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

We estimate the two-loop perturbative corrections to zero-recoil matri x 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 orde r n(f) alpha(s)(2) and substituting the dependence on the number of fl avours 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 s et 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 scal es are sufficiently large for perturbation theory to be well-behaved. The implications of our results to the extraction of \V-cb\ are briefl y discussed.