Broken $S_3$ Neutrinos

TL;DR

This paper investigates how breaking the $S_3$ symmetry in neutrino mass matrices can explain the observed nonzero reactor mixing angle $ heta_{13}$ and CP violation, aligning theoretical models with experimental data.

Contribution

It introduces a method of explicit symmetry breaking via a retrocirculant matrix to account for neutrino mixing angles and CP violation, providing a new approach to neutrino mass modeling.

Findings

Nonzero $ heta_{13}$ and $J_{CP}$ achieved through symmetry breaking.

Predicted neutrino masses and mixing angles match experimental data.

Estimated effective masses and total neutrino mass consistent with observations.

Abstract

Motivated by recent measurements which strongly support a nonzero reactor mixing angle $\theta_{13}$, we study a deviation from $S_3$ neutrino discrete symmetry by explicitly breaking the neutrino mass matrix with a general retrocirculant matrix. We show that nonzero $\theta_{13}$ and nonzero CP violation parameter $J_{CP}$ arise due to the difference between $y_2$ and $y_3$. We demonstrate that it is possible to obtain the experimentally favored results for neutrino masses and mixing angles from this mass matrix. Furthermore, we estimate the effective masses $m_{\beta}$ and $m_{\beta \beta}$ and total neutrino mass $\sum |m_i|$ predicted by this mass matrix.