Oscillations of very low energy atmospheric neutrinos

There are several new features in the production, oscillations, and detection of the atmospheric neutrinos of low energies E < or approx. 100 MeV. The flavor ratio r of muon to electron neutrino fluxes is substantially smaller than 2 and decreases with energy, a significant part of events is due to the decay of invisible muons at rest, etc. Oscillations in a two-layer medium (atmosphere-Earth) should be taken into account. We derive analytical and semianalytical expressions for the oscillation probabilities of these 'sub-sub-GeV' neutrinos. The energy spectra of the e-like events in water Cherenkov detectors are computed, and the dependence of the spectra on the 2-3 mixing angle θ23, the 1-3 mixing, and the CP-violation phase are studied. We find that variations of θ23 in the presently allowed region change the number of e-like events by about 15%-20% as well as lead to distortion of the energy spectrum. The 1-3 mixing and CP violation can lead to ∼10% effects. Detailed study of the sub-sub-GeV neutrinos will be possible in future megaton-scale detectors.