O(\alpha_s^2) corrections to semileptonic decay b \to c l \bar \nu_l

We compute the next-to-next-to-leading order (NNLO) QCD corrections to b \to c l \bar \nu_l decay rate at a fully differential level. Arbitrary cuts on kinematic variables of the decay products can be imposed. Our computation can be used to study the NNLO QCD corrections to the total decay rate as well as to the lepton energy, hadronic invariant mass and hadronic energy moments and to incorporate those corrections into global fits of inclusive semileptonic B-decays.