Bayesian Inferring Nucleon's Gravitation Form Factors via Near-threshold $J/\psi$ Photoproduction

With Bayesian inference, we investigate the impact of recent near-threshold $J/\psi$ production measurements by the $J/\psi$ 007 experiment and GlueX collaboration on the extraction of proton's gravitational form factors. We apply the generalized parton distribution framework at the next-to-leading order and demonstrate a stable expansion for the near-threshold kinematics. We find that the experimental constraints are in good agreement with the state-of-the-art lattice simulations, where negative $C_q(t)$ and $C_g(t)$ are strongly preferred. This highlights a great potential to extract them from future high-precision experiments.