Extensions of the standard model with gauge symmetry $SU(3{)}_c\otimes SU(4{)}_L\otimes U(1{)}_X$ (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 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 flavor changing neutral current 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 $K^{+}\to {\pi }^{+}\overline{\nu }\nu$, $K_L\to {\pi }^0\nu \overline{\nu }$, $K_L\to {\pi }^0{l}^{+}{l}^{-}$ ($l=e$, $\mu$) and $B_{d/s}\to {\mu }^{+}{\mu }^{-}$.

• Received 11 May 2011

DOI:https://doi.org/10.1103/PhysRevD.84.115001