# $B^*_{s,d} \rightarrow \mu ^+ \mu ^-$ and its impact on $B_{s,d} \rightarrow \mu ^+ \mu ^-$

The European Physical Journal C, Oct 2016

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.

This is a preview of a remote PDF: http://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-016-4423-z.pdf

Guang-Zhi Xu, Yue Qiu, Cheng-Ping Shen, Yu-Jie Zhang. $B^*_{s,d} \rightarrow \mu ^+ \mu ^-$ and its impact on $B_{s,d} \rightarrow \mu ^+ \mu ^-$, The European Physical Journal C, 2016, DOI: 10.1140/epjc/s10052-016-4423-z