Perturbative corrections to power suppressed effects in $\bar{B}\to X_u\ell \nu$

Abstract

We compute the $O({\alpha }_s)$ corrections to the Wilson coefficients of the dimension five operators in inclusive semileptonic $B$ decays in the limit of a massless final quark. Our calculation agrees with reparameterization invariance and with previous results for the total width and places constraints on the shape functions that enter those decays.

Comments: 20 pages, 2 figures; v2: corrected typo in Eq. (5.5)