Fermion masses and mixings and $g-2$ muon anomaly in a 3-3-1 model with $D_4$ family symmetry

TL;DR

This paper introduces a novel $SU(3)_C\times SU(3)_L\times U(1)_X$ model with $D_4$ family symmetry that explains fermion masses, mixings, and the muon $g-2$ anomaly, incorporating inverse seesaw neutrino masses and TeV-scale exotic leptons.

Contribution

It is the first to implement $D_4$ family symmetry in a 3-3-1 model with inverse seesaw neutrinos and addresses multiple experimental anomalies.

Findings

Successfully fits SM fermion masses and mixings.

Accounts for the muon $g-2$ anomaly.

Predicts TeV-scale charged exotic leptons.

Abstract

We propose a predictive model based on the $SU(3)_C\times SU(3)_L\times U(1)_X$ gauge symmetry, which is supplemented by the $D_4$ family symmetry and several auxiliary cyclic symmetries whose spontaneous breaking produces the observed SM fermion mass and mixing pattern. The masses of the light active neutrinos are produced by an inverse seesaw mechanism mediated by three right handed Majorana neutrinos. To the best of our knowledge the model corresponds to the first implementation of the $D_4$ family symmetry in a $SU(3)_C\times SU(3)_L\times U(1)_X$ theory with three right handed Majorana neutrinos and inverse seesaw mechanism. Our proposed model successfully accommodates the experimental values of the SM fermion mass and mixing parameters, the muon anomalous magnetic moment as well as the Higgs diphoton decay rate and meson oscillations constraints. The consistency of our model with the muon anomalous magnetic moment requires charged exotic vector like leptons at the TeV scale.