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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 othervarious symmetries, whose spontaneous breaking gives rise to the current SMfermion mass and mixing hierarchy. In the proposed theory the small lightactive neutrino masses are generated from a linear seesaw mechanism mediated bythree Majorana neutrinos. The model is capable of reproducing the experimentalvalues of the physical observables of both quark and lepton sectors. Our modelis predictive in the quark sector having 9 effective parameters that allow tosuccessfully reproduce the four CKM parameters and the six Standard Model (SM)quark masses. In the SM quark sector, there is particular scenario, motivatedby naturalness arguments, which allows a good fit for its ten observables, withonly six effective parameters. We also study the single heavy scalar productionvia gluon fusion mechanism at proton-proton collider. Our model is alsoconsistent with the experimental constraints arising from the Higgs diphotondecay rate.

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