Neutrino mixing with broken $S_3$ symmetry

TL;DR

This paper investigates neutrino mixing patterns by assuming the neutrino mass matrix is a combination of $S_3$ symmetry matrices with one zero eigenvalue, leading to a parameterized mixing matrix fitted to experimental data.

Contribution

It introduces a novel approach by combining $S_3$ symmetry with a zero mass eigenvalue assumption to model neutrino mixing.

Findings

Derived a parameterized mixing matrix consistent with data

Connected $S_3$ symmetry to neutrino mass structure

Provided a fit for the mixing matrix parameter

Abstract

We explore the consequences of assuming that the neutrino mass matrix is a linear combination of the matrices of a three dimensional representation of the group $S_3$ and that it has one zero mass eigenvalue. When implemented, these two assumptions allow us to express the transformation matrix relating the mass eigenstates to the flavor eigenstates in terms of a single parameter which we fit to the available data.