Infrared singularities in QCD amplitudes

TL;DR

This paper reviews the structure of infrared singularities in massless QCD amplitudes, proposing a dipole-based formula governed by the cusp anomalous dimension, and discusses potential multi-loop corrections.

Contribution

It introduces a simple dipole formula for soft singularities in massless gauge theories, derived from fundamental factorization principles, and explores possible corrections beyond this model.

Findings

Soft singularities are described by a sum over colour dipoles.

The dipole formula is governed by the cusp anomalous dimension.

Potential multi-loop corrections beyond the dipole approximation are discussed.

Abstract

We review recent progress in determining the infrared singularity structure of on-shell scattering amplitudes in massless gauge theories. We present a simple ansatz where soft singularities of any scattering amplitude of massless partons, to any loop order, are written as a sum over colour dipoles, governed by the cusp anomalous dimension. We explain how this formula was obtained, as the simplest solution to a newly-derived set of equations constraining the singularity structure to all orders. We emphasize the physical ideas underlying this derivation: the factorization of soft and collinear modes, the special properties of soft gluon interactions, and the notion of the cusp anomaly. Finally, we briefly discuss potential multi-loop contributions going beyond the sum-over-dipoles formula, which cannot be excluded at present.