We study the minimal set of higgs scalars, for models based on the local gauge group SU (3)c ⊗SU (3)L ⊗U (1)X which do not contain particles with exotic electric charges. We show that only two higgs SU (3)L triplets are needed in order to properly break the symmetry. The exact tree-level scalar mass matrices resulting from symmetry breaking are calculated at the minimum of the most general scalar potential, and the gauge bosons are obtained, together with their coupling to the physical scalar fields. We show how the scalar sector introduced is enough to produce masses for fermions in a particular model which is an E6 subgroup. By using experimental results we constraint the scale of new physics to be above 1.3 TeV.

Six different models, straightforward extensions of the standard model to SU (3)c ⊗ SU (3)L ⊗ U (1)X , which do not contain particles with exotic electric charges are presented. Two of the models are one family and four are three family models. In two of the three family models one of the families transforms different from the others, and in the other two all the three families are different.

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We carry out a systematic study of possible extensions of the standard model based on the gauge group SU (3)c⊗ SU (4)L⊗ U (1)X. We consider models with particles having exotic electric charges and also models which do not contain exotic electric charges in the gauge boson sector or in the fermion sector. For the first case an infinite number of models can, in principle, be constructed, while the restriction to non-exotic electric charges only allows for eight different anomaly-free models. Four of them are three-family models in the sense that anomalies cancel by an interplay between the three families, and another two are one-family models where anomalies cancel family by family as in the standard model. The remaining two are two-family models.

We present an extension of the standard model to the local gauge group SU(3) c SU(4) L U(1) X with a family nonuniversal treatment and anomalies canceled among the three families in a nontrivial fashion. The mass scales, the gauge boson masses, and the masses for the spin 1/2 particles in the model are analyzed. The neutral currents coupled to all neutral vector bosons in the model are studied, and particular values of the parameters are used in order to simplify the mixing between the three neutral currents present in the theory, mixing which is further constrained by experimental results from the CERN LEP, SLAC Linear Collider, and atomic parity violation.

An extension of the gauge group SU (2) L ⊗ U (1) Y of the standard model to the symmetry group SU (4) L ⊗ U (1) X (3-4-1 for short) is presented. The model does not contain exotic electric charges and anomaly cancellation is achieved with a family of quarks transforming differently from the other two, thus leading to FCNC. By introducing a discrete Z 2 symmetry we obtain a consistent fermion mass spectrum, and avoid unitarity violation of the CKM mixing matrix arising from the mixing of ordinary and exotic quarks. The neutral currents coupled to all neutral vector bosons are studied, and by using CERN LEP and SLAC Linear Collider data at Z-pole and atomic parity violation data, we bound parameters of the model related to tree-level Z − Z ′ mixing. These parameters are further constrained by using experimental input from neutral meson mixing in the analysis of sources of FCNC present in the model. Constraints coming from the contribution of exotic particles to the one-loop oblique electroweak parameters S, T and U are also briefly discussed. Finally, a comparison is done of the predictions of different classes of 3-4-1 models without exotic electric charges.

A study of the three-family local gauge group SU (3)c⊗ SU (3)L⊗ U (1)X with right-handed neutrinos is carried out. We use the minimal scalar sector able to break the symmetry in a proper way and produce, at the same time, masses for the fermion fields. We embed the structure into a simple gauge group and, by using experimental results from the CERN LEP, SLAC linear collider and atomic parity violation data, we also constrain relevant parameters for the new neutral and charged currents. We discuss the mass spectrum for the gauge boson sector and for the spin 1/2 particles. With the use of discrete symmetries and the introduction of extra scalar fields, a consistent mass spectrum could be constructed.

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