The mixing angles in matter for three generations of neutrinos and the MSW mechanism

Abstract

Mikheyev and Smirnov have recently shown that oscillations between two species of neutrinos may be amplified in matter. We give analytic expressions for the energy eigenvalues, all the mixing angles and the CP-violating phase in matter for three generations of neutrinos using the Fritzsch parametrization for the flavor mixing matrix. For clearly separated neutrino masses Δm ²₃₁ ≫Δm ²₂₁ we find two MSW resonance effects—one forv _e ↔v _µ and one forv _e ↔v _τ conversions —which can each be approximated by a separate two neutrino treatment as has been recently shown by Kuo and Pantaleone. Nearly degenerate neutrino masses Δm ²₃₁ ∼Δm ²₂₁ on the other hand lead to only one resonance region withs ^{m 2}_{1 2} no longer necessarily approaching 1 for very high densities.