Abstract
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.
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