A highly predictive $A_{4}$ flavour 3-3-1 model with radiative inverse seesaw mechanism

We build a highly predictive 3-3-1 model, where the field content is extended by including several $SU(3)_{L}$ scalar singlets and six right handed Majorana neutrinos. In our model the $SU(3)_{C}\times SU\left( 3\right) _{L}\times U\left( 1\right) _{X}$ gauge symmetry is supplemented by the $A_{4}\times Z_{4}\times Z_{6}\times Z_{16}\times Z_{16}^{\prime }$ discrete group, which allows to get a very good description of the low energy fermion flavor data. In the model under consideration, the $A_{4}\times Z_{4}\times Z_{6}\times Z_{16}\times Z_{16}^{\prime }$ discrete group is broken at very high energy scale down to the preserved $Z_{2}$ discrete symmetry, thus generating the observed pattern of SM fermion masses and mixing angles and allowing the implementation of the loop level inverse seesaw mechanism for the generation of the light active neutrino masses, respectively. The obtained values for the physical observables in the quark sector agree with the experimental data, whereas those ones for the lepton sector also do, only for the case of inverted neutrino mass spectrum. The normal neutrino mass hierarchy scenario of the model is ruled out by the neutrino oscillation experimental data. We find an effective Majorana neutrino mass parameter of neutrinoless double beta decay of $$ meV, a leptonic Dirac CP violating phase of $-81.37^{\circ}$ and a Jarlskog invariant of about $10^{-2}$ for the inverted neutrino mass hierarchy. The preserved $Z_{2}$ symmetry allows for a stable scalar dark matter candidate.