Infrared singularities of scattering amplitudes in perturbative QCD

TL;DR

This paper derives a comprehensive formula for the infrared singularities in massless QCD scattering amplitudes, valid at any loop order and for any number of particles, based on a conjecture about the structure of the anomalous-dimension matrix.

Contribution

It introduces a new exact formula for infrared singularities in massless QCD amplitudes, extending predictions to three-loop order for arbitrary n-parton processes.

Findings

Predicted three-loop coefficients of 1/epsilon^k poles for n-parton amplitudes.

Validated the conjecture about the color structure of the anomalous-dimension matrix.

Extended known two-loop results to three loops for arbitrary scattering processes.

Abstract

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.