Rephasing Invariant for Three-Neutrino Oscillations Governed by a Non-Hermitian Hamiltonian

Abstract

Time-reversal symmetry is broken for mixed and possibly unstable Dirac neutrino propagation through absorbing media. This implies that interplay between the neutrino mixing, refraction, absorption and/or decay can be described by non-Hermitian quantum dynamics. We derive an identity which sets up direct connection between the fundamental neutrino parameters (mixing angles, CP-violating phase, mass-squared splittings) in vacuum and their effective counterparts in matter.