Supernova neutrino oscillations: A simple analytical approach

Analyses of observable supernova neutrino oscillation effects require the calculation of the electron (anti)neutrino survival probability Pee along a given supernova matter density profile. We propose a simple analytical prescription for Pee, based on a double-exponential form for the crossing probability and on the concept of maximum violation of adiabaticity. In the case of two-flavor transitions, the prescription is shown to reproduce accurately, in the whole neutrino oscillation parameter space, the results of exact numerical calculations for generic (realistic or power-law) profiles. The analytical approach is then generalized to cover three-flavor transitions with (direct or inverse) mass spectrum hierarchy, and to incorporate Earth matter effects. Compact analytical expressions, explicitly showing the symmetry properties of Pee, are provided for practical calculations. PACS number(s): 14.60.Pq, 97.60.Bw Typeset using REVTEX 1