Hierarchical Fermions and Detectable $Z^\prime$ from Effective Two-Higgs-Triplet 3-3-1 Model

Abstract: We develop a ${\rm SU}(3)_C\otimes {\rm SU}(3)_L\otimes {\rm U}(1)_X$ model where the number of fermion generations is fixed by cancellation of gauge anomalies, being a type of 3-3-1 model with new charged leptons. Similarly to the economical 3-3-1 models, symmetry breaking is achieved effectively with two scalar triplets so that the spectrum of scalar particles at the TeV scale contains just two CP even scalars, one of which is the recently discovered Higgs boson, plus a charged scalar. Such a scalar sector is simpler than the one in the Two Higgs Doublet Model, hence more attractive for phenomenological studies, and has no FCNC mediated by scalars except for the ones induced by the mixing of SM fermions with heavy fermions. We identify a global residual symmetry of the model which guarantees mass degeneracies and some massless fermions whose masses need to be generated by the introduction of effective operators. The fermion masses so generated require less fine-tuning for most of the SM fermions and FCNC are naturally suppressed by the small mixing between the third family of quarks and the rest. The effective setting is justified by an ultraviolet completion of the model from which the effective operators emerge naturally. A detailed particle mass spectrum is presented, and an analysis of the $Z^\prime$ production at the LHC run II is performed to show that it could be easily detected by considering the invariant mass and transverse momentum distributions in the dimuon channel.