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.

Comments: 5 pages, published in PRD