A first glance to the kinematic moments of B → Xcℓν at third order

We study the impact of third-order QCD corrections for several kinematic moments of the inclusive semileptonic B decays, to first order in the 1/mb expansion. We consider the first four moments of the charged-lepton energy ER spectrum, the total leptonic invariant mass q2 and the hadronic invariant mass MX2. No experimental cuts are applied. Our analytic results are obtained via an asymptotic expansion around the limit mb ~ mc. After converting the scheme for the bottom mass to the kinetic scheme we compare the size of higher QCD corrections to the contributions from 1/mb2 and 1/mb3 power corrections and to the relative uncertainties.