Inclusive decay of B mesons into Ds or D ∗ s

We compute the inclusive decay rates b → D − s (D * − s)c including lowest order QCD corrections on the quark legs, and compare with existing CLEO data. Unlike the short distance QCD corrections, that are of higher order, these corrections are of order α s. In the on-shell renormalization scheme and for α s (m b) ∼ = 0.2 we find a correction of −10 % to the inclusive rate computed using factorization. This gives a total rate BR(b → D − s (D * − s)c) ∼ = 8 % consistent within 1σ with the CLEO value BR(B → D ± s X) = (10.0 ± 2.7) %. The general formulae given here include the case of vanishing mass for the final quark b → D − s (D * − s)u. The radiative correction to this rate is −17 %. We show in another place that this process can be useful for the measurement of the CKM matrix element V ub. We also give the renormalized vertex at the interesting values q 2 = 0 and q 2 = q 2 max , and compare with existing literature.