A two-loop relation between inclusive radiative and semileptonic B-decay spectra
Abstract
A shape-function independent relation is derived between the partial B->Xu+l+nu decay rate with a cut on P+=EX-PX<Delta and a weighted integral over the normalized B->Xs+gamma photon-energy spectrum. The leading-power contribution to the weight function is calculated at next-to-next-to-leading order in renormalization-group improved perturbation theory, including exact two-loop matching corrections at the scale mui2 ~ mb*LambdaQCD. The overall normalization of the weight function is obtained up to yet unknown corrections of order [alphas(mb)]2. Power corrections from phase-space factors are included exactly, while the remaining subleading contributions are included at first order in 1/mb. At this level unavoidable hadronic uncertainties enter, which are estimated in a conservative way. The combined theoretical accuracy in the extraction of |Vub| is at the level of 5% if a value of Delta near the charm threshold can be achieved experimentally.
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