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A two-loop relation between inclusive radiative and semileptonic B-decay spectra

Bjorn O. Lange·Matthias Neubert·Gil Paz
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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 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.

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Bjorn O. Lange, Matthias Neubert, Gil Paz. 2005-10-24. A two-loop relation between inclusive radiative and semileptonic B-decay spectra. https://doi.org/10.1088/1126-6708%2F2005%2F10%2F084

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