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Two-loop QCD correction to differential semi-leptonic b --> u decays in the shape-function region

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 Added by Tobias Huber
 Publication date 2008
  fields
and research's language is English
 Authors M. Beneke




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We calculate the two-loop QCD correction to the form factors of on-shell b-quark decay to an energetic massless quark, which constitutes the last missing piece required for an O(alpha_s^2) determination of |V_ub| from inclusive semi-leptonic bar B --> X_u l nu decays in the shape-function region.



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We report on the calculation of the two-loop penguin amplitudes in non-leptonic B decays in the framework of QCD factorization. We discuss the computation of this genuine two-loop, two-scale problem and provide details on the matching from QCD onto SCET, the evaluation of the master integrals, and the convolution of the hard scattering kernels with the light-cone distribution amplitude of the light meson. Preliminary results on the size of the two-loop correction are given.
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We propose a method for a QCD based calculation of one-particle inclusive decays of the form B to bar D X or B to bar D^* X. It is based on the heavy mass limit and a short distance expansion of the amplitudes, which yield a power series in the parameter 1/M^2_X for the spectra and in Lambda_QCD m_b/(m_b - m_c)^2 for the rates. We study the leading term of this expansion for the case of the semi--leptonic decays B to bar D X l^+ u.
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