Advanced predictions for moments of the (B)over-bar→Xsγ photon spectrum -: art. no. 074025

Based on a new, exact QCD factorization formula for the partial (B) over bar -> X-s gamma decay rate with a restriction on large photon energy, improved predictions are presented for the partial moments < E-gamma > and < E-gamma(2)>-< E-gamma >(2) of the photon spectrum defined with a cut E-gamma >= E-0. In the region where Delta=m(b)-2E(0) is large compared with Lambda(QCD), a theoretical description without recourse to shape functions can be obtained. However, for Delta < m(b) it is important to separate short-distance contributions arising from different scales. The leading terms in the heavy-quark expansion of the moments receive contributions from the scales Delta and root m(b)Delta only, but not from the hard scale m(b). For these terms, a complete scale separation is achieved at next-to-next-to-leading order in renormalization-group improved perturbation theory, including two-loop matching contributions and three-loop running. The results presented here can be used to extract the b-quark mass and the quantity mu(2)(pi) with excellent theoretical precision. A fit to experimental data reported by the Belle Collaboration yields m(b)(SF)=(4.62 +/- 0.10(exp)+/- 0.03(th)) GeV and mu(2,SF)(pi)=(0.11 +/- 0.19(exp)+/- 0.08(th)) GeV2 in the shape-function scheme at a scale mu(f)=1.5 GeV, while m(b)(kin)=(4.54 +/- 0.11(exp)+/- 0.04(th)) GeV and mu(2,kin)(pi)=(0.49 +/- 0.18(exp)+/- 0.09(th)) GeV2 in the kinetic scheme at a scale mu(f)=1 GeV.