The strong-CP question in SU(3)c×SU(3)L×U(1)N models

We analyze two recent models based on the gauge group SU(3)c×SU(3)L×U(1)N where each generation is not anomaly-free, but anomaly cancels when three generations are taken into account. We show that the most general Yukawa couplings of these models admit of a Peccei-Quinn symmetry. This symmetry can be extended to the entire Lagrangian by using extra fields in a very elegant way so that the resulting axion can be made invisible. Introduction In the standard model, each generation of fermions is anomaly-free. This is true for many extensions of the standard model as well, including popular grand unified models. In these models, therefore, the number of generations is completely unrestricted on theoretical grounds. Recently, an interesting class of models have been proposed which do not have this property. Each generation is anomalous, but different generations are not exact replicas of one another, and the anomalies cancel when a number of generations are taken into account. The most economical gauge group which admits of such fermion representations is SU(3)c×SU(3)L×U(1)N , which has been proposed by Pisano and Pleitez [1] and by Frampton [2] (PPF). The original model did not have right-handed neutrinos, but recently Foot, Long and Tran (FLT) [3] have included them in a non-trivial way in an interesting variation of the model. Here we show that the Yukawa couplings of these models automatically contains a Peccei-Quinn (PQ) symmetry. The symmetry can also be extended to the Higgs potential, thereby making it a symmetry of the entire Lagrangian. This solves the strong CP problem in an elegant way in these models. However, the resulting axion can be made consistent with known bounds only by introducing new fields.