Strongly-ordered infrared counterterms from factorisation

TL;DR

This paper develops a framework for constructing local infrared subtraction counterterms for strongly-ordered soft and collinear emissions, improving the cancellation of infrared divergences in higher-order QCD calculations.

Contribution

It introduces gauge-invariant definitions of strongly-ordered infrared kernels and demonstrates their use in constructing subtraction counterterms at tree and one-loop levels.

Findings

Counterterms cancel infrared poles in real-virtual contributions.

Framework applicable to NNLO and N3LO distributions.

Validated at tree level and one loop for multiple emissions.

Abstract

In the context of infrared subtraction algorithms beyond next-to-leading order, it becomes necessary to consider multiple infrared limits of scattering amplitudes, in which several particles become soft or collinear in a strongly-ordered sequence. We study these limits from the point of view of infrared factorisation, and we provide general definitions of strongly-ordered soft and collinear kernels in terms of gauge-invariant operator matrix elements. With these definitions in hand, it is possible to construct local subtraction counterterms for strongly-ordered configurations. Because of their factorised structure, these counterterms cancel infrared poles of real-virtual contributions by construction. We test these ideas at tree level for multiple emissions, and at one loop for single and double emissions, contributing to NNLO and N3LO distributions, respectively.