Suppression of scalar mediated FCNCs in a $SU(3)_c\times SU(3)_L\times U(1)_X$-model

The models based on $SU(3)_C\times SU(3)_L\times U(1)_X$ gauge symmetry (331-models) have been advocated to explain the number of fermion families. These models place one quark family to a different representation than the other two. The traditional 331-models are plagued by scalar mediated quark flavour changing neutral currents (FCNC) at tree-level. So far there has been no concrete mechanisms to suppress these FCNCs in 331-models. Recently it has been shown that the Froggatt-Nielsen mechanism can be incorporated into the 331-setting in an economical fashion (FN331-model). The FN331-model explains both the number of fermion families in nature and their mass hierarchy simultaneously. In this work we study the Higgs mediated quark FCNCs in FN331-model. The flavour violating couplings of quarks are suppressed by the ratio of the $SU(2)_L \times U(1)_Y$ and $SU(3)_L\times U(1)_X$ breaking scales. We find that the $SU(3)_L\times U(1)_X$-breaking scale can be as low as 5 TeV in order to pass the flavour bounds.