A first glance to the kinematic moments of B → Xcℓν at third order
Matteo Fael, Kay Schönwald, Matthias Steinhauser
Abstract
A bstract 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 R spectrum, the total leptonic invariant mass q 2 and the hadronic invariant mass $$ {M}_X^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>X</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> . 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 / $$ {m}_b^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>b</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> and 1 / $$ {m}_b^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>b</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:math> power corrections and to the relative uncertainties.