Study of the rare decays $B_{s,d}^* \to \mu^+ \mu^-$

We investigate the effect of scalar leptoquarks and family non-universal $Z^\prime$ boson on the rare leptonic decays of $B_{s, d}^*$ mesons, mediated by the FCNC transitions $b \to (d, s) l^+ l^-$. They are sensitive to a variety of new physics operators as opposed to the $B_{s,d}$ leptonic modes and hence, can provide an ideal testing ground to look for new physics beyond the standard model. We work out the constraint on new physics parameter space using the measured branching ratios of $B_{d, s} \to \mu^+ \mu^-$ processes and the $B_q - \bar B_q$ mixing data. Using the constrained parameters we estimate the branching ratios of $B_{d,s} \to \mu^+ \mu^-~(e^+ e^-)$ processes. We find that the branching ratios are reasonably enhanced from their corresponding standard model values in the $X(3,2,1/6)$ leptoquark model and are expected to be within the reach of Run II/III of LHC experiments.