Dressed gluon exponentiation
Einan Gardi
TL;DR
Differential cross-sections near kinematic thresholds are highly sensitive to soft and collinear gluon radiation and are affected by infrared renormalons, complicating fixed-order predictions. The paper introduces Dressed Gluon Exponentiation (DGE), which combines factorization in the light-cone gauge with a dispersive running-coupling treatment to compute the single-dressed-gluon emission and to exponentiate it, incorporating renormalon-induced power corrections. It derives a universal off-shell emission kernel, applies DGE to fragmentation, jet mass, DIS, and Drell-Yan, and analyzes perturbative and non-perturbative structure via Borel transforms, revealing factorial growth of subleading logs and observable-dependent power corrections that exponentiate into non-perturbative shape factors. This framework provides a unified approach to threshold resummation that accounts for both logarithmic and non-perturbative effects, improving phenomenological descriptions and guiding the understanding of power corrections in QCD near thresholds.
Abstract
Perturbative and non-perturbative aspects of differential cross-sections close to a kinematic threshold are studied applying ``dressed gluon exponentiation'' (DGE). The factorization property of soft and collinear gluon radiation is demonstrated using the light-cone axial gauge: it is shown that the singular part of the squared matrix element for the emission of an off-shell gluon off a nearly on-shell quark is universal. We derive a generalized splitting function that describes the emission probability and show how Sudakov logs emerge from the phase-space boundary where the gluon transverse momentum vanishes. Both soft and collinear logs associated with a single dressed gluon are computed through a single integral over the running-coupling to any logarithmic accuracy. The result then serves as the kernel for exponentiation. The divergence of the perturbative series in the exponent indicates specific non-perturbative corrections. We identify two classes of observables according to whether the radiation is from an initial-state quark, as in the Drell-Yan process, or a final-state quark, forming a jet with a constrained invariant mass, as in fragmentation functions, event-shape variables and deep inelastic structure functions.