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Guang-Zhi Xu; Yue Qiu; Cheng-Ping Shen; Yu-Jie Zhang

doi:10.1140/epjc/s10052-016-4423-z

EPJ

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

Guang-Zhi Xu¹^,2, Yue Qiu², Cheng-Ping Shen²^,3 and Yu-Jie Zhang²^,3^*

¹ Department of Physics, Liaoning University, Shenyang, 110036, China
² Beijing Key Laboratory of Advanced Nuclear Energy Materials and Physics, and School of Physics, Beihang University, Beijing, 100191, China
³ CAS Center for Excellence in Particle Physics, Beijing, 100049, China

Received: 5 April 2016
Accepted: 10 October 2016
Published online: 27 October 2016

Abstract

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.

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