Probing Saturon-like Limits in QCD Systems

TL;DR

This paper investigates the saturation limits of high-occupancy QCD matter, called saturons, in protons and nuclei at small x, using analytic and numerical solutions of the BK equation to identify conditions where entropy approaches the unitarity bound.

Contribution

It introduces a thermodynamic framework for analyzing saturation in QCD systems and demonstrates that nuclei can reach saturon-like entropy levels at small x, unlike protons.

Findings

Nuclei reach the unitarity bound in entropy at small x.

Protons remain below the saturation threshold in the studied regime.

Nuclei are promising candidates for observing saturon-like phenomena.

Abstract

High-occupancy QCD matter enters a saturated regime when its entropy or occupancy approaches the unitarity bound $\sim 1/\alpha$, the ``saturon" criterion. We test this criterion for protons and nuclei at small $x$ using analytic and numerical solutions of the BK equation. From these solutions we construct the gluon occupancy $N_g(x)$ and a thermodynamic entropy $S(x)$ via an Unruh-like temperature $T = Q_s/(2\pi)$ and an emergent gluon mass $M_g \sim Q_s$. For protons, both $N_g$ and $S$ rise toward small $x$ yet stay below $1/\alpha_s$ in our baseline setup. For nuclei, by contrast, the nuclear entropy $S_A$ attains the $1/\alpha_s$ benchmark in a small-$x$ window where the proton does not. This singles out nuclei as the natural environment to search for saturon-like behavior and motivates precision small-$x$ measurements and high-occupancy $pA$ and $AA$ collisions.