CHARM MASS DEPENDENCE OF THE O(ALPHA(2)(S)N(F)) TO INCLUSIVE B-]X(C)E(NU)OVER-BAR(E) DECAY

We compute the alpha(s)(2)n(f) 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 mu(BLM) = 0.13m(b), when the inclusive semileptonic rate is expressed in terms of the b and c quark pole masses and the ($) over bar MS strong coupling. The two-loop correction lies roughly midway between that obtained at m(c) = O and that obtained in the Shifman-Voloshin limit m(b), m(c) >> m(b) - m(c) >> Lambda(QCD) while the corresponding BLM scale is closer to that obtained in the former case.