A unique discrimination between new physics scenarios in $b\rightarrow s\mu^+\mu^-$ anomalies.

A number of observables related to the $b \to s l^+ l^-$ transition show deviations from their standard model predictions. A global fit to the current $b\rightarrow sl^+l^-$ data suggests several new physics solutions. Considering only one operator at a time and new physics only in the muon sector, it has been shown that the new physics scenarios (I) $C_9^{\rm NP}<0$, (II) $C_{9}^{\rm NP} = -C_{10}^{\rm NP}$, (III) $C_9^{\rm NP} = -C_9^{\prime \rm NP}$ can account for all data. In this paper, we develop a procedure to discriminate between these scenarios through a study of the branching ratio of $B_s \to \mu^+\mu^-$ and the distribution of $B\to K^*\mu^+\mu^-$ decay in the azimuthal angle. The scenario II predicts a significantly lower value of $\mathcal{B}(B_s\to \mu^+\mu^-)$ and can be distinguished from the other two scenarios if the experimental uncertainty comes down by a factor of three. On the other hand, a precise measurement of the CP averaged angular observables $S_3$ and $S_9$ in high $q^2$ bin of $B\to K^*\mu^+\mu^-$ decay can uniquely discriminate between the other two scenarios. We define two azimuthal angle asymmetries, proportional to $S_3$ and to $S_9$ respectively, which can be measured with small statistical uncertainty.