HIGHER-ORDER PERTURBATIVE CORRECTIONS TO B-]C TRANSITIONS AT ZERO RECOIL

We estimate the two-loop perturbative corrections to zero-recoil matrix elements of the flavour-changing currents ($) over bar c gamma(mu)b and ($) over bar c gamma(mu)gamma(5)b by calculating the terms of order n(f) alpha(s)(2) and substituting the dependence on the number of flavours by the first coefficient of the beta-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-alpha(s) corrections in the ($) over bar MS scheme, we obtain mu(V) similar or equal to 0.92 root m(b)m(c) and mu(A) similar or equal to 0.51 root m(b)m(c) 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 \V-cb\ are briefly discussed.