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

TL;DR

This paper extends the NLP factorisation formula to non-abelian corrections, defining a new jet function and verifying it through Drell-Yan NNLO calculations, advancing threshold resummation techniques.

Contribution

It introduces a non-abelian radiative jet function for NLP corrections and demonstrates its effectiveness in Drell-Yan processes up to NNLO.

Findings

Reproduces all NLP logarithms in Drell-Yan up to NNLO.

Defines a non-abelian radiative jet function at one loop.

Addresses double counting between soft and collinear regions.

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.