Broken S_3 Flavor Symmetry of Leptons and Quarks: Mass Spectra and Flavor Mixing Patterns

TL;DR

This paper explores how applying the S_3 flavor symmetry to leptons and quarks explains mass hierarchies and mixing patterns, and introduces a perturbation method to refine these models for realistic spectra.

Contribution

It presents a unified S_3 flavor symmetry framework for fermion mass matrices and introduces a simple perturbation approach to improve the realism of flavor mixing predictions.

Findings

Mass matrices have a universal form with identity and democracy matrix components.

Neutrino masses are nearly degenerate, explaining large lepton mixing angles.

Perturbations can significantly alter small mixing angles like theta_13.

Abstract

We apply the discrete S_3 flavor symmetry to both lepton and quark sectors of the standard model extended by introducing one Higgs triplet and realizing the type-II seesaw mechanism for finite neutrino masses. The resultant mass matrices of charged leptons (M_l), neutrinos (M_nu), up-type quarks (M_u) and down-type quarks (M_d) have a universal form consisting of two terms: one is proportional to the identity matrix I and the other is proportional to the democracy matrix D. We argue that the textures of M_l, M_u and M_d are dominated by the D term, while that of M_nu is dominated by the I term. This hypothesis implies a near mass degeneracy of three neutrinos and can naturally explain why the mass matrices of charged fermions are strongly hierarchical, why the quark mixing matrix is close to I and why the lepton mixing matrix contains two large angles. We discuss a rather simple perturbation ansatz to break the S_3 symmetry and obtain more realistic mass spectra of leptons and quarks as well as their flavor mixing patterns. We stress that the I term, which used to be ignored from M_l, M_u and M_d, is actually important because it can significantly modify the smallest lepton flavor mixing angle theta_13 or three quark flavor mixing angles.