The first $\Delta(27)$ flavor 3-3-1 model with low scale seesaw mechanism

We propose a viable model based on the $SU(3)_C\times SU(3)_L\times U(1)_X$ gauge group, augmented by the $U(1)_{L_g}$ global lepton number symmetry and the $\Delta(27) \times Z_3\times Z_{16}$ discrete group, capable of explaining the Standard Model (SM) fermion masses and mixings, and having a low scale seesaw mechanism which can be tested at the LHC. In addition the model provides an explanation for the SM fermion masses and mixings. In the proposed model, small masses for the light active neutrinos are generated by an inverse seesaw mechanism caused by non renormalizable Yukawa operators and mediated by three very light Majorana neutrinos and the observed hierarchy of the SM fermion masses and mixing angles is produced by the spontaneous breaking of the $\Delta(27) \times Z_{3}\times Z_{16}$ symmetry at very large energy scale. This neutrino mass generation mechanism is not presented in our previous 3-3-1 models with $\Delta(27)$ group (Nucl.Phys. B913 (2016) 792-814 and Eur.Phys.J. C76 (2016) no.5, 242), where the masses of the light active neutrinos arise from a combination of type I and type II seesaw mechanisms (Nucl.Phys. B913 (2016) 792-814) as well as from a double seesaw mechanism (Eur.Phys.J. C76 (2016) no.5, 242). Thus, this work corresponds to the first implementation of the $\Delta(27)$ symmetry in a 3-3-1 model with low scale seesaw mechanism.