Abstract :
We estimate the two-loop perturbative corrections to zero-recoil matrix elements of the flavour-changing currents c̄γμb and c̄γμγ5 b by calculating the terms of order nf α2s and substituting the dependence on the number of flavours by the first coefficient of the β-function. Both for vector and axial vector currents, we find moderate two-loop corrections below 1% in magnitude. Using the Brodsky-Lepage-Mackenzie prescription to set the scale in the order-αs corrections in the MS scheme, we obtain μV ⋍ 0.92√mbmc and μA ⋍ 0.51√mbmc in the two cases. These scales are sufficiently large for perturbation theory to be well-behaved. The implications of our results to the extraction of |Vcb| are briefly discussed.
