Non-abelian factorisation for next-to-leading-power threshold logarithms

TL;DR

The paper tackles the challenge of next-to-leading-power (NLP) threshold logarithms in QCD by developing a fully non-abelian NLP factorisation framework. It introduces a non-abelian radiative jet function and next-to-soft structures, and demonstrates how to subtract overlapping soft-collinear contributions to avoid double counting. The authors derive an all-order NLP factorisation formula, compute the radiative jet function at one loop, and validate the approach by reproducing NLP threshold terms in Drell-Yan production up to NNLO, including double-real emission. This work marks a significant step toward a general NLP threshold resummation formalism applicable to a broad class of processes beyond the abelian or leading-power limits.

Abstract

Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a non-abelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.

Figures (4)

• Figure 1: (a) Schematic factorisation of a two-point amplitude. $\widetilde{\cal H}$ and $\widetilde{\cal S}$ are the hard and next-to-soft functions, and $J$ is a non-radiative jet function; next-to-soft subtractions to $J$ are omitted for simplicity. (b) Emission of a gluon from a jet (to be described by a radiative jet function$J^\mu$); (c) Emission from the hard function. (d) Emission through a radiative next-to-soft function $\widetilde{S}^\mu$.
• Figure 2: Diagrams contributing to radiative quark jet function: (a) tree level; (b)--(h) one-loop.
• Figure 3: Example diagrams for the next-to-soft radiaive jet function, where the $p$ leg has been replaced by a generalised Wilson line, and $\bullet$ denotes a next-to-soft emission vertex, arising from Eq. (\ref{['Fmomdef']}).
• Figure 4: Sample diagrams contributing to the double radiative next-to-soft function, where $\bullet$ denotes a next-to-eikonal Feynman rule, and all other couplings to the external lines are eikonal.