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We study the impact of next-to-next-to-leading order (NNLO) QCD correctionson partial decay rates in B --> X_u l nu decays, at leading-order in the 1/m_bexpansion for shape-function kinematics. These corrections are implementedwithin a modified form of the BLNP framework, which allows for arbitraryvariations of the jet scale mu_i \sim 1.5 GeV. Our analysis includes a detailedcomparison between resummed and fixed-order perturbation theory, and betweenthe complete NNLO results and those obtained in the large-$\beta_0$approximation. For the default choice mu_i=1.5 GeV used in current extractionsof |V_ub| within the BLNP framework, the NNLO corrections induce significantdownward shifts in the central values of partial decay rates with cuts on thehadronic variable P_+, the hadronic invariant mass, and the lepton energy. Atthe same time, perturbative uncertainties are reduced, especially those at thejet scale, which are the dominant ones at next-to-leading order (NLO). Forhigher values of mu_i and in fixed-order perturbation theory, the shiftsbetween NLO and NNLO are more moderate. We combine our new results with knownpower-suppressed terms in order to illustrate the implications of our analysison the determination of |V_ub| from inclusive decays.

NNLO corrections to B --> X_u l nu and the determination of |V_ub|