Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Domenico Bonocore, Eric Laenen, Lorenzo Magnea, Leonardo Vernazza, Chris D. White

TL;DR

The paper studies next-to-leading-power (NLP) threshold logarithms in Drell–Yan production at NNLO by examining real-virtual interference diagrams with one real and one virtual gluon. It employs the method of regions to classify contributions from hard, soft, collinear, and anticollinear momentum configurations and shows that the NLP terms, including $z$-independent pieces, are fully reproduced by this region-based expansion, clarifying the origin of soft-collinear interference that disrupts simple soft-gluon factorization at next-to-eikonal order. These results validate the threshold expansion as a systematic tool for NLP cross sections and provide crucial insights for developing NLP threshold resummation, including the correct ordering of the $\epsilon$- and soft expansions. The work also informs the discussion on loop corrections to next-to-soft theorems and points to the need for new operator elements to capture non-factorizing soft radiation at NLP.

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.

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

TL;DR

The paper studies next-to-leading-power (NLP) threshold logarithms in Drell–Yan production at NNLO by examining real-virtual interference diagrams with one real and one virtual gluon. It employs the method of regions to classify contributions from hard, soft, collinear, and anticollinear momentum configurations and shows that the NLP terms, including -independent pieces, are fully reproduced by this region-based expansion, clarifying the origin of soft-collinear interference that disrupts simple soft-gluon factorization at next-to-eikonal order. These results validate the threshold expansion as a systematic tool for NLP cross sections and provide crucial insights for developing NLP threshold resummation, including the correct ordering of the - and soft expansions. The work also informs the discussion on loop corrections to next-to-soft theorems and points to the need for new operator elements to capture non-factorizing soft radiation at NLP.

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 , 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 -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.

Paper Structure

This paper contains 9 sections, 20 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Real-Virtual interference in Drell-Yan at NNLO
  3. Method of regions analysis
  4. Hard region
  5. Collinear and anticollinear regions
  6. Soft region
  7. The complete abelian-like real-virtual NNLO $K$ factor
  8. Loop effects and the soft expansion
  9. Discussion

Figures (1)

  • Figure 1: Abelian-like cut diagrams contributing to the Drell-Yan cross section at NNLO, involving one real and one virtual gluon. Diagrams obtained by interchanging $p \leftrightarrow \bar{p}$ and/or complex conjugation are not shown.