Froggatt-Nielsen mechanism in a model with \(SU(3)_c\times SU(3)_L \times U(1)_X\) gauge group

Abstract

The models with the gauge group \(SU(3)_c\times SU(3)_L \times U(1)_X\) (331-models) have been advocated to explain why there are three fermion generations in Nature. As such they can provide partial understanding of the flavour sector. The hierarchy of Yukawa-couplings in the Standard Model is another puzzle which remains without compelling explanation. We propose to use Froggatt-Nielsen -mechanism in a 331-model to explain both fundamental problems. It turns out that no additional representations in the scalar sector are needed to take care of this. The traditional 331-models predict scalar flavour changing neutral currents at tree-level. We show that they are strongly suppressed in our model.