Three-family oscillations using neutrinos from muon beams at very long baseline

The planned LBL experiments will be able to prove the hypothesis of flavor oscillation between muon and tau neutrinos. We explore the possibility of a second generation long baseline experiment at very long baseline, i.e. L in the range 5000-7000 km. This distance requires intense neutrino beams that could be available from very intense muon beams as those needed for $\mu$ colliders. Such baselines allow the study of neutrino oscillations with $E/L \approx 2\times 10^{-3} eV^2$ with neutrinos of energy $E_\nu \approx 10 GeV$, i.e. above tau threshold. Moreover, matter effects inside the Earth could lead to observable effects in $\nu_e \to \nu_\mu$ oscillations. These effects are interchanged between neutrinos and antineutrinos, and therefore they can be tested by comparing the oscillated spectra obtained running the storage ring with positive and negative muons.