Dressed gluon exponentiation

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.