Charmonium-nucleon femtoscopy as a possible probe of the nucleon gravitational form factor
We investigate the charmonium-nucleon interaction, focusing on its connection with the internal structure of the nucleon encoded in the gravitational form factors. To describe this interaction, we employ an effective potential based on the QCD multipole expansion within the leading chromoelectric dipole approximation. In this framework, the potential is expressed in terms of the energy and pressure distributions inside the nucleon. We first construct these distributions from the gravitational form factors fitted to lattice-QCD data. The remaining model parameters are then fixed by requiring that the resulting $J/\psi$-$N$ potential reproduce the HAL QCD potential outside the short-distance region, as well as the scattering phase shift estimated from the HAL QCD data. Based on this potential, we evaluate the $J/\psi$-$N$ correlation function and further investigate the $\psi(2S)$-$N$ system. We then examine the sensitivity of these correlation functions to the nucleon $D$-form factor.