arXiv2026
The advent of multi-messenger astronomy has provided abundant information for understanding the acceleration and particle-production mechanisms of cosmic rays. In this work, we present a unified study of cosmic gamma-ray and neutrino spectra within the Gluon Condensation (GC) model. Derived from Quantum Chromodynamics (QCD), the GC model predicts that, in high-energy hadronic processes, gluons may condense near a critical momentum, leading to a dramatic enhancement in secondary-pion production and imprinting a characteristic broken power-law feature on the gamma-ray spectrum. Within this framework, we first derive the neutrino spectrum corresponding to the GC scenario and then investigate three astrophysical sources with both gamma-ray observations and neutrino candidate signals: the active galactic nuclei TXS 0506+056 and NGC 1068, and the supernova remnant G54.1+0.3. Using the GC model, we fit the observed gamma-ray spectra of these sources and predict their corresponding neutrino spectra. Our results show that the gamma-ray spectra of TXS 0506+056 and NGC 1068 are well described by the GC model, and that the predicted neutrino spectra are consistent with IceCube observations within uncertainties; in particular, clear relations are found between their relative magnitudes. For SNR G54.1+0.3, however, the GC-predicted neutrino spectrum exhibits continuous hardening after the break, deviating from the typical power-law behavior expected for cosmic-ray secondaries and thus disfavoring a common GC origin. This study represents the first systematic attempt to correlate gamma-ray and neutrino spectra within the GC framework, offering a new perspective on multi-messenger emission from high-energy astrophysical sources.