B^*_{s,d} \to μ^+ μ^- and its impact on B_{s,d} \to μ^+ μ^-
Abstract
The decay of B^*_{s,d} \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}
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 \mu^+\mu^-})/{Br({B_{s,d}\to\mu^+\mu^-})}
is about \frac{0.3 \times {\rm eV}}{{\Gamma(B^*_{s,d} \to B_{s,d} \gamma)}}
. At the same time, the hadronic contribution B_{s,d} \to B^*_{s,d} \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} \to B_{s,d} \gamma)}}{100~ {\rm eV}}}
. If we choose \Gamma(B^*_{s,d} \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}
and B^*_{d}
respectively. If we choose \Gamma(B^*_{s,d} \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}
are usefully here, including dielectron decay, two-body decay with J/\psi
, and so on.