A two-loop relation between inclusive radiative and semileptonic B-decay spectra
Abstract
A shape-function independent relation is derived between the partial B->X_u+l+nu decay rate with a cut on P_+=E_X-P_X<Delta and a weighted integral over the normalized B->X_s+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 mu_i^2 ~ m_b*Lambda_{QCD}. The overall normalization of the weight function is obtained up to yet unknown corrections of order [alpha_s(m_b)]^2. Power corrections from phase-space factors are included exactly, while the remaining subleading contributions are included at first order in 1/m_b. At this level unavoidable hadronic uncertainties enter, which are estimated in a conservative way. The combined theoretical accuracy in the extraction of |V_{ub}| is at the level of 5% if a value of Delta near the charm threshold can be achieved experimentally.
Cite
@article{arxiv.hep-ph/0508178,
title = {A two-loop relation between inclusive radiative and semileptonic B-decay spectra},
author = {Bjorn O. Lange and Matthias Neubert and Gil Paz},
journal= {arXiv preprint arXiv:hep-ph/0508178},
year = {2011}
}
Comments
22 pages, 4 figures; few comments and one reference added; version to appear in JHEP