Linear correlation of the Gluon EMC effect and SRC in nuclei

Employing an effective field theory framework, we analyze gluon parton distribution functions (PDFs) in nuclear environments and establish a linear relation between the slope of the reduced cross section ratio—quantifying the gluon EMC effect—and the $J/\psi$ production cross section at a photon energy of $E_{\gamma}=$7 GeV in the nucleus rest frame, a regime dominated by short-range correlation (SRC). Numerical calculations using phenomenological nuclear PDFs (nPDFs) corroborate this relation. Validation of this linearity through forthcoming electron-ion collider (EIC) experiments will provide critical insights into the nuclear modifications of gluon PDF and advance our understanding of the subnuclear structure of nuclei.