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A QCD dipole formalism for forward-gluon production

Cyrille Marquet

TL;DR

The work develops a QCD dipole formalism for forward-gluon production in high-energy q qbar dipole scattering, deriving inclusive and diffractive cross-sections in the eikonal Wilson-line framework. It demonstrates a dipole-factorized structure for the inclusive cross-section, linking a universal gg-dipole cross-section to an effective dipole emission kernel, and shows how forward jets can be described within collinear factorization and DLL evolution. By extending to hadrons and various targets, it provides forward-jet and Mueller-Navelet jet formulas that tie collider observables to dipole-dipole cross-sections and their nonlinear evolution, enabling saturation studies. The results unify forward-jet phenomenology at HERA and hadron colliders with high-energy dipole evolution, offering a framework to test unitarization and nonlinear QCD dynamics via Wilson-line correlators.

Abstract

We derive inclusive and diffractive forward-gluon production in the scattering of a $q\bar{q}$ dipole off an arbitrary target in the high-energy eikonal approximation, suitable to study the saturation regime. We show how the inclusive cross-section is related to the total cross-section for the scattering of a colorless pair of gluons on the target: the gluon-production cross-section can be expressed as a convolution between this $gg$ dipole total cross-section and a dipole distribution. We then consider as an application the forward-jet production from an incident hadron and describe forward-jet production at HERA and Mueller-Navelet jets at Tevatron or LHC. We show how these measurements are related to the $q\bar{q}-gg$ or $gg-gg$ dipole-dipole cross-sections and why they are therefore well-suited for studying high-energy scattering in QCD.

A QCD dipole formalism for forward-gluon production

TL;DR

The work develops a QCD dipole formalism for forward-gluon production in high-energy q qbar dipole scattering, deriving inclusive and diffractive cross-sections in the eikonal Wilson-line framework. It demonstrates a dipole-factorized structure for the inclusive cross-section, linking a universal gg-dipole cross-section to an effective dipole emission kernel, and shows how forward jets can be described within collinear factorization and DLL evolution. By extending to hadrons and various targets, it provides forward-jet and Mueller-Navelet jet formulas that tie collider observables to dipole-dipole cross-sections and their nonlinear evolution, enabling saturation studies. The results unify forward-jet phenomenology at HERA and hadron colliders with high-energy dipole evolution, offering a framework to test unitarization and nonlinear QCD dynamics via Wilson-line correlators.

Abstract

We derive inclusive and diffractive forward-gluon production in the scattering of a dipole off an arbitrary target in the high-energy eikonal approximation, suitable to study the saturation regime. We show how the inclusive cross-section is related to the total cross-section for the scattering of a colorless pair of gluons on the target: the gluon-production cross-section can be expressed as a convolution between this dipole total cross-section and a dipole distribution. We then consider as an application the forward-jet production from an incident hadron and describe forward-jet production at HERA and Mueller-Navelet jets at Tevatron or LHC. We show how these measurements are related to the or dipole-dipole cross-sections and why they are therefore well-suited for studying high-energy scattering in QCD.

Paper Structure

This paper contains 8 sections, 59 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Inclusive gluon production
  3. Diffractive gluon production
  4. Dipole-factorized form of the inclusive cross-section
  5. An application: forward-jet production
  6. Forward jets in deep inelastic scattering
  7. Mueller-Navelet jets at hadron colliders
  8. Conclusions

Figures (3)

  • Figure 1: Inclusive gluon production off a $q\bar{q}$ dipole. $x_0$ and $x_1:$ transverse coordinates of the quark and antiquark; $k$ and $y:$ transverse momentum and rapidity of the measured gluon. The black points represent emission of the gluon by either the quark or the antiquark. The vertical wavy lines represents the interaction with the target. The gluon is emitted before the interaction or after the interaction in which case it comes with a minus sign as explained in the text.
  • Figure 2: Diffractive gluon production off a $q\bar{q}$ dipole. The object exchanged between the $q\bar{q}$ pair and the target is a color singlet and the target does not break up. Notations: see Fig.1.
  • Figure 3: a) Forward-jet production in a proton-lepton collison (at HERA). b) Mueller-Navelet jet production in a proton-proton (at LHC) or proton-antiproton (at Tevatron) collision. $E_T$, $E_{T_1}$, and $E_{T_2}$: cuts on the transverse momenta of the jets; $x_J,$$x_{J_1},$ and $x_{J_2}$: longitudinal momentum fraction of the jets with respect to the incident hadron; $\Delta\eta:$ rapidity intervals between the hard probes.