Advanced Predictions for Moments of the B->X_s+gamma Photon Spectrum
  Based on a new, exact QCD factorization formula for the partial B->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 \sqrt{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_pi^2 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_pi^{2,SF}=(0.11+-0.19_{exp}+-0.08_{th})GeV^2 in the shape-function scheme at a scale mu_f=1.5GeV, while m_b^{kin}=(4.54+-0.11_{exp}+-0.04_{th})GeV and mu_pi^{2,kin}=(0.49+-0.18_{exp}+-0.09_{th})GeV^2 in the kinetic scheme at a scale mu_f=1GeV. 
Matthias Neubert (Cornell University)