Predictions for $B_s \to \bar{K}^* \ell \,\ell$ in non-universal $Z'$ models

The lepton flavor universality violating (LFUV) measurements $R_K$ and $R_{K^*}$ in $B$ meson decays can be accounted for in non-universal $Z'$ models. We constrain the couplings of these $Z'$ models by performing a global fit to correlated $b \to s \ell \ell$ and $b \to d \ell \ell $ processes, and calculate their possible implications for $B_s \to \bar{K}^*\ell \ell$ observables. For real new physics (NP) couplings, the 1-$\sigma$ favored parameters allow the corresponding LFUV ratio $R_{K^*}^{(s)}$ in $B_s \to \bar{K}^*\ell \ell$ to range between 0.8 -- 1.2 at low $q^2$. Complex NP couplings improve the best fit only marginally, however they allow a significant enhancement of the branching ratio, while increasing the range of $R_{K^*}^{(s)}$ at low $q^2$ to 0.8 -- 1.8. We find that NP could cause zero-crossing in the forward-backward asymmetry $A_{FB}$ to shift towards lower $q^2$ values, and enhancement in the magnitude of integrated $A_{FB}$. The $CP$ asymmetry $A_{CP}$ may be suppressed and even change sign. The simultaneous measurements of integrated $R_{K^*}^{(s)}$ and $A_{CP}$ values to 0.1 and 1% respectively, would help in constraining the effective NP Wilson coefficient $C_9$ in $ b \to d \mu \mu$ interactions.