%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \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.