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

A number of observables related to the $b \to s \ell^+ \ell^-$ transition show deviations from their standard model predictions. A global fit to the current $b\rightarrow s\ell^+\ell^-$ 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 work, we develop a procedure to uniquely identify the correct new physics solution. 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 $S_9$ in high $q^2$ bin of $B\to K^*\mu^+\mu^-$ decay can uniquely discriminate between the other two scenarios. We propose new methods, in terms of azimuthal angle asymmetries, to measure $S_9$ with the necessary precision.