One-Particle Inclusive Semi-Leptonic B decays

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^+ \nu.