IsB→Xsγ equal tob→sγ? Spectator contributions to rare inclusiveBdecays

In B→${\mathit{X}}_{\mathit{s}}$γ, there are perturbative QCD corrections at order ${\mathrm{\alpha }}_{\mathit{s}}$ not only to the single quark line process b→sγ but also coming from a set of diagrams where the weak interaction vertex involves a gluon which interacts with the spectator quark in the B hadron. We discuss the impact of the full set of these diagrams. These can influence the decay rate and also the line shape of the photon spectrum as they favor a softer photon energy than does the pure spectator decay b→sγ. A subset of these diagrams generates differences in the decay rates for charged and neutral B’s, ${\mathit{B}}^{+}$→${\mathit{X}}_{\mathit{s}}$γ vs ${\mathit{B}}^0$→${\mathit{X}}_{\mathit{s}}$γ, which can be searched for experimentally, although our calculation indicates that the effect will be hard to observe. Bound-state effects turn out to be required to give rise to spectator corrections to the decay rate at order ${\mathrm{\alpha }}_{\mathit{s}}$. The resulting contribution to the total rate is rather small (of about 5%), although the effect is somewhat larger on portions of the photon spectrum. © 1996 The American Physical Society.