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

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.