We study the Glashow-Iliopoulos-Maiani mechanism for flavor-changing neutral-current suppression in both the gauge and Higgs sectors, for models with SU(3)z, Igt U(1)iv gauge symmetry. The models di6'er from one another only with respect to the representation content. The main features of these models are that in order to cancel the triangle anomalies the number of families must be divisible by three (the number of colors) and that the lepton number is violated by some lepton-gauge bosons and lepton-scalar interactions.

In this letter we consider that assuming: a) that the only left-handed neutral fermions are the active neutrinos, b) that B − L is a gauge symmetry, and c) that the L assignment is restricted to the integer numbers, the anomaly cancellation imply that at least three right-handed neutrinos must be added to the minimal representation content of the electroweak standard model. However, two types of models arise: i) the usual one where each of the three identical right-handed neutrinos has total lepton number L = 1; ii) and the other one in which two of them carry L = 4 while the third one carries L = −5.It is well known that it is possible to enlarge the representation content of the minimal electroweak standard model (ESM) by adding an arbitrary number of right-handed neutrinos. Since they are sterile under the interactions of that model they do not contribute to the anomaly cancellation of the gauge symmetries, then nothing determine their number. Until now, it has been a question of taste to consider a particular number of these fields in extensions of the model. It is also well known that within the ESM (no right-handed neutrinos) both, baryon (B) and total lepton (L) numbers, are conserved automatically up to anomaly effects: both global U(1) B and U(1) L are anomalous [1] (but their consequences are well suppressed at least at zero temperature) and only the combination U(1) B−L is a global anomaly free symmetry if right-handed neutrinos are added for cancelling the mixed gauge-gravitational anomaly [2].

We build a complete supersymmetric version of a 3-3-1 gauge model using the superfield formalism. We point out that a discrete symmetry, similar to R symmetry in the minimal supersymmetric standard model, is possible to be defined in this model. Hence we have both R-conserving and R-violating possibilities. Analysis of the mass spectrum of the neutral real scalar fields show that in this model the lightest scalar Higgs boson has a mass upper limit, and at the tree level it is 124.5 GeV for a given illustrative set of parameters.

We study a few ∆F = 2 and ∆F = 1 flavor changing neutral current processes in the minimal 3-3-1 model by considering, besides the neutral vector bosons Z ′ , the effects due to one CP -even and one CP -odd scalars. We find that there are processes in which the interference among all the neutral bosons is constructive or destructive, and in others the interference is negligible. We first obtain numerical values for all the unitary matrices that rotate the left-and right-handed quarks and give the correct mass of all the quarks in each charge sector and the Cabibbo-KobayashiMaskawa (CKM) mixing matrix.

In the framework of a 3-3-1 model with a minimal scalar sector we make a detailed study concerning the implementation of the PQ symmetry in order to solve the strong CP problem. For the original version of the model, with only two scalar triplets, we show that the entire Lagrangian is invariant under a PQ-like symmetry but no axion is produced since an U (1) subgroup remains unbroken. Although in this case the strong CP problem can still be solved, the solution is largely disfavored since three quark states are left massless to all orders in perturbation theory. The addition of a third scalar triplet removes the massless quark states but the resulting axion is visible.In order to become realistic the model must be extended to account for massive quarks and invisible axion. We show that the addition of a scalar singlet together with a Z N discrete gauge symmetry can successfully accomplish these tasks and protect the axion field against quantum gravitational effects. To make sure that the protecting discrete gauge symmetry is anomaly free we use a discrete version of the Green-Schwarz mechanism.