Strongly-ordered infrared limits for subtraction counterterms from factorisation

TL;DR

This paper develops a systematic method to factorise and compute strongly-ordered infrared radiation in high-order collider calculations, aiding the construction of subtraction counterterms for divergence removal.

Contribution

It introduces a new approach to refactorise soft and collinear radiation in strongly-ordered limits, enhancing subtraction algorithms for high-order perturbative calculations.

Findings

Refactorisation of soft and collinear radiation in strongly-ordered limits.

Systematic method for computing and characterising singularities.

Framework for constructing local subtraction counterterms.

Abstract

After a brief introduction to the problem of subtraction of infrared divergences for high-order collider observables, we present a preliminary study of strongly-ordered soft and collinear multiple radiation from the point of view of factorisation. We show that the matrix elements of fields and Wilson lines that describe soft and collinear radiation in factorised scattering amplitudes can be re-factorised in strongly-ordered limits, providing a systematic method to compute them, to characterise their singularity structure, and to build local subtraction counterterms for strongly-ordered configurations. Our results provide tools for a detailed organisation of subtraction algorithms, in principle to all orders in perturbation theory.