Unitarized Matching of Gluon PDF Moments and the QCD Trace Anomaly in Near-Threshold $J/ψ$ Photoproduction

Abstract: We construct a framework for near-threshold $J/ψ$ photoproduction that combines a target-mass-corrected gluon-PDF moment expansion with an explicit scalar gravitational form factor associated with the QCD trace anomaly. Both contributions are embedded into a common partial-wave K-matrix unitarization scheme, ensuring elastic unitarity at the amplitude level. The resulting hierarchy of nested models is tested against GlueX data and shown to produce distinct signatures in the differential cross section, the effective $t$-slope, and the real-to-imaginary ratio. The scalar form-factor signal is found to be robust against PDF-set variations and survives unitarization. A smooth matching to the Pomeron power-law regime at high energy is demonstrated, providing a unified description from threshold to HERA energies spanning three orders of magnitude in the center-of-mass energy.