Investigation of the background in coherent $J/\psi$ production at the EIC

Understanding fundamental properties of nucleons and nuclei are among the most important scientific goals next-generation machine, Electron-Ion Collider (EIC). With unprecedented versatility provided by EIC, it will provide answers to many standing puzzles open questions in modern nuclear physics. One golden measurements at EIC is coherent vector meson production electron-nucleus (eA) scattering order obtain spatial gluon density distribution heavy nuclei. This requires experiment overcome an overwhelmingly large background arising from incoherent diffractive production, where nucleus mostly breaks up into fragments particles far-forward direction close hadron beam rapidity. In this report, we systematically study rejection J/\psi J/ψ vetoing products breakup - protons, neutrons, photons, which modeled with BeAGLE event generator up-to-date Far-forward Interaction Region design.