文摘
This study investigates \(B^*_{s,d}\rightarrow \mu ^+\mu ^-\) in the dimuon distributions and the hadronic contribution \(B_{s,d}\rightarrow B^*_{s,d}\gamma \rightarrow \mu ^+\mu ^-\). The \(\mu ^+\mu ^-\) decay widths of the vector mesons \(B^*_{s,d}\) are approximately a factor of 700 larger than the corresponding scalar mesons \(B_{s,d}\). The ratio of the branching fractions obtained, \(\frac{Br({B_{s,d}^*\rightarrow \mu ^+\mu ^-})}{{Br({B_{s,d}\rightarrow \mu ^+\mu ^-})}}\), is approximately \(\frac{0.3\times \mathrm{eV}}{{\Gamma (B^*_{s,d}\rightarrow B_{s,d}\gamma )}}\). The hadronic contribution \(B_{s,d}\rightarrow B^*_{s,d}\gamma \rightarrow \mu ^+\mu ^-\) is also estimated. The relative increase in the \(B_{s,d}\rightarrow \mu ^+\mu ^-\) amplitude is approximately \((0.01\pm 0.006) \sqrt{\frac{{\Gamma (B^*_{s,d}\rightarrow B_{s,d} \gamma )}}{{100~\mathrm{eV}}}}\). If we select \(\Gamma (B^*_{s,d}\rightarrow B_{s,d}\gamma )=2~\)eV, then the branching fractions of the vector mesons to the lepton pair are \(5.3\times 10^{-10}\) and \(1.6\times 10^{-11}\) for \(B^*_{s}\) and \(B^*_{d}\), respectively. If we select \(\Gamma (B^*_{s,d}\rightarrow B_{s,d}\gamma )=200~\)eV, then the updated branching fractions of the scalar mesons to the 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. If we select the recent predicted M1 widths \(\Gamma (B^*_{s,d}\rightarrow B_{s,d}\gamma )=313, 1230\) eV (arXiv:1607.02169), then the updated branching fractions are \((3.8\,\pm \,0.3)\times 10^{-9}\) and \((1.2\,\pm \,0.1)\times 10^{-10}\) for \(B_{s}\rightarrow \mu ^+\mu ^-\) and \(B_{d}\rightarrow \mu ^+\mu ^-\), respectively. Further studies on \(B^*_{s,d}\), including those on dielectron decay and two-body decay with \(J/\psi \), should be conducted.