The method of regions and next-to-soft corrections in Drell-Yan production

TL;DR

This paper investigates gluon radiation beyond the soft approximation in Drell-Yan production at NNLO, using the method of regions to classify contributions and identify the breakdown of simple soft-gluon factorization.

Contribution

It applies the method of regions to classify next-to-leading power contributions in Drell-Yan, reproduces exact two-loop results, and clarifies the origin of soft-collinear interference.

Findings

Reproduces two-loop Drell-Yan K-factor accurately

Identifies the origin of soft-collinear interference

Lays groundwork for factorization of next-to-leading-power logarithms

Abstract

We perform a case study of the behavior of gluon radiation beyond the soft approximation, using as an example the Drell-Yan production cross section at NNLO. We draw a careful distinction between the eikonal expansion, which is in powers of the soft gluon energies, and the expansion in powers of the threshold variable $1 - z$, which involves important hard-collinear effects. Focusing on the contribution to the NNLO Drell-Yan K-factor arising from real-virtual interference, we use the method of regions to classify all relevant contributions up to next-to-leading power in the threshold expansion. With this method, we reproduce the exact two-loop result to the required accuracy, including $z$-independent non-logarithmic contributions, and we precisely identify the origin of the soft-collinear interference which breaks simple soft-gluon factorization at next-to-eikonal level. Our results pave the way for the development of a general factorisation formula for next-to-leading-power threshold logarithms, and clarify the nature of loop corrections to a set of recently proposed next-to-soft theorems.