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Production of q bar-q Pairs in Proton-Nucleus Collisions at High Energies

Yuri V. Kovchegov, Kirill Tuchin

TL;DR

The paper addresses heavy quark pair production in high-energy proton-nucleus collisions and deep inelastic scattering, where two hard scales, the quark mass $m$ and the saturation scale $Q_s$, govern perturbative dynamics. It develops a two-tier approach: a quasi-classical calculation in the McLerran-Venugopalan framework to obtain inclusive and double-inclusive $q\bar{q}$ cross sections, followed by the incorporation of quantum small-$x$ evolution through BK/Mueller dipole evolution, yielding evolved cross sections that account for rapidity separations between the quarks, target, and projectile. The central results (dcl_ev and single_ev) express the cross sections in terms of dipole amplitudes and Glauber-Mueller rescatterings, with large-$N_c$ simplifications enabling tractable expressions. This work provides a perturbative, nonlinear CGC-based description of heavy-quark production in dense gluon environments, offering predictions for open charm spectra in $pA$ and DIS at RHIC/LHC and guiding comparisons with experimental data.

Abstract

We calculate production of quark-antiquark pairs in high energy proton-nucleus collisions both in the quasi-classical approximation of McLerran-Venugopalan model and including quantum small-$x$ evolution. The resulting production cross section is explicitly expressed in terms of Glauber-Mueller multiple rescatterings in the classical case and in terms of dipole-nucleus scattering amplitude in the quantum evolution case. We generalize the result of one of us (K.T.) beyond the aligned jet configurations. We expand on the earlier results of Blaizot, Gelis and Venugopalan by deriving quark production cross section including quantum evolution corrections in rapidity intervals both between the quarks and the target and between the quarks and the projectile.

Production of q bar-q Pairs in Proton-Nucleus Collisions at High Energies

TL;DR

The paper addresses heavy quark pair production in high-energy proton-nucleus collisions and deep inelastic scattering, where two hard scales, the quark mass and the saturation scale , govern perturbative dynamics. It develops a two-tier approach: a quasi-classical calculation in the McLerran-Venugopalan framework to obtain inclusive and double-inclusive cross sections, followed by the incorporation of quantum small- evolution through BK/Mueller dipole evolution, yielding evolved cross sections that account for rapidity separations between the quarks, target, and projectile. The central results (dcl_ev and single_ev) express the cross sections in terms of dipole amplitudes and Glauber-Mueller rescatterings, with large- simplifications enabling tractable expressions. This work provides a perturbative, nonlinear CGC-based description of heavy-quark production in dense gluon environments, offering predictions for open charm spectra in and DIS at RHIC/LHC and guiding comparisons with experimental data.

Abstract

We calculate production of quark-antiquark pairs in high energy proton-nucleus collisions both in the quasi-classical approximation of McLerran-Venugopalan model and including quantum small- evolution. The resulting production cross section is explicitly expressed in terms of Glauber-Mueller multiple rescatterings in the classical case and in terms of dipole-nucleus scattering amplitude in the quantum evolution case. We generalize the result of one of us (K.T.) beyond the aligned jet configurations. We expand on the earlier results of Blaizot, Gelis and Venugopalan by deriving quark production cross section including quantum evolution corrections in rapidity intervals both between the quarks and the target and between the quarks and the projectile.

Paper Structure

This paper contains 4 sections, 51 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Inclusive Cross Section in the Quasi-Classical Approximation
  3. Including Quantum Evolution
  4. Summary

Figures (3)

  • Figure 1: Three main contributions to quark-antiquark production in the quasi-classical approximation.
  • Figure 2: Diagrams contributing to quark--anti-quark pair production in the quasi-classical approximation. Disconnected $t$-channel gluon lines imply summation over all possible connections to the adjacent $s$-channel quark and gluon lines.
  • Figure 3: An example of a pomeron fan diagram contributing to the $q\bar{q}$ production cross section in proton-nucleus collisions or in DIS as calculated in equations (\ref{['dcl_ev']}) and (\ref{['single_ev']}). The produced quark and anti-quark are marked by crosses.