Inclusive distributions near kinematic thresholds

TL;DR

This paper reviews the Dressed Gluon Exponentiation (DGE) method, a formalism that improves the calculation of inclusive cross sections near kinematic thresholds in QCD by combining resummation techniques and addressing non-perturbative effects.

Contribution

It introduces and discusses the DGE formalism, demonstrating its effectiveness in extending perturbative QCD calculations into threshold regions and analyzing B decay data.

Findings

DGE effectively extends perturbation theory into threshold regions.

DGE helps identify relevant non-perturbative corrections.

Application to B decays aids data interpretation.

Abstract

The main challenge in computing inclusive cross sections and decay spectra in QCD is posed by kinematic thresholds. The threshold region is characterized by stringent phase-space constraints that are reflected in large perturbative corrections due to soft and collinear radiation as well as large non-perturbative effects. Major progress in addressing this problem was made in recent years by Dressed Gluon Exponentiation (DGE), a formalism that combines Sudakov and renormalon resummation in moment space. DGE has proven effective in extending the range of applicability of perturbation theory well into the threshold region and in identifying the relevant non-perturbative corrections. Here we review the method from a general perspective using examples from deep inelastic structure functions, event-shape distributions, heavy-quark fragmentation and inclusive decay spectra. A special discussion is devoted to the applications of DGE to radiative and semileptonic B decays that have proven valuable for the interpretation of data from the B factories.