QCD corrections to the Darwin coefficient in inclusive semileptonic B → X u e ν <overline> e decays

In this paper, we compute alpha s corrections to the matching coefficients of the dimension -six operators in the heavy quark expansion of the inclusive semileptonic heavy hadron decay rate and leptonic invariant mass spectrum with a massless quark and both a massive or massless lepton in the final state, analytically. The obtained results can be applied to the inclusive semileptonic BX u e nu <overline> e ( e = e , mu, tau) and D - X e nu <overline> e ( e = e , mu) decays. The main application of our results is the background subtraction of the BX u e nu <overline> e decay in the measurement of the BX c e nu <overline> e decay, which is important for the precise extraction of V cb and R ( D (*) ) . They also play a role in the computation of lifetimes of heavy hadrons.