Intermediate pseudoscalar resonance contributions toB→Xsγγ

Abstract

We calculate the decay rate $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}\ensuremath{\gamma}\ensuremath{\gamma})$ via intermediate pseudoscalar charmonium ${\ensuremath{\eta}}_{c}.$ This process is thought to be the main long-distance contribution which dominates the corresponding inclusive rare $B$ decay. We point out that once the momentum dependence of the ${\ensuremath{\eta}}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ conversion strength, due to the off-shellness of the intermediate ${\ensuremath{\eta}}_{c},$ is taken into account, the rate of this decay mode is reduced. The change in differential decay rate in the region of the spectrum immediately below ${m}_{{\ensuremath{\eta}}_{c}}$ is more significant. On the other hand, we point out that the unexpectedly large branching ratio for $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}{\ensuremath{\eta}}^{\ensuremath{'}}$ which was recently observed by CLEO could indicate a potentially larger long-distance contribution via ${\ensuremath{\eta}}^{\ensuremath{'}}$ resonance.