Ordering multiple soft gluon emissions

TL;DR

This paper derives a comprehensive QCD amplitude expression for multiple soft gluon emissions at one-loop accuracy, facilitating the development of all-orders algorithms that incorporate full color structure and both real and imaginary contributions.

Contribution

It introduces a novel formulation of the QCD amplitude for multiple soft gluon emissions, using two equivalent operator-based approaches, advancing theoretical tools for high-energy particle scattering.

Findings

Provides a new expression for the QCD amplitude with multiple soft gluons.

Offers two equivalent formulations: operator-ordered and loop-expanded currents.

Aims to enable all-orders algorithms including full color and complex contributions.

Abstract

We present an expression for the QCD amplitude for a general hard scattering process with any number of soft gluon emissions, to one-loop accuracy. The amplitude is written in two different but equivalent ways: as a product of operators ordered in dipole transverse momentum and as a product of loop-expanded currents. We hope that these results will help in the development of an all-orders algorithm for multiple emissions that includes the full colour structure and both the real and imaginary contributions to the amplitude.