The Cronin Effect, Quantum Evolution and the Color Glass Condensate

TL;DR

The paper investigates the Cronin effect within Color Glass Condensate and McLerran–Venkugopalan frameworks using real-time lattice simulations of classical SU(3) Yang–Mills dynamics to model gluon production in heavy-ion collisions. It demonstrates a Cronin enhancement at intermediate transverse momentum in AA collisions and analyzes how color neutrality and non-factorized contributions influence low-$p_t$ suppression. For pA collisions, the study shows that quantum evolution via the BK equation preserves the Cronin enhancement when cross sections are normalized to the leading-twist limit, though the peak position shifts with energy and anomalous dimension changes. The work highlights the role of initial-state multiple scattering in generating the Cronin effect and compares its results with other CGC approaches, contributing to the interpretation of RHIC data and the understanding of NRQCD-like initial-state effects in high-energy nuclear collisions.

Abstract

We show that the numerical solution of the classical SU(3) Yang-Mills equations of motion in the McLerran-Venugopalan model for gluon production in central heavy ion collisions leads to a suppresion at low $p_t$ and an enhancement at the intermediate $p_t$ region as compared to peripheral heavy ion and pp collisions at the same energy. Our results are compared to previous, Color Glass Condensate inspired calculations of gluon production in heavy ion collisions. We revisit the predictions of the Color Glass Condensate model for $pA$ ($dA$) collisions in Leading Order and show that quantum evolution--in particular the phenomenon of geometric scaling and change of anomalous dimensions--preserves the Cronin enhancement of $pA$ cross section (when normalized to the leading twist term) in the Leading Order approximation even though the $p_t$ spectrum can change. We comment on the case when gluon radiation is included.

Figures (4)

• Figure 1: $R_{CP}$ from the McLerran Venugopalan model for an SU(3) gauge theory. Here $\Lambda_{s0}=2$ GeV, where $\Lambda^2_{s0}$ is the color charge squared per unit transverse area in the center of each nucleus. (The value of $\Lambda_s$ averaged over the entire nucleus is smaller $\sim 1.4$ GeV.) This result is obtained for a $256\times256$ lattice.
• Figure 2: $R_{AA}$ for an SU(2) gauge theory. $R_{AA}$ is the ratio of the $p_t$ distribution of gluons for $Au$-$Au$ collisions ($\Lambda_{s0}=2$ GeV) divided by $p$-$p$ collisions ($\Lambda_{s0}=0.2$ GeV) and normalized by the ratio of their asymptotic values at large $p_t$. Here MV denotes the McLerran-Venugopalan model with color neutrality imposed globally; Color Neutral I & II impose color neutrality on each configuration at the nucleon level-see text for discussion.
• Figure 3: Schematic diagram of mono-jet gluon production amplitude in $k_t$ factorized form (left figure) vs the non-factorized contributions arising from solutions of classical Yang-Mills equations (right figure).
• Figure 4: Mono-jet production cross section in $k_t$ factorized form.