Perturbative corrections to power suppressed effects in $\bar B\to X_u\ellν$

We compute the $O(α_s)$ 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.

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