Neutrino propagation when mass eigenstates and decay eigenstates mismatch

TL;DR

This paper develops a formalism for two-flavor neutrino propagation in matter with decay, revealing that the Hamiltonian components cannot be simultaneously diagonalized, and provides analytic expressions for survival and conversion probabilities.

Contribution

It introduces a novel formalism accounting for the mismatch between mass and decay eigenstates in neutrino propagation, with explicit analytic probability formulas.

Findings

Hermitian and anti-Hermitian parts of the Hamiltonian cannot be simultaneously diagonalized.

Derived compact analytic expressions for neutrino survival and conversion probabilities.

Quantified effects of the mismatch parameter on neutrino oscillation probabilities.

Abstract

We point out that the Hermitian and anti-Hermitian components of the effective Hamiltonian for decaying neutrinos cannot be simultaneously diagonalized by unitary transformations for all matter densities. We develop a formalism for the two-flavor neutrino propagation through matter of uniform density, for neutrino decay to invisible states. Employing a resummation of the Zassenhaus expansion, we obtain compact analytic expressions for neutrino survival and conversion probabilities, to first and second order in the "mismatch parameter" $\bar{\gamma}$.