FCNC in Concurrent Dark Photon and Dark $Z$ Models

In this work we fit the available binned data of the differential decay distribution of the exclusive $B \to K^{(*)} \ell^+ \ell^-$ and $B_s \to \phi \mu^+ \mu^-$ decays to the mass and mixing parameters of a light dark vector boson model. Due to an incorrect assessment of the dominant contribution of the dark $Z$ model to the FCNC B-meson decays, a previous work in literature reported that $\mathcal{O}(1)$ mixings were allowed by the data. In this talk we report the correct calculations and constraints on the mixing parameters as well as the mass of the dark vector boson using the marginalization technique. We also study other relevant bounds on the parameter space from low energy experiments such as the atomic parity violation, $K^+ \to \mu^+ + invisible$ decay, $B_s - \overline{B}_s$ mixing etc and find that inspite of obtaining a good fit to the experimental $b \to s \ell^+ \ell^-$ data, the entire parameter space gets ruled out from some of the above bounds. In case of a model with tiny mixing and additional interaction of the dark $Z$ to the muon, some bounds are relaxed while some others are violated.