$b \to s$ Transitions in Family-dependent $U(1)^\prime$ Models

We analyze flavor-changing-neutral-current (FCNC) effects in the $b\to s$ transitions that are induced by family non-universal $U(1)'$ gauge symmetries. After systematically developing the necessary formalism, we present a correlated analysis for the $\Delta B =1, 2$ processes. We adopt a model-independent approach in which we only require family-universal charges for the first and second generations and small fermion mixing angles. We analyze the constraints on the resulting parameter space from $B_s - \bar B_s$ mixing and the time-dependent CP asymmetries of the penguin-dominated $B_d \to (\pi, \phi, \eta', \rho, \omega, f_0)K_S$ decays. Our results indicate that the currently observed discrepancies in some of these modes with respect to the Standard Model predictions can be consistently accommodated within this general class of models.