Gluon gravitational form factors of protons from charmonium photoproduction

Inspired by the recent near-threshold $J\mathrm{/}\psi$ photoproduction measurements, we discuss gluon gravitational form factors (GFFs) and internal properties of the proton. This work presents a complete analysis of the proton gluon GFFs connecting the gluon part of the energy-momentum tensor and the heavy quarkonium photoproduction. In particular, a global fitting of the $J\mathrm{/}\psi$ differential and total cross section experimental data is used to determine the gluon GFFs as functions of the squared momentum transfer $t$. Combined with the quark contributions to the $D$-term form factor extracted from the deeply virtual Compton scattering experiment, the total $D$-term is obtained to investigate their applications in describing the proton mechanical properties. These studies provide a unique perspective on investigating the proton gluon GFFs and important information for enhancing QCD constraints on the gluon GFFs.