A first glance to the kinematic moments of B → X$_c$ℓν 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/m$_b$ expansion. We consider the first four moments of the charged-lepton energy E$_ℓ$ spectrum, the total leptonic invariant mass q$^2$ and the hadronic invariant mass M$_X^2$. No experimental cuts are applied. Our analytic results are obtained via an asymptotic expansion around the limit m$_b$≃m$_c$. After converting the scheme for the bottom mass to the kinetic scheme we compare the size of higher QCD corrections to the contributions from $1/m_b^2$ and $1/m_b^3$ power corrections and to the relative uncertainties.