Broken $S_3$ Symmetry in the Neutrino Mass Matrix

TL;DR

This paper investigates how breaking $S_3$ flavor symmetry in the neutrino mass matrix can explain observed neutrino mixing patterns and predicts small deviations from tribimaximal mixing consistent with experimental data.

Contribution

It introduces a perturbation approach to $S_3$ symmetry breaking, resulting in a neutrino mass matrix compatible with current neutrino oscillation data.

Findings

Neutrino mixing angles are consistent with experimental data after third-order perturbation.

The model predicts small deviations from tribimaximal mixing.

Effective Majorana mass is strongly suppressed, within experimental reach.

Abstract

We explore the feasibility of the discrete flavor symmetry $S_3$ to explain the pattern of neutrino masses and mixings. In the flavor basis, the neutrino mass matrix is taken to be invariant under $S_3$ symmetry at the zeroth order. The effects of breaking $S_3$ symmetry by matrices invariant under different $S_2$ subgroups of $S_3$ are studied. The resulting retrocirculant perturbation matrix leads to the perturbed $S_3$ neutrino mass matrix having a trimaximal eigenvector as suggested by the solar neutrino data. It is found that after the third order perturbation the neutrino mixings only depend on the perturbation parameter and are consistent with the current experimental data leading to very small deviations from tribimaximal mixing. These perturbations in the $S_3$ invariant neutrino mass matrix result in interesting interplay between the solar and the reactor neutrino mixing angles. We also get a strongly suppressed range of effective Majorana mass which lies well within the reach of the ongoing experiments.