New physics effects in purely leptonic $B^*_s$ decays

Recently several measurements in the neutral current sector $b\rightarrow s l^+l^-$ ($l=e$ or $\mu$) as well as in the charged current sector $b \rightarrow c \tau \bar{\nu}$ show significant deviations from their Standard Model predictions. It has been shown that two different new physics solutions can explain all the anomalies in $b\rightarrow s l^+l^-$ sector. Both these solutions are in the form of linear combinations of the two operators $(\bar{s}\gamma^{\alpha}P_Lb)(\bar{\mu}\gamma_{\alpha}\mu)$ and $(\bar{s}\gamma^{\alpha}P_Lb)(\bar{\mu}\gamma_{\alpha}\gamma_5\mu)$. We show that the longitudinal polarization asymmetry of the muons in $B^*_s\rightarrow \mu^+\,\mu^-$ decay is a good discriminant between the two solutions if it can be measured to a precision of $10\%$, provided the new physics Wilson coefficients are real. If they are complex, the theoretical uncertainties in this asymmetry are too large to provide effective discrimination. We also investigate the potential impact of $b \rightarrow c \tau \bar{\nu}$ anomalies on $b \rightarrow s \tau^+ \tau^-$ transitions. We consider a model where the new phyics contributions to these two transitions are strongly correlated. We find that the branching ratio of $B^*_s\rightarrow \tau^+\,\tau^-$ can be enhanced by three orders of magnitude.