A first glance to the kinematic moments of $B \to X_c \ell \nu$ at third order

TL;DR

This paper calculates third-order QCD corrections to kinematic moments in inclusive semileptonic B decays, providing precise theoretical predictions crucial for extracting fundamental parameters in flavor physics.

Contribution

It presents the first analytic computation of third-order QCD corrections for multiple kinematic moments in B decays within the $1/m_b$ expansion, enhancing theoretical accuracy.

Findings

Third-order QCD corrections are quantified for various moments.

Higher QCD corrections are comparable to power corrections and uncertainties.

Results are obtained in the kinetic mass scheme, improving theoretical precision.

Abstract

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 $E_\ell$ 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 $m_b \simeq m_c$. 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.