Fermion masses and mixings and [Formula omitted] muon anomaly in a 3-3-1 model with [Formula omitted] family symmetry

We propose a predictive model based on the [Formula omitted] gauge symmetry, which is supplemented by the [Formula omitted] 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 [Formula omitted] family symmetry in a [Formula omitted] 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.