# Fermion masses and mixings and some phenomenological aspects of a 3-3-1 model with linear seesaw mechanism

## TL;DR

This paper introduces a 3-3-1 gauge model with an S4 symmetry that explains fermion mass hierarchies and neutrino masses via a linear seesaw, successfully fitting quark and lepton data and analyzing collider phenomenology.

## Contribution

The paper presents a novel 3-3-1 model with S4 symmetry incorporating a linear seesaw for neutrino masses, achieving accurate fermion mass and mixing predictions with minimal parameters.

## Key findings

- Successfully reproduces quark and lepton mixing parameters
- Predicts collider signatures of heavy scalars consistent with Higgs data
- Provides a minimal parameter fit for quark sector observables

## Abstract

We propose a viable theory based on the $SU(3)_C\times SU(3)_L\times U(1)_X$ gauge group supplemented by the $S_4$ discrete group together with other various symmetries, whose spontaneous breaking gives rise to the current SM fermion mass and mixing hierarchy. In the proposed theory the small light active neutrino masses are generated from a linear seesaw mechanism mediated by three Majorana neutrinos. The model is capable of reproducing the experimental values of the physical observables of both quark and lepton sectors. Our model is predictive in the quark sector having 9 effective parameters that allow to successfully reproduce the four CKM parameters and the six Standard Model (SM) quark masses. In the SM quark sector, there is particular scenario, motivated by naturalness arguments, which allows a good fit for its ten observables, with only six effective parameters. We also study the single heavy scalar production via gluon fusion mechanism at proton-proton collider. Our model is also consistent with the experimental constraints arising from the Higgs diphoton decay rate.