The S_3 flavor symmetry in 3-3-1 models

TL;DR

This paper introduces two 3-3-1 models utilizing S_3 flavor symmetry to explain fermion masses and mixings, fitting neutrino oscillation data and predicting specific symmetry breaking patterns and mass splittings.

Contribution

The paper develops two novel 3-3-1 models based on S_3 symmetry, incorporating neutrino mass mechanisms and symmetry breaking pathways, with implications for fermion mass hierarchies.

Findings

Models fit neutrino oscillation data with specific symmetry breaking

Degenerate fermion masses are separated by S_3 breaking

TeV-scale seesaw mechanism is naturally realized

Abstract

We propose two 3-3-1 models (with either neutral fermions or right-handed neutrinos) based on S_3 flavor symmetry responsible for fermion masses and mixings. The models can be distinguished upon the new charge embedding (\mathcal{L}) relevant to lepton number. The neutrino small masses can be given via a cooperation of type I and type II seesaw mechanisms. The latest data on neutrino oscillation can be fitted provided that the flavor symmetry is broken via two different directions S_3 \rightarrow Z_2 and S_3 \rightarrow Z_3 (or equivalently in the sequel S_3 \rightarrow Z_2 \rightarrow Identity), in which the second direction is due to a scalar triplet and another antisextet as small perturbation. In addition, breaking of either lepton parity in the model with neutral fermions or lepton number in the model with right-handed neutrinos must be happened due to the \mathcal{L}-violating scalar potential. The TeV seesaw scale can be naturally recognized in the former model. The degenerate masses of fermion pairs (\mu, \tau), (c, t) and (s, b) are respectively separated due to the S_3 \rightarrow Z_3 breaking.