We calculate the hadronic tensor for inclusive semileptonic B decay to O(alpha_s). This allows O(alpha_s Lambda_{ QCD}/mb) corrections to hadronic invariant mass observables to be directly evaluated with experimentally required cuts on phase space. Several moments of phenomenological interest are presented to O(alpha_s Lambda_{ QCD}/mb) and O(Lambda_{ QCD}^3/mb^3), allowing a consistent extraction of the HQET parameters up to O(Lambda_{ QCD}^3/mb^3) and the b quark mass with theoretical error ~ 50 MeV. The hadronic invariant mass spectrum is examined with a general moment to obtain observables that test the theoretical error estimate assigned to these parameters; in particular, fractional moments that directly test the OPE for inconsistencies in the hadronic invariant mass spectrum are reported. The mb Lambda_{ QCD}/mc^2 expansion present for fractional moments of the hadronic invariant mass spectum is discussed and shown to introduce a numerically suppressed uncertainty of O(mb^4 Lambda_{ QCD}^4/mc^8).
Categories: hep-ph