Charm mass dependence of the O(αs2nf) correction to inclusive B → Xceνe decay

We compute the αs2nf perturbative QCD contribution to semileptonic B decay, including the finite mass of the charm quark. This result provides an estimate of the size of the two-loop correction, which is found to be about 50% of the one-loop correction. We use these results to set the scale for the one-loop correction using the scheme of Brodsky, Lepage and Mackenzie and find a BLM scale of μBLM = 0.13mb, when the inclusive semileptonic rate is expressed in terms of the b and c quark pole masses and the MS strong coupling. The two-loop correction lies roughly midway between that obtained at mc = 0 and that obtained in the Shifman-Voloshin limit mb, mc ⪢ mb − mc ⪢ ΛQCD while the corresponding BLM scale is closer to that obtained in the former case.