Two-loop QCD Corrections to Semileptonic b Decays at Maximal Recoil

We present a complete O(α_s²) correction to the differential width of the inclusive semileptonic decay b→clν_l at the kinematical point of vanishing invariant mass of the leptons, q² = 0. Together with the recently computed O(α_s²) correction at the upper boundary of the lepton invariant mass spectrum, this new information permits an estimate of the O(α_s²) effect in the total inclusive semileptonic decay width b→clν_l. We argue that the non–Brodsky-Lepage-Mackenzie (BLM) part of the O(α_s²) correction gives at most 1% correction to the inclusive semileptonic decay width b→clν_l. This significantly improves the credibility of extracting |V_cb| from the inclusive semileptonic decays of the b hadrons.