New physics effects in radiative leptonic $B_s$ decay

There are several anomalous measurements in the decays induced by the quark level transition $b \to s \mu^+ \mu^-$, which do not agree with the predictions of the Standard Model. These measurements could be considered as signatures of physics beyond the Standard Model. Working within the framework of effective field theory, several groups have performed global fits to all $b \to s \mu^+ \mu^-$ data to identify the Lorentz structure of possible new physics. Many new physics scenarios have been suggested to explain the anomalies in the $b \to s \mu^+ \mu^-$ sector. In this work, we investigate the impact of these new physics scenarios on the radiative leptonic decay of $B_s$ meson. We consider the branching ratio of this decay along with the ratio $R_{\gamma}$ of the differential distribution $B_s \to \mu^+ \mu^- \gamma$ \& $B_s \to e^+ e^- \gamma$ and the muon forward-backward asymmetry $A_{FB}$. We find that the predicted values of the branching ratio and $A_{FB}$ are close to the SM results for all allowed new physics solutions whereas some of the solutions allow large deviation in $R_{\gamma}$ from its SM prediction.