running in the neutrino horn polarity plus five additional years in
the anti-neutrino mode. We consider a systematic error on the
knowledge of the $\nu_e$ component of 5$\%$. Given the superb $\pi^0$
identification capabilities of GLACIER, the contamination on $\pi^0$
is negligible.

An off-axis search for $\nu_e$ appearance is performed with the
GLACIER detector located at 850 km from CERN. For an off-axis angle of
0.75$^o$, we observe that $\theta_{13}$ can be discovered with 100$\%$
probability (full $\delta_{CP}$ coverage) for $\sin^22\theta_{13}>0.004$ at
$3\sigma$ (see Fig.~\ref{fig:fract_disc_theta}). 

\begin{figure}
\includegraphics[width=\columnwidth]{./figures/CNGS_Fraction_th13Disc_NH.eps}
\caption{\label{fig:fract_disc_theta}
Sensitivity to discover $\theta_{13}$: the fraction of $\delta_{CP}$
coverage as a function of $\sin^22\theta_{13}$.}
\end{figure}

At this rather modest baseline, the effect of CP-violation and matter effects 
cannot be disentangled. In fact, the determination of mass hierarchy
with at half-coverage (50$\%$) is reached only for $\sin^22\theta_{13}>0.03$ at
$3\sigma$. A bigger baseline (1050~km) and a bigger off-axis angle
(1.5$^o$) allows to be sensitive to the first minimum and the second
maximum of the oscillation. This is key to resolve the issue of mass
hierarchy. With this detector configuration, full coverage 
for $\delta_{CP}$ to determine the mass
hierarchy can be reached for $\sin^22\theta_{13}>0.04$ at
$3\sigma$. The sensitivity to mass hierarchy determination can be
improved by considering two off-axis detectors: one of 30 kton at 850
km and off-axis angle 0.75$^o$, a second one of 70 kton at 1050 km and
1.5$^0$ off-axis. Full coverage 
for $\delta_{CP}$ to determine the mass
hierarchy can be reached for $\sin^22\theta_{13}>0.02$ at
$3\sigma$ (see Fig.~\ref{fig:fract_disc_dm}). 
This two-detector configuration reaches very similar
sensitivities to the ones of the T2KK proposal \cite{Ishitsuka:2005qi}.  

\begin{figure}
\includegraphics[width=\columnwidth]{./figures/CNGS850_1050_Fraction_excMass_NH.eps}
\caption{\label{fig:fract_disc_dm}
Mass hierarchy determination for a two detector configuration at
baselines of 850~km and 1050~km.}
\end{figure}
%A. Bueno 3/11/06 END
%
%JEC 27/4/06 END
\subsection{The CERN-SPL Super Beam}
\label{sec:CERN-SPL}
%%JEC 27/4/06 START : make it shorter
The CERN-SPL Super Beam project  
is a conventional neutrino beam although based on a 4MW SPL (Superconducting Proton Linac) \cite{Gerigk:2006qi}
proton driver impinging a liquid mercury target to generate
an intense $\pi^+$ ($\pi^-$) beam with small contamination of kaon mesons. 

%The expected neutrino fluxes of the optimized version of the SPL beam line are shown on \refFig{fig:Phys-Acc-SPLBBfluxes}.
%%
% \begin{figure}
%  \centerline{\epsfig{file=./figures/show_fluxes_new.eps,width=0.25\textwidth}}
%  \caption{Neutrino flux of $\beta$-Beam ($\gamma=100$)
%   and CERN-SPL Super Beam, 3.5~GeV, at 130~km of distance (Fréjus).}
%  \label{fig:Phys-Acc-SPLBBfluxes}
% \end{figure}
%%
%
\begin{figure}
  \includegraphics[width=\columnwidth]{./figures/SPLBBMEMPHYS-fig8.eps}
  \caption{\label{fig:Phys-SPL-atm-params} Allowed regions of $\Delta
  m^2_{31}$ and $\sin^2\theta_{23}$ at 99\%~CL (2 d.o.f.)  after 5~yrs
  of neutrino data taking for SPL, T2K phase~I, T2HK, and the
  combination of SPL with 5~yrs of atmospheric neutrino data in the
  MEMPHYS detector. For the true parameter values we use $\Delta
  m^2_{31} = 2.2\, (2.6) \times 10^{-3}~\mathrm{eV}^2$ and
  $\sin^2\theta_{23} = 0.5 \, (0.37)$ for the test point 1 (2), and
  $\theta_{13} = 0$ and the solar parameters as: $\Delta m^2_{21} = 7.9 \times 10^{-5}~\mathrm{eV}^2$,
  $\sin^2\theta_{12} = 0.3$. The shaded region corresponds to the
  99\%~CL region from present SK and K2K data \cite{Maltoni:2004ei}.}
\end{figure}

The use of a near and far detector
 will allow for both $\nu_{\mu}$ disappearance and
 $\nu_{\mu} \rightarrow \nu_e$ appearance studies.
 The physics potential of the SPL Super Beam
 with MEMPHYS has been extensively studied (see  \cite{Campagne:2006yx,Baldini:2006fi,ISS06} for recent studies); however, the beam simulation will need some retuning after HARP results \cite{Catanesi:2001gi}.
 
After 5 years exposure in $\nu_\mu$ disappearance mode, a $3\sigma$ accuracy of (3-4)\% can be acheived on $\Delta m^2_{31}$, and an accuracy of 22\% (5\%) on $\sin^2\theta_{23}$ if the true value is $0.5$ (0.37) that is to say in case of a maximal mixing or a non-maximal mixing (\refFig{fig:Phys-SPL-atm-params}). The use of atmospheric neutrinos (ATM) can alleviate the octant ambiguity in case of non-maximal mixing as it is shown in \refFig{fig:Phys-SPL-atm-params}. Note however, thanks to a higher energy beam ($\sim 750$~MeV), the T2HK project\footnote{Here, we make reference to the project where a 4MW proton driver may be build at KEK laboratory to deliver an intense neutrino beam, which send to Kamioka mine is detected by a large \WC\ detector.} can benefit from a much lower dependance on the Fermi motion to obtain a better energy resolution and consequently better results.

In appearance mode (2 years $\nu_\mu$ plus
8 years \nubarmu), a $3\sigma$ discovery of non-zero $\theta_{13}$, irrespective of the actual true value of $\delCP$, is achieved for $\stheta\gtrsim 4\ 10^{-3}$ ($\thetaot \gtrsim 3.6^\circ$) as shown on \refFig{fig:Phys-SPLBB-th13}. For maximal CP violation ($\delCP^\mathrm{true} = \pi/2, \, 3\pi/2$) the same discovery level can be achieved for $\stheta\gtrsim 8\ 10^{-4}$ ($\thetaot \gtrsim 0.8^\circ$). The best sensitivity for testing CP violation (i.e the data cannot be fitted with $\delCP =0$ nor $\delCP=\pi$) is achieved for $\stheta\approx 10^{-3}$ ($\thetaot \approx 0.9^\circ$) as shown on \refFig{fig:Phys-SPLBB-CPV}. The maximal sensitivity is achieved for $\stheta\sim 10^{-2}$ where the CP violation can be established at 3$\sigma$ for 73\% of all the $\delCP^\mathrm{true}$.
%
\begin{figure}
  \includegraphics[width=\columnwidth]{./figures/SPLBBMEMPHYS-fig9.eps}
  \caption{$3\sigma$ discovery sensitivity to $\stheta$ for
  \BB, SPL, and T2HK as a function of the true value of \delCP\
  (left panel) and as a function of the fraction of all possible
  values of \delCP\ (right panel). The width of the bands corresponds
  to values for the systematical errors between 2\% and 5\%. The
  dashed curve corresponds to the \BB\ sensitivity with the fluxes reduced by a factor 2.\label{fig:Phys-SPLBB-th13}}
\end{figure}
%
\begin{figure}
   \includegraphics[width=\columnwidth]{./figures/SPLBBMEMPHYS-fig11.eps}
   \caption{CPV discovery potential for \BB, SPL, and T2HK: For
   parameter values inside the ellipse-shaped curves CP conserving
   values of \delCP\ can be excluded at $3\sigma$ $(\Delta\chi^2>9)$.
   The width of the bands corresponds to values for the systematical
   errors from 2\% to 5\%. The dashed curve is described in \refFig{fig:Phys-SPLBB-th13}.\label{fig:Phys-SPLBB-CPV}}
\end{figure}
%
\subsection{The CERN-\BB\ baseline scenario}
\label{sec:BetaBeam}
%
Although quite powerful, the SPL Super Beam is a conventional neutrino beam with known limitations due to 1) a lower production rate of anti-neutrinos compared to neutrinos which in addition to a smaller charged current cross-section impose to run 4 times longer in anti-neutrino modes; 2) the difficulty to setup a accurate beam simulation which implies to the design of a non-trivial near detector setup (cf. K2K, MINOS, T2K) to master the background level. Thus, a new type of neutrino beam, the so-called \BB is being considered. 

The idea is to generate pure, well collimated and intense
\nue  (\nubare) beams by producing, collecting, accelerating radioactive ions.
The resulting \BB\  spectra
can be easily computed knowing the beta decay spectrum of the parent
ion and the Lorentz boost factor $\gamma$, and these beams are virtually 
background free from other flavors. The best ion candidates so far
 are  $^{18}$Ne  and $^6$He for \nue and \nubare,  respectively.

A baseline study for the \BB\ has been initiated at CERN, and is now
going on within the European FP6 design study for EURISOL. 
The potential of such \BB\ sent to MEMPHYS has been studied in the
context of the baseline scenario, using reference fluxes of $5.8 {\cdot}
10^{18}$ \He\ useful
decays/year and $2.2{\cdot}10^{18}$ \Ne\  decays/year, corresponding to a
reasonable estimate by experts in the field of the ultimately
achievable fluxes.  The optimal values is actually $\gamma = 100$
for both species, and the corresponding performances have been recently reviewed in reference \cite{Campagne:2006yx,Baldini:2006fi,ISS06}.

On Figs.~\ref{fig:Phys-SPLBB-th13},\ref{fig:Phys-SPLBB-CPV} the results of running a \BB\ during 10 years (5 years with neutrinos and 5 years with anti-neutrinos) is shown and prove to be far better compared to a SPL Super beam run, especially for maximal CP violation  where a non-zero $\thetaot$ value can be stated at $3\sigma$ for $\stheta\gtrsim 2\ 10^{-4}$ ($\thetaot \gtrsim 0.4^\circ$). Moreover, it is noticeable that the \BB\ is less affected by systematic errors on the background compared to the SPL Super beam and T2HK.

%
%%%%%%%%%%%%%
%%T. Marrodan Undagoitia 01.11.06 START : make it shorter

%T. Marrodan Undagoitia  10/4/06 START
%JEC 2/5/06 START
Before combining the two possible CERN beams, let us consider LENA as
potential detector.
%JEC 2/5/06 END
%T. Marrodan Undagoitia  12/12/06 START Small corrections
%\REDBLA{
 LENA (with a fiducial volume of $\sim 45$~kt) can as well be used as
detector for a low-energy \BB\ oscillation experiment. In the energy
range $0.2-1.2$~GeV, the performed simulations show that muon events
are separable from electron events due to their different track
lengths in the detector and due to the electron emitted in the muon
decay.
%}
%T. Marrodan Undagoitia  12/12/06 END Small corrections


For high energies, muons travel longer than electrons as electrons
undergo scattering and bremsstrahlung. This results in different
distributions of the number of photons and the timing pattern, which
can be used to distinguish between the two classes of events. For low
energies, muons can be recognized by observing the electron of its
succeeding decay after a mean time of 2.2~$\mu$s. 
%T. Marrodan Undagoitia  12/12/06 START Small corrections
%\REDBLA{
 Using both criteria, an efficiency of $\sim 90$~\% for muon appearance
has been calculated with acceptance of 1~\% electron background.
%}
%T. Marrodan Undagoitia  12/12/06 END Small corrections


The advantage of using a liquid scintillator detector for such an
experiment is the good energy reconstruction of the neutrino beam.
%T. Marrodan Undagoitia  12/12/06 START Small corrections
%\REDBLA{
 However, neutrinos of these energies can produce delta resonances
which subsequently decay into a nucleon and a pion. In \WC\ detectors,
pions with energies under the \v{C}erenkov threshold contribute to the
uncertainty of the neutrino energy. In LENA these particles can be
detected. The effect of pion production and similar reactions is
currently under investigation in order to estimate the actual energy
resolution.
%}
%T. Marrodan Undagoitia  12/12/06 END Small corrections



%T. Marrodan Undagoitia  10/4/06 END 

%%T. Marrodan Undagoitia 01.11.06 END 

%%%%%%%%%%%%%
To conclude this section, let us mention a very recent development 
of the \BB\ concept: first, authors of reference \cite{Rubbia:2006pi} are considering a very
promising alternative for the 
production of ions, and secondly, the
possibility to have monochromatic, single flavor neutrino beams
by using ions decaying 
through the electron capture process \cite{Bernabeu:2005jh,Sato:2005ma}.
Such beams would in
particular be perfect to
precisely measure neutrino cross sections in a near detector with the
possibility of an energy scan by varying
the $\gamma$ value of the ions.
%
\subsection{combining SPL Beam and \BB\ with MEMPHYS at Fréjus}
%
Since a \BB\ uses only a small fraction of the protons available from the
SPL, Super and Beta beams can be run at the same time. The combination of Super and $\beta$ beams offers advantages, from the experimental point of view, since the
same parameters $\theta_{13}$ and $\delta_{CP}$ may be measured in many
different ways, using 2 pairs of CP related channels, 2 pairs of T related
channels, and 2 pairs of CPT related channels which should all give
coherent results. In this way the estimates of the systematic errors,
different for each beam, will be experimentally cross-checked.
And, needless to say, the unoscillated data for a given beam will give a large
sample of events corresponding to the small searched-for signal with the
other beam, adding more handles on the understanding of the detector
response.

Their combination after 10 years leads to minor improvements on the sensitivity on $\theta_{13}$ and $\delCP$ compare to the \BB\ alone results as shown on \refFig{fig:Phys-SPLBB-th13}. But, the important point considering the combination of the \BB\ and the Super Beam is looking at neutrino modes only: $\nu_\mu$ for SPL
and $\nu_e$ for \BB. If CPT symmetry is assumed, all the information can be 
obtained as $P_{\bar\nu_e\to\bar\nu_\mu} = P_{\nu_\mu\to\nu_e}$ and
$P_{\bar\nu_\mu\to\bar\nu_e} = P_{\nu_e\to\nu_\mu}$. We illustrate this
synergy in \refFig{fig:Phys-SPLBB-th13-5yrs}. In this scenario, time
consuming anti-neutrino running can be avoided keeping the same physics discovery potential. 
%
\begin{figure}
   \includegraphics[width=\columnwidth]{./figures/SPLBBMEMPHYS-fig14.eps}
%   
   \caption{Discovery potential of a finite value of $\stheta$ at
   $3\sigma$ $(\Delta\chi^2>9)$ for 5~yrs neutrino data from
   \BB, SPL, and the combination of \BB\ + SPL compared to
   10~yrs data from T2HK (2~yrs neutrinos + 8~yrs antineutrinos).
   \label{fig:Phys-SPLBB-th13-5yrs}}
\end{figure}
%

One can also combine SPL, \BB\ and the atmospheric neutrinos (ATM) to alleviate the
parameter degeneracies which lead to disconnected regions on the multi-dimensional space of oscillation parameters\footnote{See reference \cite{Burguet-Castell:2001ez,Minakata:2001qm,Fogli:1996pv} for the definitions of {\it intrinsic}, {\it hierarchy}, and {\it octant} degeneracies}. Atmospheric neutrinos, mainly multi-GeV $e$-like events, are sensitive to the
neutrino mass hierarchy if $\theta_{13}$ is sufficiently large due to
Earth matter effects, whilst sub-GeV $e$-like events provide sensitivity to the octant of
$\theta_{23}$ due to oscillations with $\Delta m^2_{21}$.

The result of running during 5 years on neutrino mode for SPL and \BB, adding further the ATM data, is shown on \refFig{fig:Phys-SPLBB-degeneracies_5yrs} \cite{Campagne:2006yx}. One can appreciate that practically all the degeneracies can be eliminated as only the solution with the wrong sign survives with a $\Delta \chi^2 = 3.3$. This last degeneracy can be completely eliminated using neutrino mode combined with anti-neutrino mode and ATM data \cite{Campagne:2006yx}, however the example shown is a favorable case with $\sin^2\theta_{23}=0.6$, and in general for $\sin^2\theta_{23}<0.5$ the impact of the atmospheric data is weaker. 

So, as a generic case, for the CERN-MEMPHYS project, one is left with the four intrinsic degeneracies. However, the important observation of \refFig{fig:Phys-SPLBB-degeneracies_5yrs} is that
degeneracies have only a very small impact on the CP violation
discovery, in the sense that if the true solution is CP violating also
the fake solutions are located at CP violating values of
$\delCP$. Therefore, thanks to the relatively short baseline without matter effect, even if degeneracies
affect the precise determination of $\theta_{13}$ and $\delCP$, they
have only a small impact on the CP violation discovery potential. Furthermore, one would quote explicitly the four possible set of parameters with their respective confidential level. It is also clear from the figure that the sign($\Delta
m^2_{31}$) degeneracy has practically no effect on the $\theta_{13}$
measurement, whereas the octant degeneracy has very little impact on
the determination of $\delCP$.
%
\begin{figure}
\includegraphics[width=\columnwidth]{./figures/SPLBBMEMPHYS-fig7.eps}
%
  \caption{Allowed regions in $\sin^22\theta_{13}$ and
  $\delta_{CP}$ for 5~years data (neutrinos only) from \BB,
  SPL, and the combination. $\mathrm{H^{tr/wr} (O^{tr/wr})}$ refers to
  solutions with the true/wrong mass hierarchy (octant of
  $\theta_{23}$). For the colored regions in the left panel also
  5~years of atmospheric data are included; the solution with the
  wrong hierarchy has $\Delta\chi^2 = 3.3$. The true parameter
  values are $\delta_{CP} = -0.85 \pi$, $\sin^22\theta_{13} =
  0.03$, $\sin^2\theta_{23} = 0.6$. For the \BB\
  only analysis (middle panel) an external accuracy of 2\% (3\%) for
  $|\Delta m^2_{31}|$ ($\theta_{23}$) has been assumed, whereas for
  the left and right panel the default value of 10\% has been used.}
\label{fig:Phys-SPLBB-degeneracies_5yrs}
\end{figure}
%
Some other features of the ATM data are presented in \refSec{sec:Phys-Atm-neut}.
% is to provide a non-trivial sensitivity to the neutrino mass hierarchy (i.e.
%the sign of $\Delta m^2_{31}$) as shown on \refFig{fig:Phys-SPLBB-hierarchy} for 10 years run. The mass hierarchy can
%be identified at $2\sigma$ CL provided
%$\sin^22\theta_{13} \gtrsim 0.02$ for \BB\ and SPL combined \cite{Campagne:2006yx}. 
%\begin{figure}
%\centering
%  \includegraphics[width=0.50\textwidth]{./figures/SPLBBMEMPHYS-fig16.eps}
%%
%  \caption{Sensitivity to the mass hierarchy at $2\sigma$
%  $(\Delta\chi^2 = 4)$ as a function of the true values of
%  $\sin^22\theta_{13}$ and $\delta_{CP}$ (left), and the
%  fraction of true values of $\delCP$ (right). The solid curves are
%  the sensitivities from the combination of long-baseline and
%  atmospheric neutrino data, the dashed curves correspond to
%  long-baseline data only. For comparison we show in the right panel
%  also the sensitivities of NO$\nu$A and NO$\nu$A+T2K extracted from
%  Fig.~13.14 of Ref.~\cite{Ayres:2004js}. For the curve labeled
%  ``NO$\nu$A (p.dr.)+T2K@4~MW'' a proton driver has been assumed for
%  NO$\nu$A and the T2K beam has been up-graded to 4~MW, see
%  Ref.~\cite{Ayres:2004js} for details.}
%  \label{fig:Phys-SPLBB-hierarchy}
%\end{figure}
 %
\subsection{Neutrino Factory LAr detector}
%
%Antonio Bueno 24/03/06 START
In order to fully address the oscillation processes at a neutrino
factory, a detector should
be capable of identifying  and measuring all three charged lepton flavors
produced in charged current interactions {\it and} of measuring 
their charges to discriminate the incoming neutrino helicity. 
%This is an experimentally
%challenging
%task, given the required detector mass for long-baseline experiments. 
The GLACIER concept (in its non-magnetized option) 
%offers a high granularity,
%excellent calorimetry non magnetized target detector, which
provides a background free identification of electron neutrino charged current 
and a kinematical selection of tau neutrino charged current
interactions.
We can assume that charge discrimination is available
for muons reaching an external magnetized-Fe spectrometer.
Another interesting and extremely 
challenging possibility would consist on magnetizing the whole 
liquid argon volume~\cite{Badertscher:2005te}. This set-up allows the clean
classification of events into electron, right-sign muon, wrong-sign
muon and no-lepton categories.
In addition, high granularity permits a clean detection
of quasi-elastic events, which by detecting the final state
proton, provide a selection
of the neutrino electron helicity without the need of an electron charge
measurement. 
%From quantitative analyses of neutrino oscillation scenarios, we
%conclude that in many cases the discovery sensitivities and the measurements of
%the oscillation parameters
%are dominated by the ability to measure the muon charge.
%However, we identify cases where identification of electron and tau samples 
%contributes significantly.

Table~\ref{tab:rates} summarizes the expected rates for
GLACIER and $10^{20}$ muon decays at a neutrino factory with stored muons 
having an energy of 30 GeV~\cite{Bueno:2000fg}. 
$N_{tot}$ is
the total number of events and $N_{qe}$ is the number
of quasi-elastic events. 

\begin{table}
\caption{\label{tab:rates}Expected events rates for the GLACIER detector in
case no oscillations occur for $10^{20}$ muon decays. We assume E$_\mu$=30 GeV. 
$N_{tot}$ is the total number of events and $N_{qe}$ is the number
of quasi-elastic events.}

%\begin{tabular}{|cc|c|c|c|c|c|c|}
\begin{tabular}{cccccccc}
\hline\hline
\multicolumn{8}{c}{Event rates for various baselines} \\ 
%\hline
\hline
 & & \multicolumn{2}{c}{L=732 km} & \multicolumn{2}{c}{L=2900 km} & 
\multicolumn{2}{c}{L=7400 km} \\
%\cline{3-8}
 & & $N_{tot}$ & $N_{qe}$ & $N_{tot}$ & $N_{qe}$ & $N_{tot}$ & $N_{qe}$ \\
 %\hline
 & $\numu$ CC & 2260000 & 90400 & 144000 & 5760 & 22700 & 900 \\
$\mu^-$ & $\numu$ NC &  673000 & $-$ &  41200 & $-$ & 6800 & $-$  \\
$10^{20}$ decays & $\anue$ CC &  871000 & 34800 & 55300 & 2200 & 8750 & 350 \\
 & $\anue$ NC &  302000 & $-$  & 19900 & $-$  &  3000 & $-$  \\ \hline
 %\hline
 & $\anumu$ CC & 1010000 & 40400 & 63800 & 2550 & 10000 & 400 \\
$\mu^+$ & $\anumu$ NC &  353000 & $-$ & 22400 & $-$ &  3500 & $-$ \\
$10^{20}$ decays & $\nue$ CC &  1970000 & 78800 & 129000 & 5160 & 19800 & 800 \\
 & $\nue$ NC &  579000 & $-$ & 36700 & $-$ &  5800 & $-$ \\ \hline
 \hline
\end{tabular}
\end{table}

Figure~\ref{fig:t13sensitivity} 
shows the expected sensitivity in the measurement of $\theta_{13}$ 
for a baseline of 
7400 km. The maximal sensitivity to $\theta_{13}$ is achieved for very small
background levels, since we are looking in this case for small 
signals; most of the information is coming from the clean
wrong-sign muon class and from quasi-elastic events. 
On the other hand,  if its value is not too small, for a 
measurement of $\theta_{13}$, the signal/background ratio could be
not so crucial, and also the other event classes can contribute to 
this measurement.

A $\nu$-Factory should have among its aims
the over constraining of the oscillation pattern, in order to look for
unexpected new physics effects. This can be achieved in global
fits of the parameters, where the unitarity of the mixing matrix is 
not strictly assumed.
Using a detector able to identify the $\tau$ lepton production via
kinematic means, it is possible to verify the unitarity in 
$\nu_\mu\to\nu_\tau$ and $\nu_e\to\nu_\tau$ transitions. 
%For this 
%latter, the possibility of a kinematical $\tau$ identification
%for wrong-sign muon events could allow for the first time a clear
%identification of this type of oscillations.

\begin{figure}
\includegraphics[width=\columnwidth]{./figures/s2_l7400_sensi_t13.eps}
\caption{\label{fig:t13sensitivity} GLACIER sensitivity for $\theta_{13}$.}
\end{figure}

The study of CP violation in the lepton system probably 
is the most ambitious goal of 
an experiment at a neutrino factory. 
Matter effect can mimic CP violation; however, a multi parameter fit
at the right baseline can allow a simultaneous determination of
matter and CP-violating parameters. 
To detect CP violation effects, the most favorable choice of 
neutrino energy $E_\nu$ and baseline $L$ is in the region of 
the ``first maximum'', given by $(L/E_\nu)^{max}\simeq 500$ km/GeV 
for $|\Delta m^2_{32}|=2.5\times 10^{-3}\rm\ eV^2$~\cite{Bueno:2001jd}. 
To study oscillations in this region, 
one has to require that the energy of the ``first-maximum'' be smaller than 
the MSW resonance energy: 
$2\sqrt{2}G_Fn_eE^{max}_\nu\lesssim\Delta m^2_{32}\cos 2\theta_{13}$. 
This fixes a limit on the baseline $L_{max} \approx$5000 km 
beyond which matter effects spoil the sensitivity.

As an example, \refFig{fig:cpsensitivity} shows the sensitivity 
on the CP violating phase $\delta_{CP}$ for two concrete cases. 
We have classified the events in the five categories previously mentioned, 
assuming an electron charge confusion of 0.1$\%$. We have computed the exclusion 
regions in the $\Delta m^2_{12} - \delta_{CP}$ plane fitting the 
visible energy distributions, provided that the 
electron detection efficiency is $\sim 20\%$. The excluded regions 
extend up to values of $|\delta_{CP}|$ close to $\pi$, 
even when $\theta_{13}$ is left free.

\begin{figure}
\includegraphics[width=\columnwidth]{./figures/CPsensi.eps}
\caption{\label{fig:cpsensitivity} GLACIER 90\% C.L. sensitivity on the $CP$-phase $\delta_{CP}$ as a function of
$\Delta m^2_{21}$ for the two considered baselines.
The reference oscillation parameters are
$\Delta m^2_{32}=3\times 10^{-3}\ \rm eV^2$,
$\sin^2 \theta_{23} = 0.5$,
$\sin^2 \theta_{12} = 0.5$,
$\sin^2 2\theta_{13} = 0.05$ and
$\delta_{CP} = 0$.
The lower curves are made fixing all parameters to the reference values
while for the upper curves $\theta_{13}$ is free.}
\end{figure}

%Antonio Bueno 24/03/06 END
