M. Luke et al., CHARM MASS DEPENDENCE OF THE O(ALPHA(2)(S)N(F)) TO INCLUSIVE B-]X(C)E(NU)OVER-BAR(E) DECAY, Physics letters. Section B, 345(3), 1995, pp. 301-306
We compute the alpha(s)(2)n(f) perturbative QCD contribution to semile
ptonic B decay, including the finite mass of the charm quark. This res
ult 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 res
ults 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.