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Higher-Order QCD Corrections in Hadron Collisions: Soft-Gluon Resummation and Exponentiation

Stefano Catani

TL;DR

The paper surveys soft-gluon resummation and exponentiation in hadron collisions, illustrating how infrared-safe observables acquire large logarithmic corrections near threshold. It develops a Mellin-space (N) framework for exponentiating DL and subleading terms, and introduces the Minimal Prescription to reliably invert back to x-space while avoiding Landau-pole issues. Phenomenological results show that soft-gluon effects can be modest in some processes (e.g., top-quark production at the Tevatron) but can be sizable (10–15%) for jet-pair production near threshold, underscoring the importance of resummation for precision predictions. The work points toward incorporating resummed anomalous dimensions and NLL corrections to improve QCD cross sections and PDF evolution.

Abstract

I briefly review some recent results on soft-gluon resummation and present applications to heavy-quark and jet production in hadron collisions.

Higher-Order QCD Corrections in Hadron Collisions: Soft-Gluon Resummation and Exponentiation

TL;DR

The paper surveys soft-gluon resummation and exponentiation in hadron collisions, illustrating how infrared-safe observables acquire large logarithmic corrections near threshold. It develops a Mellin-space (N) framework for exponentiating DL and subleading terms, and introduces the Minimal Prescription to reliably invert back to x-space while avoiding Landau-pole issues. Phenomenological results show that soft-gluon effects can be modest in some processes (e.g., top-quark production at the Tevatron) but can be sizable (10–15%) for jet-pair production near threshold, underscoring the importance of resummation for precision predictions. The work points toward incorporating resummed anomalous dimensions and NLL corrections to improve QCD cross sections and PDF evolution.

Abstract

I briefly review some recent results on soft-gluon resummation and present applications to heavy-quark and jet production in hadron collisions.

Paper Structure

This paper contains 8 sections, 17 equations, 2 figures.

Table of Contents

  1. INTRODUCTION
  2. SOFT-GLUON EFFECTS
  3. RESUMMATION AND EXPONENTIATION
  4. IMPLEMENTING RESUMMED FORMULAE IN HADRON COLLISIONS: THE MINIMAL PRESCRIPTION
  5. PHENOMENOLOGICAL STUDIES
  6. Heavy-quark production
  7. Jet production
  8. SUMMARY AND OUTLOOK

Figures (2)

  • Figure 1: Contribution of gluon resummation at order $\alpha_S^4$ and higher, relative to the NLO result, for the individual subprocesses and for the total, as a function of the top mass in $p\bar{p}$ collisions at 1.8 TeV.
  • Figure 2: Contribution of gluon resummation at order $\alpha_S^4$ and higher, relative to the truncated ${\cal O}(\alpha_S^3)$ result, for the invariant-mass distribution of jet pairs at the Tevatron.