A CLOSER LOOK AT PERTURBATIVE CORRECTIONS IN THE b→c SEMILEPTONIC TRANSITIONS

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Abstract
We comment on two recent calculations of the second order perturbative corrections in the heavy flavor semileptonic transitions within the Brodsky-Lepage-Mackenzie approach. It is pointed out that the results do not show significant enhancement either in the inclusive b→c decays or in the exclusive amplitudes at zero recoil provided that the expansion parameter is chosen in a way appropriate to the kinematics at hand. The values of the second order coefficients inferred from the BLM type calculations appear to be of order unity in both cases. Thus, in both cases no significant uncertainty in extracting Vcb can be attributed to perturbative effects. The theoretical accuracy is mostly determined by the existing uncertainty in nonperturbative corrections in the exclusive B→D* amplitude, and, to a lesser extent, by the uncertainty in the estimated value of the kinetic energy matrix element in the case of Γsl(b→c). The theoretical accuracy of the inclusive method of determining Vcb seemingly competes with and even exceeds the experimental accuracy.

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