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.