Renormalization-group improved calculation of the B→Xsγ branching ratio

Using results on soft-collinear factorization for inclusive B-meson decay distributions, a systematic study of the partial B -> X-s gamma decay rate with a cut E-gamma >= E-0 on photon energy is performed. For values of E-0 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 B -> X-s gamma branching ratio depends on three large scales: m(b), root m(b)Delta, and Delta = m(b) - 2E(0). Logarithms associated with these scales are resummed at next- to-next-to- leading logarithmic order. While power corrections in Lambda(QCD)/Delta turn out to be small, the sensitivity to the scale Delta approximate to 1.1 GeV (for E-0 approximate to 1.8 GeV) introduces significant perturbative uncertainties, which so far have been ignored. The new theoretical prediction for the B -> X-s gamma branching ratio with E-gamma = 1.8 GeV is Br(B -> X-s gamma) = (3.38(-0.42)(+0.31) +/- 0.31) x 10(-4), , where the first error is an estimate of perturbative uncertainties and the second one reflects uncertainties in input parameters. With this cut (89 (+6)(-7) +/- 1)% of all events are contained. When this fraction is combined with the previously best prediction for the total decay rate, one obtains Br(B -> X-s gamma) = (3.30(-0.35)(+0.31) +/- 0.17) x 10(-4), with a somewhat less conservative estimate of parametric uncertainties. 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.