FCNC, CP violation and implications for some rare decays in an SU(4)_L X U(1)_X extension of the standard model

Extensions of the standard model (SM) with gauge symmetry SU(3)_c X SU(4)_L X U(1)_X (3-4-1 extensions) where anomaly cancellation takes place between the fermion families (three-family models) predict the existence of two new heavy neutral gauge bosons which transmit flavor changing neutral currents (FCNC) at tree-level. In this work, in the context of a three-family 3-4-1 extension which does not contain particles with exotic electric charges, we study the constraints coming from neutral meson mixing on the parameters of the extension associated to tree level FCNC effects. Taking into account experimental measurements of observables related to K and B meson mixing and including new CP-violating phases, we study the resulting bounds for angles and phases in the mixing matrix for the down-quark sector, as well as the implications of these bounds for the modifications in the amplitudes of the clean rare decays K^+ -> \pi^+ \bar\nu \nu, K_{L} -> \pi^0 \nu \bar\nu, K_L -> \pi^0 l^+ l^- (l=e,\mu) and B_{d/s} -> \mu^+ \mu^-.