New rare meson decay constraints on a light vector in $U(1{)}_{B-L},U(1{)}_R$ and the dark photon

We evaluate constraints from flavor changing rare meson decays to a light vector boson $X$, followed by the decay of the on-shell $X$ into the SM fermions. The flavor changing meson decay emitting the light $X$ is induced by loop processes where the up-type quarks, the $W$ boson, or charged scalar bosons are running inside loops. We calculate all one-loop diagrams with neglecting all masses of light quarks except for the top quark in a general anomaly free extra $U(1)$ model. Our theoretical evaluation of the branching ratio of charged $B$ meson decay and charged kaon decay is compared to experimental results, and we derive new constraints for dark photon, $U(1{)}_{B-L}$ and $U(1{)}_R$ models.