The 3-3-1 model with S_4 flavor symmetry

TL;DR

This paper develops a 3-3-1 particle physics model incorporating S_4 family symmetry to explain neutrino and quark masses, achieving tribimaximal neutrino mixing and diagonal quark mixing, with insights into symmetry breaking and mass generation mechanisms.

Contribution

It introduces a novel 3-3-1 model with S_4 symmetry, detailing the role of lepton charge and parity, and explaining vacuum alignment and small seesaw contributions.

Findings

Achieves tribimaximal neutrino mixing.

Ensures diagonal quark mixing.

Explains small seesaw contributions.

Abstract

We construct a 3-3-1 model based on family symmetry S_4 responsible for the neutrino and quark masses. The tribimaximal neutrino mixing and the diagonal quark mixing have been obtained. The new lepton charge \mathcal{L} related to the ordinary lepton charge L and a SU(3) charge by L=2/\sqrt{3} T_8+\mathcal{L} and the lepton parity P_l=(-)^L known as a residual symmetry of L have been introduced which provide insights in this kind of model. The expected vacuum alignments resulting in potential minimization can origin from appropriate violation terms of S_4 and \mathcal{L}. The smallness of seesaw contributions can be explained from the existence of such terms too. If P_l is not broken by the vacuum values of the scalar fields, there is no mixing between the exotic and the ordinary quarks at the tree level.