Breaking flavor democracy with symmetric perturbations

TL;DR

This paper explores how small symmetric perturbations to democratic fermion mass matrices can generate realistic mass hierarchies and mixing patterns in quarks and leptons, considering symmetry breaking patterns.

Contribution

It introduces a framework for symmetry breaking from $S_3$ to $S_2$ in fermion mass matrices, explaining fermion masses and mixings with minimal assumptions.

Findings

Reproduces quark and lepton mass hierarchies

Explains mixing angles consistent with observations

Shows robustness across neutrino mass hierarchies

Abstract

Flavor democracy broken in the fermion mass matrix by means of small perturbations can give rise to hierarchical fermion masses. We study the breaking of the $S^L_3 \times S^R_3$ symmetry associated with democratic mass matrices to a smaller exchange symmetry $S^L_2 \times S^R_2$ in the charged lepton, up and down quark sectors. An additional breaking of the $S^L_2 \times S^R_2$ symmetry is necessary for the down quark mass matrix, which yields arbitrary perturbations in that sector. On the other hand, we require the neutrino mass matrix to be diagonal at the leading order, with the perturbations left arbitrary due to the absence of any guiding symmetry. We show that the interplay between these two kinds of perturbations reproduces the quark and lepton mass and mixing observables for either hierarchy of neutrino masses.