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High energy pA collisions in the color glass condensate approach II. Quark production

J. P. Blaizot, F. Gelis, R. Venugopalan

TL;DR

This work extends the Color Glass Condensate framework to quark-antiquark pair production in high-energy proton-nucleus collisions, deriving a general amplitude that is not $k_\perp$-factorizable and demonstrating how multi-parton correlations at small $x$ appear through Wilson-line correlators. The authors show that the pair- and single-quark cross-sections require 2-, 3-, and 4-point Wilson-line correlators and discuss their leading-twist Gaussian (MV) limits, where a simpler factorized structure is recovered. A Lipatov-vertex interpretation emerges for the production mechanisms, and the results provide a bridge to JIMWLK evolution equations describing the quantum small-$x$ dynamics. The findings offer a concrete framework to test high-energy QCD and the role of multi-parton correlations in upcoming collider data.

Abstract

We compute the production of quark-antiquark pairs in high energy collisions between a small and a large projectile, as in proton-nucleus collisions, in the framework of the Color Glass Condensate. We derive a general expression for quark pair-production, which is not k_t-factorizable. However, k_t-factorization is recovered in the limit of large mass pairs or large quark--anti-quark momenta. Our results are amenable to a simple interpretation and suggest how multi-parton correlations at small x can be quantified in high-energy proton/deuteron-nucleus collisions.

High energy pA collisions in the color glass condensate approach II. Quark production

TL;DR

This work extends the Color Glass Condensate framework to quark-antiquark pair production in high-energy proton-nucleus collisions, deriving a general amplitude that is not -factorizable and demonstrating how multi-parton correlations at small appear through Wilson-line correlators. The authors show that the pair- and single-quark cross-sections require 2-, 3-, and 4-point Wilson-line correlators and discuss their leading-twist Gaussian (MV) limits, where a simpler factorized structure is recovered. A Lipatov-vertex interpretation emerges for the production mechanisms, and the results provide a bridge to JIMWLK evolution equations describing the quantum small- dynamics. The findings offer a concrete framework to test high-energy QCD and the role of multi-parton correlations in upcoming collider data.

Abstract

We compute the production of quark-antiquark pairs in high energy collisions between a small and a large projectile, as in proton-nucleus collisions, in the framework of the Color Glass Condensate. We derive a general expression for quark pair-production, which is not k_t-factorizable. However, k_t-factorization is recovered in the limit of large mass pairs or large quark--anti-quark momenta. Our results are amenable to a simple interpretation and suggest how multi-parton correlations at small x can be quantified in high-energy proton/deuteron-nucleus collisions.

Paper Structure

This paper contains 28 sections, 117 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Yang-Mills gauge field produced in pA collisions
  3. Pair production amplitude
  4. Generalities
  5. Regular terms
  6. Singular terms
  7. Complete time-ordered amplitude
  8. Physical interpretation and limits of eq. (\ref{['eq:Mf-final']})
  9. Pair production cross-section
  10. Average over the color sources
  11. Leading twist approximation
  12. $k_\perp$-factorization for pair production ?
  13. Single quark cross-section
  14. Conclusions
  15. Gaussian averages of Wilson lines
  16. ...and 13 more sections

Figures (3)

  • Figure 1: Regular terms in the time-ordered pair production amplitude. The gluon line terminated by a cross denotes a classical field insertion. The black dot denotes multiple insertions of the field $A_{_A}^\mu$ (with at least one insertion).
  • Figure 2: Singular term in the time-ordered pair production amplitude. The gluon line terminated by a cross denotes a classical field insertion.
  • Figure 3: Top: the contributions to the Feynman amplitude. The shaded area represents the nucleus. A gluon is emitted by the proton, and splits into a pair: after the collisions with the nucleus (left), inside the nucleus (middle) or before the collision (right). Bottom: the same contributions for the retarded amplitude.