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

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 flavor sector. The hierarchy of Yukawa couplings in the Standard Model is another puzzle that remains without a compelling explanation. We propose to use the 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 unsuppressed scalar flavor-changing neutral currents at tree level. We show that they are strongly suppressed in our model.