Oscillations of very low energy atmospheric neutrinos

Abstract

There are several new features in the production, oscillations, and detection of the atmospheric neutrinos of low energies $E\ensuremath{\lesssim}100\text{ }\text{ }\mathrm{MeV}$. 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 ${\ensuremath{\theta}}_{23}$, the 1-3 mixing, and the $CP$-violation phase are studied. We find that variations of ${\ensuremath{\theta}}_{23}$ 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 $\ensuremath{\sim}10%$ effects. Detailed study of the sub-sub-GeV neutrinos will be possible in future megaton-scale detectors.