Quark mass and mixing in the 3-3-1 model with neutral leptons based on $D_4$ flavor symmetry

TL;DR

This paper updates a $D_4$ flavor symmetry model within a 3-3-1 gauge framework to successfully generate realistic quark masses and mixing matrices, aligning with experimental data.

Contribution

It introduces an updated $D_4$ flavor model in a 3-3-1 gauge theory that achieves realistic quark mass and mixing predictions at first-order perturbation.

Findings

All quarks have consistent masses.

Realistic quark mixing matrix achieved.

Model aligns with experimental data.

Abstract

The $D_4$ flavor model based on $\mathrm{SU}(3)_C \otimes \mathrm{SU}(3)_L \otimes \mathrm{U}(1)_X$ gauge symmetry that aims at describing quark mass and mixing is updated. After spontaneous breaking of flavor symmetry, with the constraint on the Higgs vacuum expectation values (VEVs) in the Yukawa couplings, all of quarks have consistent masses, and a realistic quark mixing matrix can be realized at the first order of perturbation theory.