Refactorisation and Subtraction

TL;DR

This paper develops a framework for analyzing multiple infrared limits in scattering amplitudes, introducing gauge-invariant definitions for strongly-ordered kernels to improve subtraction algorithms beyond next-to-leading order.

Contribution

It provides general, gauge-invariant definitions for strongly-ordered soft and collinear kernels, aiding the construction of local subtraction counterterms for complex infrared configurations.

Findings

Validated at tree level for multiple emissions

Validated at one loop for single and double emissions

Framework facilitates IR pole cancellation in subtraction algorithms

Abstract

Infrared subtraction algorithms beyond next-to-leading order necessitate the analysis of multiple infrared limits of scattering amplitudes, where several particles sequentially become soft or collinear. In this contribution, we report on the study performed in arXiv:2403.11975, which investigates these limits from the perspective of infrared factorisation, offering general definitions for strongly-ordered soft and collinear kernels, expressed in terms of gauge-invariant operator matrix elements. These definitions facilitate the identification of local subtraction counterterms for strongly-ordered configurations, whose integrals are designed to cancel the IR poles of real-virtual counterterms. This framework is validated at tree level for multiple emissions, and at one loop for single and double emissions.