A two-loop relation between inclusive radiative and semileptonicB-decay spectra

A shape-function independent relation is derived between the partialB->X_u+l+nu decay rate with a cut on P_+=E_X-P_XX_s+gamma photon-energy spectrum. The leading-powercontribution to the weight function is calculated at next-to-next-to-leadingorder in renormalization-group improved perturbation theory, including exacttwo-loop matching corrections at the scale mu_i^2 ~ m_b*Lambda_{QCD}. Theoverall normalization of the weight function is obtained up to yet unknowncorrections of order [alpha_s(m_b)]^2. Power corrections from phase-spacefactors are included exactly, while the remaining subleading contributions areincluded at first order in 1/m_b. At this level unavoidable hadronicuncertainties enter, which are estimated in a conservative way. The combinedtheoretical accuracy in the extraction of |V_{ub}| is at the level of 5% if avalue of Delta near the charm threshold can be achieved experimentally.Comment: 22 pages, 4 figures; few comments and one reference added; version to appear in JHE