Discriminating New Physics in $b\rightarrow s\mu^+\mu^-$ via Transverse Polarization Asymmetry of $K^*$ Meson

Abstract

A global fit to current $b\rightarrow s\ell^+\ell^-$ data suggests several new physics solutions. Considering either only one operator or a pair of similar operators at a time and new physics only in the muon sector, it has been shown that the three scenarios (I) $C_9^{\rm NP}<0$, (II) $C_{9}^{\rm NP} = -C_{10}^{\rm NP}$, (III) $C_9^{\rm NP} = -C_9^{\rm 'NP}$ can account for all the data. In order to discriminate between these scenarios one needs to have a handle on additional observables in $b \to s\mu^+ \mu^-$ sector. In this work, we study the transverse polarization asymmetry of $K^*$ polarization in $B\rightarrow K^*\mu^+\mu^-$ decay, $A_T$, to explore its sensitivity to discriminate between the three scenarios. We show that a measurement of this asymmetry with an accuracy of one percent can pick out which new physics scenario is the true solution, at better than 3$\sigma$ C.L.