A dispersive approach to Sudakov resummation

TL;DR

This paper introduces a dispersive framework for all-order Sudakov resummation in QCD, linking spectral densities and characteristic functions to improve understanding of power corrections and infrared behavior.

Contribution

It develops a novel dispersive formulation of Sudakov resummation that unifies scheme-invariant Borel and dispersive approaches, incorporating power corrections and infrared fixed points.

Findings

Spectral density functions encode non-Abelian interactions.

The approach relates to Dressed Gluon Exponentiation.

Infrared fixed point is universal and linked to cusp anomalous dimension.

Abstract

We present a general all-order formulation of Sudakov resummation in QCD in terms of dispersion integrals. We show that the Sudakov exponent can be written as a dispersion integral over spectral density functions, weighted by characteristic functions that encode information on power corrections. The characteristic functions are defined and computed analytically in the large-beta_0 limit. The spectral density functions encapsulate the non-Abelian nature of the interaction. They are defined by the time-like discontinuity of specific effective charges (couplings) that are directly related to the familiar Sudakov anomalous dimensions and can be computed order-by-order in perturbation theory. The dispersive approach provides a realization of Dressed Gluon Exponentiation, where Sudakov resummation is enhanced by an internal resummation of running-coupling corrections. We establish all-order relations between the scheme-invariant Borel formulation and the dispersive one, and address the difference in the treatment of power corrections. We find that in the context of Sudakov resummation the infrared-finite-coupling hypothesis is of special interest because the relevant coupling can be uniquely identified to any order, and may have an infrared fixed point already at the perturbative level. We prove that this infrared limit is universal: it is determined by the cusp anomalous dimension. To illustrate the formalism we discuss a few examples including B-meson decay spectra, deep inelastic structure functions and Drell-Yan or Higgs production.