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.
Highlights
Its coupling strengths to the SM fermions
In particular for Higgs physics, it is expected that the leading source of uncertainty on SM observables will be due to theoretical predictions
At the next-to-leading order (NLO), exploration of this infrared and collinear (IRC) behavior of amplitudes has led to the establishment of subtraction methods [29, 30] as the standard approach, in which real-emission corrections, which exhibit IRC divergences when integrated over phase space, are made integrable by the addition of suitable counterterms
Summary
This section is dedicated to introducing momentum mappings with explicit examples, setting up definitions and providing a resource where the different approaches used in the literature and their properties are described. We will first review the example of CoLoRFul subtraction for final-state NLO singularities, which is built on both a soft and a collinear mapping, allowing us to illustrate both important aspects and possible issues relating to mappings. We move on to discuss the three main different types of mappings and their realisations in different subtraction schemes. We discuss how these elementary mappings can be combined to handle counterterms where disjoint sets of particles become unresolved
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