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Probing saturonlike limits in QCD systems

Wei Kou1,2,3,4,* and Xurong Chen1,2,3,4,†

  • *Contact author: kouwei@impcas.ac.cn
  • †Contact author: xchen@impcas.ac.cn
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Phys. Rev. D 113, 034031 – Published 26 February, 2026

DOI: https://doi.org/10.1103/f7gd-q26l

Abstract

High-occupancy quantum chromodynamics (QCD) matter enters a saturated regime when its entropy or occupancy approaches the unitarity bound ∼1/α, 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 Ng(x) and a thermodynamic entropy S(x) via an Unruh-like temperature T=Qs/(2π) and an emergent gluon mass Mg∼Qs. For protons, both Ng and S rise toward small x yet stay below 1/αs in our baseline setup. For nuclei, by contrast, the nuclear entropy SA attains the 1/αs 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.

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Phys. Rev. D 113, 034031– Published 26 February, 2026
  • Received 22 November 2025
  • Accepted 11 February 2026
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