  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.
