Perturbative corrections to power suppressed effects in B ¯ $$ \overline{B} $$ → X u ℓν

We compute the O(αs) 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 reparametrization invariance and with previous results for the total width and improves the constraints on the shape functions that enter those decays.