$B_{s,d}^{\ast }\to {\mu }^{+}{\mu }^{-}$ and its impact on $B_{s,d}\to {\mu }^{+}{\mu }^{-}$

The decay of $B_{s,d}^{\ast }\to {\mu }^{+}{\mu }^{-}$~ and its impact on $B_{s,d} \to \mu^+ \mu^-$isstudiedhere\mathrm{.}The$ \mu^+ \mu^-$decaywidthsofvectormesons$B^{s,d}$ are about a factor of 700 larger than the corresponding scalar mesons $B_{s,d}$. The obtained ratio of the branching fractions $Br(B_{s,d}^{\ast }\to {\mu }^{+}{\mu }^{-})\mathrm{/}Br(B_{s,d}\to {\mu }^{+}{\mu }^{-})$ is about $\frac{0.3\times \mathrm{e}\mathrm{V}}{\mathrm{\Gamma }(B_{s,d}^{\ast }\to B_{s,d}\gamma )}$. At the same time, the hadronic contribution $B{s,d} \to B^{s,d} \gamma \to \mu^+ \mu^-$isestimatedtoo\mathrm{.}Therelativeincreaseoftheamplitudeof$B{s,d}\to \mu^+\mu^-$isabout$(0.01\pm 0.006) \sqrt{\frac{{\Gamma(B^{s,d} \to B{s,d} \gamma)}}{{100~ {\rm eV}}}}$\mathrm{.}Ifwechoose$\Gamma(B^{s,d} \to B{s,d} \gamma)=2~$eV,thebranchingfractionsofthevectormesonstoleptonpairare$(6.2 \pm 0.6) \times 10^{-10}$and$(1.7 \pm 0.2) \times 10^{-11}$for$B^_{s}$and$B^{d}$respectively\mathrm{.}Ifwechoose$\Gamma(B^*{s,d} \to B_{s,d} \gamma)=200~$eV, the updated branching fractions of the scalar mesons to muon pair are $(3.78\pm 0.25)\times {10}^{-9}$ and $(1.09 \pm 0.09)\times 10^{-10}$for$B_{s}$and$B_{d}$respectively\mathrm{.}Furtherstudieson$B^*_{s,d}$areusefullyhere,includingdielectrondecay,two-bodydecaywith$J/\psi$, and so on.