QCD Corrections and the Endpoint of the Lepton Spectrum in Semileptonic B Decays

TL;DR

Addresses how perturbative QCD affects Neubert's shape-function description of the B→X_u eν endpoint. Demonstrates that leading nonperturbative singularities can be captured by averaging the free-quark decay over the b-quark residual momentum, yielding a shape function that extends past the free endpoint. Analyzes radiative corrections, showing Sudakov double logarithms dominate near the endpoint and must be summed along with subleading logs; proposes using residual-momentum averaging on the radiatively corrected spectrum to obtain the leading nonperturbative structure. Relates the endpoint to the photon spectrum in b→sγ and to HQET matrix elements, enabling constraints on the shape function and a more robust extraction of V_ub.

Abstract

Recently, Neubert has suggested that a certain class of nonperturbative corrections dominates the shape of the electron spectrum in the endpoint region of semileptonic $B$ decay. Perturbative QCD corrections are important in the endpoint region. We study the effects of these corrections on Neubert's proposal. The connection between the endpoint of the electron spectrum in semileptonic $B$ decay and the photon spectrum in $b\rightarrow sγ$ is outlined.