A predictive $331$ model with $A_{4}$ flavour symmetry

TL;DR

This paper introduces a predictive particle physics model based on an extended gauge and discrete symmetry group, accurately describing fermion masses, mixing, and neutrino properties, including specific predictions for neutrinoless double beta decay.

Contribution

It presents a novel $SU(3)_C\times SU(3)_L\times U(1)_X$ model with $A_4$ flavor symmetry that explains fermion mass hierarchies and mixing patterns, incorporating an inverse seesaw mechanism.

Findings

Model's predictions align with experimental data for quark and lepton sectors.

Predicts a vanishing leptonic Dirac CP phase.

Provides specific effective Majorana neutrino mass values for neutrinoless double beta decay.

Abstract

We propose a predictive model based on the $SU(3)_{C}\otimes SU(3)_{L}\otimes U(1)_{X}$ gauge group supplemented by the $A_{4}\otimes Z_{3}\otimes Z_{4}\otimes Z_{6}\otimes Z_{16}$ discrete group, which successfully describes the SM fermion mass and mixing pattern. The small active neutrino masses are generated via inverse seesaw mechanism with three very light Majorana neutrinos. The observed charged fermion mass hierarchy and quark mixing pattern are originated from the breaking of the $Z_{4}\otimes Z_{6}\otimes Z_{16}$ discrete group at very high scale. The obtained values for the physical observables for both quark and lepton sectors are in excellent agreement with the experimental data. The model predicts a vanishing leptonic Dirac CP violating phase as well as an effective Majorana neutrino mass parameter of neutrinoless double beta decay, with values $m_{\beta \beta }=$ 2 and 48 meV for the normal and the inverted neutrino mass hierarchies, respectively.