Neutrino mixing in matter

TL;DR

This paper analyzes three-neutrino mixing in matter using evolution equations and a rephasing invariant parametrization, providing approximate solutions validated by numerical comparison and revealing notable patterns in the mixing matrix elements as matter density changes.

Contribution

It introduces an analytic approach to neutrino mixing in matter with a rephasing invariant parametrization, offering approximate solutions and identifying distinctive patterns in the mixing matrix.

Findings

Analytic approximate solutions match numerical results.

Mixing matrix elements show striking patterns with changing matter density.

Rephasing invariant parametrization simplifies the analysis.

Abstract

Three-neutrino mixing in matter is studied through a set of evolution equations which are based on a rephasing invariant parametrization. Making use of the known properties of measured neutrino parameters, analytic, approximate, solutions are obtained. Their accuracy is confirmed by comparison with numerical integration of these equations. The results, when expressed in the elements squared of the mixing matrix, exhibit striking patterns as the matter density varies.