Broken Democracy with Intermediate $\mathbb S_2 \times \mathbb S_2$ Residual Symmetry and Random Perturbations

TL;DR

This paper explores how breaking democratic flavor symmetry down to an intermediate  symmetry, followed by random perturbations, can explain fermion mass hierarchies and mixing angles, with implications for neutrinoless double beta decay.

Contribution

It introduces a novel symmetry-breaking sequence from  to , combined with random perturbations, to explain fermion masses and mixings.

Findings

Predicts specific neutrinoless double beta decay rates

Provides a mechanism for fermion mass hierarchies

Shows intermediate symmetry breaking aligns with observed data

Abstract

The democratic mass matrix is an intriguing possibility for explaining the observed fermion mixings due to its inherent hierarchical mass eigenvalues and large mixing angles. Nevertheless, two of the three mass eigenvalues are zero if the flavor democracy is exact, in obvious contradiction with the experimental observations. One possibility is breaking the flavor democracy with anarchical perturbations as we proposed in an earlier work. However, even within the first two generations, the charged fermion masses are also hierarchical which may not be a coincidence. The democratic $\mathbb S^L_3 \times \mathbb S^R_3$ symmetry of the three generations may first be broken down to an intermediate $\mathbb S^L_2 \times \mathbb S^R_2$ symmetry among the first two generations to regulate the sequential hierarchies, followed by random perturbations, that generate the correct size of all measured observables. Unique predictions for neutrinoless double beta decay are also found.