Family Non-universal $U(1)^\prime$ Gauge Symmetries and $b\to s$ Transitions

We present a correlated analysis for the $\Delta B =1, 2$ processes which occur via $b\to s$ transitions within models with a family non-universal $U(1)^\prime$. We take a model-independent approach, and only require family universal charges for the first and second generations and small fermion mixing angles. The results of our analysis show that within this class of models, the anomalies in $B_s - \bar B_s$ mixing and the time-dependent CP asymmetries of the penguin-dominated $B_d \to (\pi, \phi, \eta', \rho, \omega, f_0)K_S$ decays can be accommodated.