Coherence of oscillations in matter andsupernova neutrinos

Abstract

We study the propagation coherence for neutrino oscillations inmedia with different density profiles.For each profile, we find the dependence of thecoherence length, Lcoh, on neutrino energy andaddress the issue of correspondenceof results in the distance and energy-momentum representations.The key new feature in matter is existence ofenergy ranges with enhanced coherence around the energiesE0 of “infinite coherence” at which Lcoh→∞.In the configuration space, the infinite coherence correspondsto equality of the (effective) group velocities of the eigenstates.In constant density medium, there is a unique E0, which coincides with the MSW resonance energy of oscillations of mass states and is close to the MSW resonance energy of flavor states.In the case of massless neutrinos or negligible masses in a very densemediumthe coherence persists continuously.In the adiabatic case, the infinite coherence is realized for periodicdensity change. Adiabaticity violation changes the shape factors ofthe wave packets (WPs) and leads to their spread. In a medium with sharp densitychanges (jumps), splitting of the eigenstates occurs at crossingof each jump. We study the increase of the coherence lengthin a single jump and periodic density jumps — castle-wall (CW) profiles.For the CW profile, there are several E0 corresponding to parametric resonances. We outlined applications of the results for supernova neutrinos.In particular, we show that coherence between two shock wave fronts leads to observable oscillation effects, and our analysis suggests that the decoherence can be irrelevant for flavor transformations in the central parts of collapsing stars.