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Looking for Condensed Gluons: A Cross-Scale Journey from the Deep Structure of Protons to High-Energy Cosmic Rays -- A Mini-Review

Wei Zhu, Yuchen Tang, Ye-Yin Zhao, Bo Yang, Yu-Chen Xiong

arXiv (Cornell University), 2026

Abstract

Quark-gluon dynamics within protons and high-energy radiation phenomena in the universe are typically regarded as two entirely distinct fields. This paper aims to demonstrate that gluon condensation (GC) may serve as a direct bridge between these two fields. We review three key aspects of GC research: first, the Zhu-Shen-Ruan (ZSR) equation, as a nonlinear evolution equation based on structural symmetry, exhibits self-consistent connections with the DGLAP, BFKL and GLR-MQ-ZRS equations, providing a theoretical foundation for the generation of GC; second, the chaotic solutions and the shadowing-antishadowing synergy inherent in this equation can drive gluons to aggregate near the critical momentum, thereby forming a novel type of high-density, strongly interacting matter; third, these changes in microstructure manifest themselves as a broken-power-law feature in high-energy cosmic gamma-ray spectra, thereby offering new insights into the hadronic scenarios underlying certain astrophysical sources. Consequently, GC not only concerns the novel behaviour of quantum chromodynamics under extreme conditions but may also serve as a vital window for probing the deep structure of protons using cosmic-ray signals. With the advancement of higher-precision gamma-ray observations, hadron collision experiments and related theoretical research, the physical picture of GC and its observational criteria are expected to undergo more rigorous testing. Should this picture be confirmed, certain…

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