A detailed and general study of the fermionic structure of the 331 models with β arbitrary is carried out based on the criterion of cancellation of anomalies. We consider models with an arbitrary number of lepton and quark generations, but requiring to associate only one lepton and one quark SU (3) L multiplet for each generation, and at most one right-handed singlet per each left-handed fermion. We see that the number of quark left-handed multiplets must be three times the number of leptonic left-handed multiplets. Furthermore, we consider a model with four families and β = −1/ √ 3 where the additional family corresponds to a mirror fermion of the third generation of the Standard Model. We also show how to generate ansatzs about the mass matrices of the fermions according to the phenomenology. In particular, it is possible to get a natural fit for the neutrino hierarchical masses and mixing angles. Moreover, by means of the mixing between the third quark family and its mirror fermion, a possible solution for the A b F B discrepancy is obtained.

A complete study of the Higgs sector of the SU(3) c SU(3) L U(1) X model is carried out, obtaining all possible cases of vacuum expectation values that permit the spontaneous symmetry breaking pattern SU (3) We find the most general Higgs potentials that contain three Higgs triplets and one sextet. A detailed study of the scalar sector for different models with three Higgs triplets is done. The models end up in an electroweak two Higgs doublet model after the first symmetry breakdown; we find that the low energy limit depends on a trilinear parameter of the Higgs potential, and that the decoupling limit from the electroweak two Higgs doublet model to the minimal standard model can be obtained quite naturally.

In the context of the 331 models, we consider constraints on the extra neutral boson Z ′ predicted by the model, where three different quark family assignments are identified. Using the ansatz of Matsuda as an specific texture for the quark mass matrices, we obtain allowed regions associated with the Z-Z' mixing angle, the mass of the Z ′ boson and the parameter β which determines different 331 models. The Z 1 and Z 2 decays with and without flavor changing are also considered. The flavor changing decays of the Z 1 boson into quarks at tree level are highly suppressed by the Z − Z ′ mixing angle, obtaining the same order of magnitude as the standard model prediction at one loop level. The Z 2 decay widths are calculated with and without flavor changing, where oblique radiative corrections at one loop accounts for about 1% − 4% deviations. *

We propose a new anomaly-free and family nonuniversal U(1) extension of the standard model with the addition of two scalar singlets and a new scalar doublet. The quark sector is extended by adding three exotic quark singlets, while the lepton sector includes two exotic charged lepton singlets, three right-handed neutrinos and three sterile Majorana leptons to obtain the fermionic mass spectrum of the standard model. The lepton sector also reproduces the elements of the PMNS matrix and the squared-mass differences data from neutrino oscillation experiments. Also, analytical relations of the PMNS matrix are derived via the inverse see-saw mechanism, and numerical predictions of the parameters in both normal and inverse order scheme for the mass of the phenomenological neutrinos are obtained. We employed a simple seesaw-like method to obtain analytical mass eigenstates of the CP-even 3 × 3 mass matrix of the scalar sector.

We propose a new non-universal U (1) ′ extension of the standard model with the addition of three exotic quark singlets, two scalar singlets and one additional scalar doublet. We obtain family dependent couplings with a new Z ′ boson in the quark sector and universal couplings with the lepton sector. From experimental data on Z ′ research at CERN-LHC collider, we find limit regions in the U (1) ′ free parameters (Z ′ mass and coupling constant), which we use to obtain total decay width and invariantmass distributions. By introducing discrete symmetries and mixing couplings between ordinary and exotic fermions, we obtain predictable mass relations in the quark sector compatible with the phenomenological values without large fine tuning of the Yukawa couplings and with few free parameters, where hierarchies between quark families can be understood from the existence of heavy beyond standard model particles.