More distant possibilities

Blondel [96] and Gavela [20] described the possibilities for a future neutrino factory, which has been discussed for CERN or Fermilab [97,33]. A neutrino factory refers to intense and precisely understood $\nu_e$, $\nu_\mu$, $\bar{\nu}_e$, and $\bar{\nu}_\mu$ beams produced at a dedicated muon storage ring. Compared to more convention alternatives, a $\nu$ factory would produce the best physics, but would be very expensive and require a long time scale. However, it could be the first step towards a muon collider.

Dydak [98] compared and contrasted the possibilities of a $\nu$ factory with those of a superbeam, which refers to a much more intense (e.g., by 100) version of the conventional beams from $\pi$ and $K$ decay. A superbeam could be built, for example, at the Japan Hadron Facility (JHF), or at CERN or Fermilab. A superbeam might be much less expensive and faster to build than a $\nu$ factory, and might be built first or instead. However, given the nature of conventional beams (less well understood energies, $\nu_e$ contamination) the detector needs might increase the costs unacceptably. In particular, the 1% $\nu_e$ contained in a conventional wide band beam might be fatal for oscillation studies. It has been suggested that this could be reduced by using a low energy narrow band beam generated by low energy (1-2 GeV) protons [99], but the rate is reduced by 100, and there is still a 0.1% $\nu_e$ contamination from $\mu$ decay. There are also uncertainties in the flux estimates. Another alternative is to use low energy (few hundred MeV) $\nu_e$ produced by the PRISM muon source [100], which might allow the observation of CP violation without needing matter effects.

The motivations for a neutrino factory (or conventional alternative) are especially strong if the LMA solution for the solar neutrinos turns out to be correct. The goals include:

• A precise determination of the atmospheric parameters $U_{\mu 3}$ and $\vert\Delta m^2_{23}\vert$.
• A measure of the admixture $U_{e3}$ of $\nu_e$ into $\nu_3$, with a sensitivity down to $\vert U_{e3}\vert^2 \sim 10^{-3}-10^{-4}$.
• The sign of $\Delta m^2_{23}$, which distinguishes the hierarchical and inverted models, can be determined provided $\vert U_{e3}\vert^2 \ne 0$ can be observed.
• The CP-violating phase $\delta$ in the leptonic mixing might be observable, provided that the parameters correspond to the LMA with $\Delta m^2_{12} > 2 \mbox{$\times$}10^{-5}$ eV$^2$ and $\vert U_{e3}\vert^2 \ne 0$.
• It will be necessary to determine $\delta$, $\vert U_{e3}\vert^2$, and matter effects simultaneously. They can in principle be separated by exploiting their different $L/E$ dependences. In principle one could use the $E$ dependence at a single detector, but in practice one needs 2 or preferably 3 detectors to handle systematics. Typical distances considered include $\sim 700$ km (Cern-Gran Sasso), 3000 km (Fermilab to California or Cuba, Cern to Canary Islands or northern Norway), or 7300 km (Fermilab-Gran Sasso). The latter would require an extremely challenging nearly vertical beam.
• The physics possibilities would be much easier and richer in most 4 $\nu$ schemes.
• One could carry out a fine program of other physics, such as deep inelastic scattering.

Learned [83] emphasized that future large-scale oscillation experiments (e.g., the far detector at a neutrino factory) should also be designed to search for proton decay, with the goal of sensitivity to a $10^{35}$ yr lifetime.