We consider a gauge model based on a SU(3)@U(1) symmetry in which the lepton number is violated explicitly by charged scalar and gauge bosons, including a vector field with double electric charge. PACS number(s): 12.15.Cc, 14.80.-j

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.

The SU(3) c ⊗SU(3) L ⊗U(1) N model of Pisano and Pleitez extends the Standard Model in a particularly nice way, so that for example the anomalies cancel only when the number of generations is divisible by three. The original version of the model has some problems accounting for the lepton masses. We resolve this problem by modifying the details of the symmetry breaking sector in the model.

Assuming the existence of right-handed neutrinos, we consider an electroweak model based on the gauge symmetry SU (4) L ⊗ U (1) N . We study the neutral currents coupled to all neutral vector bosons present in the theory. There are no flavor changing neutral currents at tree level, coupled with the lightest neutral vector boson.

We consider a simple way of solving the flavor question by embedding the three-family standard model in a semisimple gauge group extending minimally the weak isospin factor. Quantum chiral anomalies between families of fermions cancel with a matching of the number of families and the number of color degrees of freedom. Our demonstration shows how the theory leads to determination of families structure when the standard model is the input at low energies. The new physics is limited to start below a few TeVs within the reach of the next generation colliders.