Momentum mappings for subtractions at higher orders in QCD

TL;DR

This paper reviews and extends momentum mappings used in subtraction schemes for higher-order QCD calculations, enabling more flexible and comprehensive phase space parametrizations including massive particles and multiple soft or collinear clusters.

Contribution

It introduces new momentum mappings for final-collinear and soft counterterms that work with massive particles and multiple unresolved emissions, unifying and expanding existing methods.

Findings

New mappings handle massive particles and multiple unresolved emissions.

Unified framework for existing momentum mappings.

Enhanced subtraction methods for higher-order QCD computations.

Abstract

Subtraction schemes provide a systematic way to compute fully-differential cross sections beyond the leading order in the strong coupling constant. These methods make singular real-emission corrections integrable in phase space by the addition of suitable counterterms. Such counterterms may be defined using momentum mappings, which are parametrisations of the phase space that factorise the variables that describe the particles becoming unresolved in some infrared or collinear limit from the variables that describe an on-shell phase space for the resolved particles. In this work, we review existing momentum mappings in a unified framework and introduce new ones for final-collinear and soft counterterms. The new mappings work in the presence of massive particles and with an arbitrary number of soft particles or of clusters of collinear particles, making them fit for subtraction methods at any order in perturbation theory. The new mapping for final-collinear counterterms is also used to elucidate relations among existing final-collinear mappings.