Linear relation between short range correlation and EMC effect of gluons in nuclei

Abstract: We explore the EMC effect of gluons through heavy quark production in deep inelastic scattering (DIS) and the nucleon-nucleon short range correlation (SRC) from sub-threshold photoproduction of the $J/\psi$. Applying an effective field theory analysis, we scrutinize the gluon parton distribution functions in nuclear environment and propose a linear relation between the slope of reduced cross section ratio, which reflects the magnitude of gluon EMC effect, and the $J/\psi$ production cross section at the photon energy $E_\gamma = 7.0\,\textrm{GeV}$ in the nucleus rest frame, a characteristic representative of SRC. This finding is supported by a numerical calculation using the available phenomenological results for gluon nuclear parton distribution functions (nPDFs). Examining this linear relation by the forthcoming experimental data on electron-ion collider allows to decipher nuclear effects of gluon distributions and enhance our comprehension of the substructure in bound nuclei.