Using results on soft-collinear factorization for inclusive B-meson decay
distributions, a systematic study of the partial BβXsβΞ³ decay rate
with a cut EΞ³β>E0β on photon energy is performed. For values of E0β
below about 1.9 GeV, the rate can be calculated without reference to shape
functions using a multi-scale operator product expansion (MSOPE). The
transition from the shape-function region to the MSOPE region is studied
analytically. The resulting prediction for the BβXsβΞ³ branching ratio
depends on three large scales: mbβ, mbβΞβ, and
Ξ=mbββ2E0β. Logarithms associated with these scales are resummed at
next-to-next-to-leading logarithmic order. While power corrections in
ΞQCDβ/Ξ turn out to be small, the sensitivity to the scale
Ξβ1.1 GeV (for E0ββ1.8 GeV) introduces significant
perturbative uncertainties, which so far have been ignored. The new theoretical
prediction for the BβXsβΞ³ branching ratio with EΞ³ββ₯1.8 GeV
is Br(BβXsβΞ³)=(3.38β0.42β0.30+0.31+0.32β)Γ10β4, where
the first error is an estimate of perturbative uncertainties and the second one
reflects uncertainties in input parameters. With this cut (89β7+6βΒ±1) of all events are contained. The implications of larger theory
uncertainties for New Physics searches are briefly explored with the example of
the type-II two-Higgs-doublet model, for which the lower bound on the
charged-Higgs mass is reduced compared with previous estimates to approximately
200 GeV at 95% confidence level.Comment: 39 pages, 3 figures. Results for two-loop anomalous dimensions
(Appendix A.1) corrected, correlations between input parameters included,
numerical analysis update