%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Neutrino oscillation physics}
\label{sec:oscillations}

%
\subsubsection{With the CERN-SPL SuperBeam}
\label{sec:CERN-SPL}
%
 In  the initial CERN-SPL SuperBeam project  
\cite{SPL,SPL-Physics,SPL-Physics2,SPL-Physics3,YELLOW}
 the planned 4MW SPL (Superconducting Proton Linac)  would deliver a 2.2  GeV/c
 proton beam sent 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 is 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 $K$ is suppressed by threshold effects and
amounts to 0.4\%.
 The use of a near and far detector (the latter 130~km away
 at Fr\'ejus \cite{Mosca}, see Sec.~\ref{sec:undlab})
 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 \v{C}erenkov far detector 
with a fiducial mass of 440 kton,  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{Campagne:2004wt},
 to produce more copious secondary mesons
 and to focus them more efficiently. This increase in energy is made possible
 by using state of the art RF cavities instead of the previously
 foreseen LEP cavities \cite{Garoby-SPL}.

The focusing system (magnetic horns) originally 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 that
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 800~MeV
to get a mean neutrino energy of $300$~MeV.
The increase in kaon production rate, giving higher \nue contamination,
has been taken into account, and should be refined using HARP results
 \cite{Harp}.


 In this upgraded configuration, the neutrino flux is increased 
by a factor $\sim 3$ 
 with respect to the 2.2 GeV configuration, 
and the number of expected $\nu_\mu$ charged currents 
is about $95$ per ${\rm kton \cdot yr}$ in MEMPHYS.

A sensitivity $\sin^2(2\thetaot) < 0.8 \cdot 10^{-3}$ 
is obtained  in a 2 years $\nu_\mu$ plus
8 year \nubarmu\ run (for $\delta = 0$,
intrinsic degeneracy accounted for, sign and octant
 degeneracies not accounted for), allowing
for a discovery of CP violation (at 3 $\sigma$ level) for 
$\delta \geq 60^\circ$
for $\sin^2(2\thetaot) = 1.8 \cdot 10^{-3}$ %$\theta_{13} = 1.2^\circ$, 
and improving to $\delta \geq 20^\circ$ for
$\sin^2(2\thetaot) \geq 2 \cdot 10^{-2}$ % $\theta_{13} \geq 4^\circ$ 
\cite{MMNufact04, Campagne}. These 
 performances are shown in Fig.~\ref{fig:th13}, they are found equivalent to
Hyper-Kamiokande. 
These limits have been obtained first using realistic simulations
based on Super-Kamiokande performances (Background level, signal efficiencies,
and associated systematics at the level of 2\%), and more recently confirmed
using GLoBES \cite{Globes}.

Let us conclude this section by mentioning that further studies of the
SPL superbeam will take place inside the Technical Design Study to be submitted 
to Europe by the neutrino factory community towards the end of 2006.

%
\subsubsection{With the CERN BetaBeams}
\label{sec:BetaBeam}

 \begin{figure}
  \centerline{\epsfig{file=./figures/show_fluxes_new.eps,width=0.5\textwidth}}
  \caption{\it Neutrino flux of $\beta$-Beam ($\gamma=100$)
   and CERN-SPL SuperBeam, 3.5 GeV, at 130 Km of distance.}
  \label{fig:fluxes}
 \end{figure}

BetaBeams  have been proposed by 
P. Zucchelli in 2001 \cite{Zucchelli:2002sa}.
The idea is to generate pure, well collimated and intense
\nue\  (\nubare) beams by producing, collecting, accelerating radioactive ions
and storing them in a decay ring in 10 ns long bunches, to suppress
the atmospheric neutrino backgrounds.
The resulting BetaBeam  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.
The schematic layout of a Beta Beam is shown in figure~\ref{fig:sketch}.
It consists of three parts\,:
\begin{enumerate}
\item A low energy part, where a small fraction (lower than 10\%) of the
protons accelerated by the SPL are shot on specific target to produce
$^{18}$Ne or $^6$He; these ions are then collected by an ECR source
of new generation \cite{Sortais} which delivers ion bunches with 100 keV
energy, then accelerated in a LINAC up to 100 MeV/u. This part could be
shared with nuclear physicists involved in 
the EURISOL project \cite{Eurisol,Rubbia:2006pi}.
\item The acceleration to the final energy uses a rapid cycling cyclotron
(labelled PSB) which further accelerates and bunches the ions before sending
them to the PS and the SPS, where they reach their final energy ($\gamma$
around 100). In this process, 16 bunches (150 ns long) in the booster
are transformed into 4 bunches (10 ns long) in the SPS.
\item Ions of the required energy are then stored in a decay ring, with 2500~m
long straight sections for a total length of 7000~m, so that 36\% of the decays
give a strongly collimated and ultra pure neutrino beam aimed at the Fr\'ejus
detector.
\end{enumerate}
A baseline study for the betabeam has been initiated at CERN, and is now
going on within the european FP6 design study for EURISOL.
A specific task is devoted to the study of the high energy part (last 2 items
above). A complete conceptual design for the decay ring has already been
performed. The injection in the ring uses the asymetric merging scheme,
validated by experimental tests at CERN. The actual performances of the new
ECR sources will also be studied with prototypes in the framework of the
EURISOL design study.

The potential of such betabeams 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.  


\begin{figure}
 \centerline{\epsfig{file=./figures/beta_sketch.eps,width=0.60\textwidth}  }
\caption{\it 
A schematic layout of the BetaBeam complex. On the left, the low energy part is
largely similar to the EURISOL project \cite{Eurisol}.
 The central part (PS and SPS) uses
existing facilities. On the right, the decay ring has to be built.}
\label{fig:sketch}
\end{figure}
%


\begin{figure}
    \epsfig{file=./figures/theta13_deltaCP-sensi.eps,width=0.54\textwidth}   
    \hfill
    \epsfig{file=./figures/delta_cp-3sigmadiscov.eps,width=0.43\textwidth}  
    \caption{\it LEFT: \thetaot \  90\% 
             C.L. sensitivity as function of $\delta_{CP}$ for
             $\dmtt=2.5{\cdot}10^{-3}eV^2$, $\sigdm=1$, 2\%
             systematic errors.
             SPL-SB  sensitivities have been computed for a
             2 year \numu + 8 year \nubarmu run, $\beta$B ($\gamma$ = 100)
             for a 5 year \nue + 5 year \nubare run, 200 MeV energy bins for
             both beams.
             The combination of SPL-SB and $\beta$B is also shown.
             HK and NuFACT curves are adapted from \cite{VolutaDaAndrea}:
%hep-ph/0204352\,:
             HK curves corresponds to Hyper-Kamiokande with the same fiducial mass,
             running time and systematics as MEMPHYS, using the 4MW beam from
             JAERI.
             The NuFACT curve corresponds to 5 year runs for each polarity,
             two 50kton iron detectors located at 3000 and 7000 km receiving
             neutrinos from 10$^{21}$ useful 50 GeV muon decays per year,
             detector systematics set at 2\%, matter profile uncertainty set at
             5\%, energy threshold set at 4 GeV.
      RIGHT: $\delta_{CP}$ discovery potential 
             at $3 \sigma$  computed for the same
             conditions.}
  \label{fig:th13}
\end{figure}

First oscillation physics studies 
\cite{Mezzetto:2003ub,Bouchez:2003fy,Mezzetto:2004gs,Donini:2004hu}
 used $\gamma_{\He}=60$ and $\gamma_{\Ne}=100$.
But it was soon realized that the optimal values were actually $\gamma = 100$
for both species, and the corresponding performances are shown in 
figure~\ref{fig:th13}, exhibiting a strong improvement over SPL superbeam
performances, extending the range of sensitivity for 
$\sin^2(2\theta_{13})$ down to $2\cdot 10^{-4}$
%$\theta_{13}$ down to 0.4 degree, 
and improving CP violation sensitivity at lower values
of $\theta_{13}$.

To conclude this section, let us mention a very recent development 
of the Beta Beam concept leading to the
possibility to have monochromatic, single flavor neutrino beams
by using ions decaying 
through the electron capture process \cite{Bernabeu,Sato}.
A suitable ion candidate exists\,: $^{150}$Dy, whose performances have
been already delineated \cite{Bernabeu}. 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.

For a review of the different  Beta Beam configurations, see~\cite{Volpe:2006in}.

\subsubsection{Combining SPL Super Beam and Beta Beam}
Since betabeams use only a small fraction of the protons available from the
SPL, both beta beam and superbeam can be run at the same time.
The combination of superbeam and betabeam results further improves the
sensitivity on $\theta_{13}$ and $\delta$, as shown on figure~\ref{fig:th13}.
It is better in all cases than Hyper-Kamiokande sensitivity, except maybe for very 
large values of $\sin^2(2\theta_{13})$ above $0.04$ %6$^\circ$.
The sensitivity on CP violation is even better than that of a neutrino factory
for $\sin^2(2\theta_{13})$ above $3.5\cdot 10^{-3}$ %1.7$^\deg$ 
(but neutrino factories are still a factor 3
better for $\theta_{13}$ sensitivity).
This combination of super and betabeams offers other advantages, 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.

The MEMPHYS  detector performances  in conjunction with  the SPL
SuperBeam and the $\gamma=100$ Beta Beam have been recently revised in
\cite{Campagne:2006yx}. In this paper are also computed the experimental
capabilities of measuring sign$(\Delta{m}^2_{23}) $ and the $\theta_{23}$
octant by combining atmospheric neutrinos, detected with large
statistics in a megaton scale water \v{C}erenkov detector, with
neutrino beams; as initially pointed out in \cite{latestJJ}. Following
these studies, the MEMPHYS detector could unambiguously measure all
the today unknown neutrino oscillation parameters. It's worth to
stress the fact that the short baseline allows to measure leptonic CP
violation without any subtraction of the fake CP signals induced by
matter effects, still having a sizable sensitivity on the mass
hyerarchy determination thanks to the atmospheric neutrinos. 

%Finally, a common criticism made to projects like MEMPHYS using sub-GeV beams
%is that they get no sensitivity on the mass hierarchy, contrary to other
%projects with higher energy beams. However, a recent study 
%\cite{Schwetz} has shown that
%low energy Super Beam and Beta Beam can profit of atmospheric neutrino
%oscillations, detected with large statistics in a megaton scale 
%water \v{C}erenkov detector,
%to solve degeneracies and measure \sigdm . 

\subsubsection{Comparison with other projects}
\label{oscComp}
Before the advent of megaton class detectors receiving neutrino 
from a Super Beam
and/or Beta Beam, several beam experiments (MINOS, OPERA, T2K, NoVA) and
reactor experiments (such as Double-CHOOZ) will have improved our knowledge on
$\theta_{13}$.\\
If $\theta_{13}$ is found by these experiments, it will be "big" 
($\sin^2(2\theta_{13})>0.02$) %(above 4 degrees), 
and megaton detectors will be the perfect tool to study CP violation,
with no need for a neutrino factory. If on the contrary, only an upper limit
around $5\cdot 10^{-3}$ to $10^{-2}$ is given on $\sin^2(2\theta_{13})$, 
%around 2 to 3 degrees is given on $\theta_{13}$, 
one might consider an
alternative between a staged strategy, starting with megaton detectors, to
explore $\sin^2(\theta_{13})$ down to $3\cdot 10^{-4}$ %0.5 degree 
and start a rich program of non
oscillation physics, eventually followed by a neutrino factory if $\theta_{13}$
is not found; or a more aggressive strategy, aiming directly 
at neutrino factories to explore 
$\sin^2(2\theta_{13})$ down to $10^{-4}$ %0.3 degree, 
but with
no guarantee of success; in the latter case, the non-oscillation physics 
(proton decay, sypernovae) is lost, but would be replaced by precision
muon physics (which has to be assessed and compared with other projects in this
field).\\
There is no doubt that a neutrino factory has a bigger potential than megaton
detectors for very low values of $\theta_{13}$ (below $5\cdot 10^{-3}$), 
and the only 
competition in that case could come from so-called high energy beta-beams.
An abundant litterature has been published on this subject
(see \cite{latestJJ,HighEnergy,HighEnergy2,HuberBB,SuperSPS,MigNufact05}), 
but most authors have
taken as granted that the neutrino fluxes from betabeams
could be kept the same at
higher energies, which is far from evident \cite{MatsPrivate}
and implies a lot of R\&D on the
required accelerators and storage rings before a useful comparison can be made
with neutrino factories.

Presently, the only pertinent comparison is between the several megaton
projects, namely UNO, Hyperkamiokande and MEMPHYS, or their variants using
liquid argon technology (such as FLARE in the USA, GLACIER in Europe).
In this document, we have shown a comparison between Hyperkamiokande and
MEMPHYS, showing a definite advantage for the latter, due to the betabeam.
However, recent variants of Hyperkamiokande using a second detector in Korea
would have to be considered. UNO, for the time being, refers to a study of a
very long baseline (2500 km) neutrino wide band superbeam produced at
Brookhaven, which gives a disappointing sensitivity on $\theta_{13}$ at the
level of 0.02 %4 degrees 
(this is due to the fact that this multiGeV beam leads
to high $\pi^0$ backgrounds in a water \v{C}erenkov detector, as explained
before).\\
Liquid argon detector performances have to be studied, but they will probably
suffer from their lower mass for the lower limit on $\theta_{13}$, while
a better visibility of event topologies would probably help for high values
of $\theta_{13}$, when statistics become important and systematics dominate;
all this has still to be carefully quantified.

Let us mention that a unified way to compare different projects has been made
available to the community , this is the GLoBES package \cite{Globes}.
Figure~\ref{fig:th13} in this document was actually produced using GLoBES, and
some of us are actively pursuing GLoBES-based comparisons in the framework of
the International Scoping Study (ISS), with results expected by mid-2006.     
They will also address the best way to solve problems related to the 
degeneracies on parameter
estimates due to the sign of $\Delta m_{23}^2$, the quadrant ambiguity on
$\theta_{23}$, as well as intrinsic (analytic) ambiguities (In the
present document,
we have supposed $\theta_{23}$ equal to 45$^\circ$, and the absence of matter
effects at low energies make the results insensitive to the mass hierarchy).
But the main point is to feed GLoBES with realistic estimates of the expected
performances of the different projects, in terms of background rejection,
signal
efficiencies and the various related
systematic uncertainties. A coordinated effort
to get realistic numbers for the different projects will be, if successful,
an important achievement of the ISS initiative.





