[387] | 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 2 | \subsection{Neutrino oscillation physics} |
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| 3 | \label{sec:oscillations} |
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| 4 | |
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| 5 | % |
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| 6 | \subsubsection{With the CERN-SPL SuperBeam} |
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| 7 | \label{sec:CERN-SPL} |
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| 8 | % |
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| 9 | In the initial CERN-SPL SuperBeam project |
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| 10 | \cite{SPL,SPL-Physics,SPL-Physics2,SPL-Physics3,YELLOW} |
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| 11 | the planned 4MW SPL (Superconducting Proton Linac) would deliver a 2.2 GeV/c |
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| 12 | proton beam sent on a Hg target to generate |
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| 13 | an intense $\pi^+$ ($\pi^-$) beam focused by a suitable |
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| 14 | magnetic horn in a short decay tunnel. As a result, an intense |
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| 15 | $\nu_{\mu}$ beam is produced |
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| 16 | mainly via the $\pi$-decay, $\pi^+ \rightarrow \nu_{\mu} \; \mu^+$ providing a |
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| 17 | flux $\phi \sim 3.6 {\cdot} 10^{11} \nu_{\mu}$/year/m$^2$ at 130 Km |
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| 18 | of distance, and an average energy of 0.27 GeV. |
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| 19 | The $\nu_e$ contamination from $K$ is suppressed by threshold effects and |
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| 20 | amounts to 0.4\%. |
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| 21 | The use of a near and far detector (the latter 130~km away |
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| 22 | at Fr\'ejus \cite{Mosca}, see Sec.~\ref{sec:undlab}) |
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| 23 | will allow for both $\nu_{\mu}$-disappearance and |
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| 24 | $\nu_{\mu} \rightarrow \nu_e$ appearance studies. |
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| 25 | The physics potential of the 2.2 GeV SPL SuperBeam (SPL-SB) |
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| 26 | with a water \v{C}erenkov far detector |
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| 27 | with a fiducial mass of 440 kton, has been extensively |
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| 28 | studied \cite{SPL-Physics}. |
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| 29 | |
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| 30 | New developments show that the potential of the SPL-SB potential could be |
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| 31 | improved by rising the SPL energy to 3.5 GeV \cite{Campagne:2004wt}, |
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| 32 | to produce more copious secondary mesons |
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| 33 | and to focus them more efficiently. This increase in energy is made possible |
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| 34 | by using state of the art RF cavities instead of the previously |
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| 35 | foreseen LEP cavities \cite{Garoby-SPL}. |
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| 36 | |
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| 37 | The focusing system (magnetic horns) originally optimized in the context of a |
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| 38 | Neutrino Factory \cite{SIMONE1,DONEGA} has been |
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| 39 | redesigned considering the specific |
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| 40 | requirements of a Super Beam. |
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| 41 | The most important points are that |
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| 42 | the phase spaces that are covered by the two types |
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| 43 | of horns are different, and that for a Super Beam the pions to be focused |
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| 44 | should have |
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| 45 | an energy of the order of 800~MeV |
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| 46 | to get a mean neutrino energy of $300$~MeV. |
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| 47 | The increase in kaon production rate, giving higher \nue contamination, |
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| 48 | has been taken into account, and should be refined using HARP results |
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| 49 | \cite{Harp}. |
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| 50 | |
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| 51 | |
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| 52 | In this upgraded configuration, the neutrino flux is increased |
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| 53 | by a factor $\sim 3$ |
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| 54 | with respect to the 2.2 GeV configuration, |
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| 55 | and the number of expected $\nu_\mu$ charged currents |
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| 56 | is about $95$ per ${\rm kton \cdot yr}$ in MEMPHYS. |
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| 57 | |
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| 58 | A sensitivity $\sin^2(2\thetaot) < 0.8 \cdot 10^{-3}$ |
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| 59 | is obtained in a 2 years $\nu_\mu$ plus |
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| 60 | 8 year \nubarmu\ run (for $\delta = 0$, |
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| 61 | intrinsic degeneracy accounted for, sign and octant |
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| 62 | degeneracies not accounted for), allowing |
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| 63 | for a discovery of CP violation (at 3 $\sigma$ level) for |
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| 64 | $\delta \geq 60^\circ$ |
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| 65 | for $\sin^2(2\thetaot) = 1.8 \cdot 10^{-3}$ %$\theta_{13} = 1.2^\circ$, |
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| 66 | and improving to $\delta \geq 20^\circ$ for |
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| 67 | $\sin^2(2\thetaot) \geq 2 \cdot 10^{-2}$ % $\theta_{13} \geq 4^\circ$ |
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| 68 | \cite{MMNufact04, Campagne}. These |
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| 69 | performances are shown in Fig.~\ref{fig:th13}, they are found equivalent to |
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| 70 | Hyper-Kamiokande. |
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| 71 | These limits have been obtained first using realistic simulations |
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| 72 | based on Super-Kamiokande performances (Background level, signal efficiencies, |
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| 73 | and associated systematics at the level of 2\%), and more recently confirmed |
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| 74 | using GLoBES \cite{Globes}. |
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| 75 | |
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| 76 | Let us conclude this section by mentioning that further studies of the |
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| 77 | SPL superbeam will take place inside the Technical Design Study to be submitted |
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| 78 | to Europe by the neutrino factory community towards the end of 2006. |
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| 79 | |
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| 80 | % |
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| 81 | \subsubsection{With the CERN BetaBeams} |
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| 82 | \label{sec:BetaBeam} |
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| 83 | |
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| 84 | \begin{figure} |
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| 85 | \centerline{\epsfig{file=./figures/show_fluxes_new.eps,width=0.5\textwidth}} |
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| 86 | \caption{\it Neutrino flux of $\beta$-Beam ($\gamma=100$) |
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| 87 | and CERN-SPL SuperBeam, 3.5 GeV, at 130 Km of distance.} |
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| 88 | \label{fig:fluxes} |
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| 89 | \end{figure} |
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| 90 | |
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| 91 | BetaBeams have been proposed by |
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| 92 | P. Zucchelli in 2001 \cite{Zucchelli:2002sa}. |
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| 93 | The idea is to generate pure, well collimated and intense |
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| 94 | \nue\ (\nubare) beams by producing, collecting, accelerating radioactive ions |
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| 95 | and storing them in a decay ring in 10 ns long bunches, to suppress |
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| 96 | the atmospheric neutrino backgrounds. |
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| 97 | The resulting BetaBeam spectra |
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| 98 | can be easily computed knowing the beta decay spectrum of the parent |
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| 99 | ion and the Lorentz boost factor $\gamma$, and these beams are virtually |
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| 100 | background free from other flavors. |
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| 101 | The best ion candidates so far |
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| 102 | are $^{18}$Ne and $^6$He; for \nue\ and \nubare\ respectively. |
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| 103 | The schematic layout of a Beta Beam is shown in figure~\ref{fig:sketch}. |
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| 104 | It consists of three parts\,: |
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| 105 | \begin{enumerate} |
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| 106 | \item A low energy part, where a small fraction (lower than 10\%) of the |
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| 107 | protons accelerated by the SPL are shot on specific target to produce |
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| 108 | $^{18}$Ne or $^6$He; these ions are then collected by an ECR source |
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| 109 | of new generation \cite{Sortais} which delivers ion bunches with 100 keV |
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| 110 | energy, then accelerated in a LINAC up to 100 MeV/u. This part could be |
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| 111 | shared with nuclear physicists involved in |
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| 112 | the EURISOL project \cite{Eurisol,Rubbia:2006pi}. |
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| 113 | \item The acceleration to the final energy uses a rapid cycling cyclotron |
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| 114 | (labelled PSB) which further accelerates and bunches the ions before sending |
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| 115 | them to the PS and the SPS, where they reach their final energy ($\gamma$ |
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| 116 | around 100). In this process, 16 bunches (150 ns long) in the booster |
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| 117 | are transformed into 4 bunches (10 ns long) in the SPS. |
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| 118 | \item Ions of the required energy are then stored in a decay ring, with 2500~m |
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| 119 | long straight sections for a total length of 7000~m, so that 36\% of the decays |
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| 120 | give a strongly collimated and ultra pure neutrino beam aimed at the Fr\'ejus |
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| 121 | detector. |
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| 122 | \end{enumerate} |
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| 123 | A baseline study for the betabeam has been initiated at CERN, and is now |
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| 124 | going on within the european FP6 design study for EURISOL. |
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| 125 | A specific task is devoted to the study of the high energy part (last 2 items |
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| 126 | above). A complete conceptual design for the decay ring has already been |
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| 127 | performed. The injection in the ring uses the asymetric merging scheme, |
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| 128 | validated by experimental tests at CERN. The actual performances of the new |
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| 129 | ECR sources will also be studied with prototypes in the framework of the |
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| 130 | EURISOL design study. |
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| 131 | |
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| 132 | The potential of such betabeams sent to MEMPHYS has been studied in the |
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| 133 | context of the baseline scenario, using reference fluxes of $5.8 {\cdot} |
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| 134 | 10^{18}$ \He\ useful |
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| 135 | decays/year and $2.2{\cdot}10^{18}$ \Ne\ decays/year, corresponding to a |
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| 136 | reasonable estimate by experts in the field of the ultimately |
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| 137 | achievable fluxes. |
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| 138 | |
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| 139 | |
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| 140 | \begin{figure} |
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| 141 | \centerline{\epsfig{file=./figures/beta_sketch.eps,width=0.60\textwidth} } |
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| 142 | \caption{\it |
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| 143 | A schematic layout of the BetaBeam complex. On the left, the low energy part is |
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| 144 | largely similar to the EURISOL project \cite{Eurisol}. |
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| 145 | The central part (PS and SPS) uses |
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| 146 | existing facilities. On the right, the decay ring has to be built.} |
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| 147 | \label{fig:sketch} |
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| 148 | \end{figure} |
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| 149 | % |
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| 150 | |
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| 151 | |
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| 152 | \begin{figure} |
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| 153 | \epsfig{file=./figures/theta13_deltaCP-sensi.eps,width=0.54\textwidth} |
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| 154 | \hfill |
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| 155 | \epsfig{file=./figures/delta_cp-3sigmadiscov.eps,width=0.43\textwidth} |
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| 156 | \caption{\it LEFT: \thetaot \ 90\% |
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| 157 | C.L. sensitivity as function of $\delta_{CP}$ for |
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| 158 | $\dmtt=2.5{\cdot}10^{-3}eV^2$, $\sigdm=1$, 2\% |
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| 159 | systematic errors. |
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| 160 | SPL-SB sensitivities have been computed for a |
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| 161 | 2 year \numu + 8 year \nubarmu run, $\beta$B ($\gamma$ = 100) |
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| 162 | for a 5 year \nue + 5 year \nubare run, 200 MeV energy bins for |
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| 163 | both beams. |
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| 164 | The combination of SPL-SB and $\beta$B is also shown. |
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| 165 | HK and NuFACT curves are adapted from \cite{VolutaDaAndrea}: |
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| 166 | %hep-ph/0204352\,: |
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| 167 | HK curves corresponds to Hyper-Kamiokande with the same fiducial mass, |
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| 168 | running time and systematics as MEMPHYS, using the 4MW beam from |
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| 169 | JAERI. |
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| 170 | The NuFACT curve corresponds to 5 year runs for each polarity, |
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| 171 | two 50kton iron detectors located at 3000 and 7000 km receiving |
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| 172 | neutrinos from 10$^{21}$ useful 50 GeV muon decays per year, |
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| 173 | detector systematics set at 2\%, matter profile uncertainty set at |
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| 174 | 5\%, energy threshold set at 4 GeV. |
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| 175 | RIGHT: $\delta_{CP}$ discovery potential |
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| 176 | at $3 \sigma$ computed for the same |
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| 177 | conditions.} |
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| 178 | \label{fig:th13} |
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| 179 | \end{figure} |
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| 180 | |
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| 181 | First oscillation physics studies |
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| 182 | \cite{Mezzetto:2003ub,Bouchez:2003fy,Mezzetto:2004gs,Donini:2004hu} |
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| 183 | used $\gamma_{\He}=60$ and $\gamma_{\Ne}=100$. |
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| 184 | But it was soon realized that the optimal values were actually $\gamma = 100$ |
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| 185 | for both species, and the corresponding performances are shown in |
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| 186 | figure~\ref{fig:th13}, exhibiting a strong improvement over SPL superbeam |
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| 187 | performances, extending the range of sensitivity for |
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| 188 | $\sin^2(2\theta_{13})$ down to $2\cdot 10^{-4}$ |
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| 189 | %$\theta_{13}$ down to 0.4 degree, |
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| 190 | and improving CP violation sensitivity at lower values |
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| 191 | of $\theta_{13}$. |
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| 192 | |
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| 193 | To conclude this section, let us mention a very recent development |
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| 194 | of the Beta Beam concept leading to the |
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| 195 | possibility to have monochromatic, single flavor neutrino beams |
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| 196 | by using ions decaying |
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| 197 | through the electron capture process \cite{Bernabeu,Sato}. |
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| 198 | A suitable ion candidate exists\,: $^{150}$Dy, whose performances have |
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| 199 | been already delineated \cite{Bernabeu}. Such beams would in |
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| 200 | particular be perfect to |
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| 201 | precisely measure neutrino cross sections in a near detector with the |
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| 202 | possibility of an energy scan by varying |
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| 203 | the $\gamma$ value of the ions. |
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| 204 | |
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| 205 | For a review of the different Beta Beam configurations, see~\cite{Volpe:2006in}. |
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| 206 | |
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| 207 | \subsubsection{Combining SPL Super Beam and Beta Beam} |
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| 208 | Since betabeams use only a small fraction of the protons available from the |
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| 209 | SPL, both beta beam and superbeam can be run at the same time. |
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| 210 | The combination of superbeam and betabeam results further improves the |
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| 211 | sensitivity on $\theta_{13}$ and $\delta$, as shown on figure~\ref{fig:th13}. |
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| 212 | It is better in all cases than Hyper-Kamiokande sensitivity, except maybe for very |
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| 213 | large values of $\sin^2(2\theta_{13})$ above $0.04$ %6$^\circ$. |
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| 214 | The sensitivity on CP violation is even better than that of a neutrino factory |
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| 215 | for $\sin^2(2\theta_{13})$ above $3.5\cdot 10^{-3}$ %1.7$^\deg$ |
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| 216 | (but neutrino factories are still a factor 3 |
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| 217 | better for $\theta_{13}$ sensitivity). |
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| 218 | This combination of super and betabeams offers other advantages, since the |
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| 219 | same parameters $\theta_{13}$ and $\delta_{CP}$ may be measured in many |
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| 220 | different ways, using 2 pairs of CP related channels, 2 pairs of T related |
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| 221 | channels, and 2 pairs of CPT related channels which should all give |
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| 222 | coherent results. In this way the estimates of the systematic errors, |
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| 223 | different for each beam, will be experimentally cross-checked. |
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| 224 | And, needless to say, the unoscillated data for a given beam will give a large |
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| 225 | sample of events corresponding to the small searched-for signal with the |
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| 226 | other beam, adding more handles on the understanding of the detector |
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| 227 | response. |
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| 228 | |
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| 229 | The MEMPHYS detector performances in conjunction with the SPL |
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| 230 | SuperBeam and the $\gamma=100$ Beta Beam have been recently revised in |
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| 231 | \cite{Campagne:2006yx}. In this paper are also computed the experimental |
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| 232 | capabilities of measuring sign$(\Delta{m}^2_{23}) $ and the $\theta_{23}$ |
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| 233 | octant by combining atmospheric neutrinos, detected with large |
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| 234 | statistics in a megaton scale water \v{C}erenkov detector, with |
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| 235 | neutrino beams; as initially pointed out in \cite{latestJJ}. Following |
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| 236 | these studies, the MEMPHYS detector could unambiguously measure all |
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| 237 | the today unknown neutrino oscillation parameters. It's worth to |
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| 238 | stress the fact that the short baseline allows to measure leptonic CP |
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| 239 | violation without any subtraction of the fake CP signals induced by |
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| 240 | matter effects, still having a sizable sensitivity on the mass |
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| 241 | hyerarchy determination thanks to the atmospheric neutrinos. |
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| 242 | |
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| 243 | %Finally, a common criticism made to projects like MEMPHYS using sub-GeV beams |
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| 244 | %is that they get no sensitivity on the mass hierarchy, contrary to other |
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| 245 | %projects with higher energy beams. However, a recent study |
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| 246 | %\cite{Schwetz} has shown that |
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| 247 | %low energy Super Beam and Beta Beam can profit of atmospheric neutrino |
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| 248 | %oscillations, detected with large statistics in a megaton scale |
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| 249 | %water \v{C}erenkov detector, |
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| 250 | %to solve degeneracies and measure \sigdm . |
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| 251 | |
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| 252 | \subsubsection{Comparison with other projects} |
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| 253 | \label{oscComp} |
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| 254 | Before the advent of megaton class detectors receiving neutrino |
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| 255 | from a Super Beam |
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| 256 | and/or Beta Beam, several beam experiments (MINOS, OPERA, T2K, NoVA) and |
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| 257 | reactor experiments (such as Double-CHOOZ) will have improved our knowledge on |
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| 258 | $\theta_{13}$.\\ |
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| 259 | If $\theta_{13}$ is found by these experiments, it will be "big" |
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| 260 | ($\sin^2(2\theta_{13})>0.02$) %(above 4 degrees), |
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| 261 | and megaton detectors will be the perfect tool to study CP violation, |
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| 262 | with no need for a neutrino factory. If on the contrary, only an upper limit |
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| 263 | around $5\cdot 10^{-3}$ to $10^{-2}$ is given on $\sin^2(2\theta_{13})$, |
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| 264 | %around 2 to 3 degrees is given on $\theta_{13}$, |
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| 265 | one might consider an |
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| 266 | alternative between a staged strategy, starting with megaton detectors, to |
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| 267 | explore $\sin^2(\theta_{13})$ down to $3\cdot 10^{-4}$ %0.5 degree |
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| 268 | and start a rich program of non |
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| 269 | oscillation physics, eventually followed by a neutrino factory if $\theta_{13}$ |
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| 270 | is not found; or a more aggressive strategy, aiming directly |
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| 271 | at neutrino factories to explore |
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| 272 | $\sin^2(2\theta_{13})$ down to $10^{-4}$ %0.3 degree, |
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| 273 | but with |
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| 274 | no guarantee of success; in the latter case, the non-oscillation physics |
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| 275 | (proton decay, sypernovae) is lost, but would be replaced by precision |
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| 276 | muon physics (which has to be assessed and compared with other projects in this |
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| 277 | field).\\ |
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| 278 | There is no doubt that a neutrino factory has a bigger potential than megaton |
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| 279 | detectors for very low values of $\theta_{13}$ (below $5\cdot 10^{-3}$), |
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| 280 | and the only |
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| 281 | competition in that case could come from so-called high energy beta-beams. |
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| 282 | An abundant litterature has been published on this subject |
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| 283 | (see \cite{latestJJ,HighEnergy,HighEnergy2,HuberBB,SuperSPS,MigNufact05}), |
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| 284 | but most authors have |
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| 285 | taken as granted that the neutrino fluxes from betabeams |
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| 286 | could be kept the same at |
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| 287 | higher energies, which is far from evident \cite{MatsPrivate} |
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| 288 | and implies a lot of R\&D on the |
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| 289 | required accelerators and storage rings before a useful comparison can be made |
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| 290 | with neutrino factories. |
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| 291 | |
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| 292 | Presently, the only pertinent comparison is between the several megaton |
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| 293 | projects, namely UNO, Hyperkamiokande and MEMPHYS, or their variants using |
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| 294 | liquid argon technology (such as FLARE in the USA, GLACIER in Europe). |
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| 295 | In this document, we have shown a comparison between Hyperkamiokande and |
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| 296 | MEMPHYS, showing a definite advantage for the latter, due to the betabeam. |
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| 297 | However, recent variants of Hyperkamiokande using a second detector in Korea |
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| 298 | would have to be considered. UNO, for the time being, refers to a study of a |
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| 299 | very long baseline (2500 km) neutrino wide band superbeam produced at |
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| 300 | Brookhaven, which gives a disappointing sensitivity on $\theta_{13}$ at the |
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| 301 | level of 0.02 %4 degrees |
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| 302 | (this is due to the fact that this multiGeV beam leads |
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| 303 | to high $\pi^0$ backgrounds in a water \v{C}erenkov detector, as explained |
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| 304 | before).\\ |
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| 305 | Liquid argon detector performances have to be studied, but they will probably |
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| 306 | suffer from their lower mass for the lower limit on $\theta_{13}$, while |
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| 307 | a better visibility of event topologies would probably help for high values |
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| 308 | of $\theta_{13}$, when statistics become important and systematics dominate; |
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| 309 | all this has still to be carefully quantified. |
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| 310 | |
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| 311 | Let us mention that a unified way to compare different projects has been made |
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| 312 | available to the community , this is the GLoBES package \cite{Globes}. |
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| 313 | Figure~\ref{fig:th13} in this document was actually produced using GLoBES, and |
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| 314 | some of us are actively pursuing GLoBES-based comparisons in the framework of |
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| 315 | the International Scoping Study (ISS), with results expected by mid-2006. |
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| 316 | They will also address the best way to solve problems related to the |
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| 317 | degeneracies on parameter |
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| 318 | estimates due to the sign of $\Delta m_{23}^2$, the quadrant ambiguity on |
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| 319 | $\theta_{23}$, as well as intrinsic (analytic) ambiguities (In the |
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| 320 | present document, |
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| 321 | we have supposed $\theta_{23}$ equal to 45$^\circ$, and the absence of matter |
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| 322 | effects at low energies make the results insensitive to the mass hierarchy). |
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| 323 | But the main point is to feed GLoBES with realistic estimates of the expected |
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| 324 | performances of the different projects, in terms of background rejection, |
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| 325 | signal |
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| 326 | efficiencies and the various related |
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| 327 | systematic uncertainties. A coordinated effort |
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| 328 | to get realistic numbers for the different projects will be, if successful, |
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| 329 | an important achievement of the ISS initiative. |
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| 330 | |
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| 331 | |
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| 332 | |
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| 333 | |
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| 334 | |
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