Near-Threshold J/$ψ\to μ^+μ^-$ Photoproduction and the Gluonic Gravitational Form Factors of the Proton

We report on the measurement of the two-dimensional differential cross section for near-threshold J/$ψ\to μ^+μ^-$ photoproduction from the J/$ψ$-007 experiment in Hall C at Jefferson Lab. Our results agree with the previously published J/$ψ\to e^+e^-$ results. We extract the integrated photoproduction cross section and find no evidence for open-charm contributions. A combined analysis of both decay channels following a Holographic QCD approach yields improved experimental constraints on the gluonic gravitational form factor $\mathcal{C}_g(t)$. Our results agree with recent lattice QCD calculations and we obtain $\mathcal{C}_g(t)$ with a comparable statistical precision to lattice QCD. Our results support a spatial picture where gluons dominate at larger radii with a confining inward pressure. This work provides new input for exploring the mechanical properties of gluons inside the proton.