$B^*_{s,d} \to μ^+ μ^-$ and its impact on $B_{s,d} \to μ^+ μ^-$

The decay of $B^*_{s,d} \to μ^+ μ^-$~ and its impact on $B_{s,d} \to μ^+ μ^-$ is studied here. The $μ^+ μ^-$ decay widths of vector mesons $B^*_{s,d}$ are about a factor of 700 larger than the corresponding scalar mesons $B_{s,d}$. The obtained ratio of the branching fractions $Br({B_{s,d}^*\to μ^+μ^-})/{Br({B_{s,d}\toμ^+μ^-})}$ is about $\frac{0.3 \times {\rm eV}}{{Γ(B^*_{s,d} \to B_{s,d} γ)}}$. At the same time, the hadronic contribution $B_{s,d} \to B^*_{s,d} γ\to μ^+ μ^-$ is estimated too. The relative increase of the amplitude of $B_{s,d}\to μ^+μ^-$ is about $(0.01\pm 0.006) \sqrt{\frac{{Γ(B^*_{s,d} \to B_{s,d} γ)}}{100~ {\rm eV}}}$. If we choose $Γ(B^*_{s,d} \to B_{s,d} γ)=2~$eV, the branching fractions of the vector mesons to lepton pair are $(6.2 \pm 0.6) \times 10^{-10}$ and $(1.7 \pm 0.2) \times 10^{-11}$ for $B^*_{s}$ and $B^*_{d}$ respectively. If we choose $Γ(B^*_{s,d} \to B_{s,d} γ)=200~$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. Further studies on $B^*_{s,d}$ are usefully here, including dielectron decay, two-body decay with $J/ψ$, and so on.

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