NNLO corrections to inclusive semileptonic B decays in the shape-function region

We compute 2-loop QCD corrections to the hard coefficient functions which arise in the factorization formula for B -> X(u)l nu decays in the shape-function region. Our calculation provides the last missing piece required for a NNLO analysis of inclusive semileptonic B decays, which may significantly reduce the theoretical uncertainty in the extraction of the CKM matrix element vertical bar V(ub)broken vertical bar. Among the technical aspects, we find that the 2-loop hard coefficient functions are free of infrared singularities as predicted by the factorization framework. We perform a brief numerical analysis of the NNLO corrections and include a discussion on charm mass effects. (C) 2009 Elsevier B.V. All rights reserved.