Advanced Predictions for Moments of the B->Xₛ+gamma Photon Spectrum

Original · EN

Based on a new, exact QCD factorization formula for the partial B->Xₛ+gamma decay rate with a restriction on large photon energy, improved predictions are presented for the partial moments <Egamma> and <Egamma²>-<Egamma>² of the photon spectrum defined with a cut Egamma>E₀. In the region where Delta=mb-2E₀ is large compared with LambdaQCD, a theoretical description without recourse to shape functions can be obtained. However, for Delta<<mb 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 √mb Delta only, but not from the hard scale mb. 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 muₚi² with excellent theoretical precision. A fit to experimental data reported by the Belle Collaboration yields mbSF=(4.62+-0.10exp+-0.03th)GeV and muₚi2,SF=(0.11+-0.19exp+-0.08th)GeV² in the shape-function scheme at a scale muf=1.5GeV, while mbkin=(4.54+-0.11exp+-0.04th)GeV and muₚi2,kin=(0.49+-0.18exp+-0.09th)GeV² in the kinetic scheme at a scale muf=1GeV.