Extrapolating Exclusive Charmonium Photoproduction to the Forward Regime Using Gaussian Process

Accessing the forward kinematic regime of exclusive vector meson photoproduction is essential for probing the structure of the proton, yet this region is often experimentally inaccessible. We present a novel extrapolation of near-threshold $\gamma p \to J/\psi p$ differential cross section data to the forward regime $d\sigma/dt|_{t=0}$ by applying a non-parametric Gaussian Process (GP) regression. By employing a two-dimensional GP dependent on both the squared momentum transfer $t$ and the center-of-mass energy $W$, we perform a coherent analysis of world data and provide a robust quantification of the extrapolation uncertainties. Furthermore, we apply the GP in the determination of the proton mass radius from the $J/\psi$ photoproduction data. We find that the extracted radius is subject to large systematic uncertainties, highlighting the challenge in precisely constraining this quantity with current experimental precision. This work demonstrates that GP is a powerful and systematic tool for phenomenological studies in hadron physics, particularly for extrapolations into unmeasured kinematic domains.