Renormalization-Group Improved Calculation of the B->Xs+gamma Branching Ratio

Matthias Neubert

Paper

Renormalization-Group Improved Calculation of the B->Xs+gamma Branching Ratio

Abstract

Using results on soft-collinear factorization for inclusive B-meson decay distributions, a systematic study of the partial

decay rate with a cut

on photon energy is performed. For values of

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

branching ratio depends on three large scales:

, and

. Logarithms associated with these scales are resummed at next-to-next-to-leading logarithmic order. While power corrections in

turn out to be small, the sensitivity to the scale

GeV (for

GeV) introduces significant perturbative uncertainties, which so far have been ignored. The new theoretical prediction for the

branching ratio with

GeV is

, where the first error is an estimate of perturbative uncertainties and the second one reflects uncertainties in input parameters. With this cut

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.