Doubly perturbed $S_3$ neutrinos and the $s_{13}$ mixing parameter

TL;DR

This paper extends a neutrino mass and mixing model by introducing a weaker perturbation, resulting in a non-zero $s_{13}$ parameter and providing bounds based on existing measurements, under the assumption of no CP violation.

Contribution

It introduces a new perturbation approach to a neutrino model, allowing for a non-zero $s_{13}$ and analyzing its implications with simplified CP phase assumptions.

Findings

Non-zero $s_{13}$ achieved through weaker perturbation.

Strong bounds on $s_{13}$ from $s_{23}$ measurements.

Model predictions consistent with current experimental constraints.

Abstract

We further study a predictive model for the masses and mixing matrix of three Majorana neutrinos. At zeroth order the model yielded degenerate neutrinos and a generalized ``tribimaximal" mixing matrix. At first order the mass splitting was incorporated and the tribimaximal mixing matrix emerged with very small corrections but with a zero value for the parameter $s_{13}$. In the present paper a different, assumed weaker, perturbation is included which gives a non zero value for $s_{13}$ and further corrections to other quantities. These corrections are worked out and their consequences discussed under the simplifying assumption that the conventional CP violation phase vanishes. It is shown that the existing measurements of the parameter $s_{23}$ provide strong bounds on $s_{13}$ in this model.