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

Abstract

The decay of $B_{s,d}^{\ast }\to {\mu }^{+}{\mu }^{-}$~ and its impact on $B_{s,d}\to {\mu }^{+}{\mu }^{-}$ is studied here. The ${\mu }^{+}{\mu }^{-}$ decay widths of vector mesons $B_{s,d}^{\ast }$ are about a factor of 700 larger than the corresponding scalar mesons $B_{s,d}$. The obtained ratio of the branching fractions $Br(B_{s,d}^{\ast }\to {\mu }^{+}{\mu }^{-})/Br(B_{s,d}\to {\mu }^{+}{\mu }^{-})$ is about $\frac{0.3\times \mathrm{eV}}{\Gamma (B_{s,d}^{\ast }\to B_{s,d}\gamma )}$. At the same time, the hadronic contribution $B_{s,d}\to B_{s,d}^{\ast }\gamma \to {\mu }^{+}{\mu }^{-}$ is estimated too. The relative increase of the amplitude of $B_{s,d}\to {\mu }^{+}{\mu }^{-}$ is about $(0.01\pm 0.006)\sqrt{\frac{\Gamma (B_{s,d}^{\ast }\to B_{s,d}\gamma )}{100\mathrm{eV}}}$. If we choose $\Gamma (B_{s,d}^{\ast }\to B_{s,d}\gamma )=2$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 $B_s^{\ast }$ and $B_d^{\ast }$ respectively. If we choose $\Gamma (B_{s,d}^{\ast }\to B_{s,d}\gamma )=200$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. Further studies on $B_{s,d}^{\ast }$ are usefully here, including dielectron decay, two-body decay with $J/\psi$, and so on.

Comments: Comments and suggestions are welcome