On the role of $J\mathrm{/}\psi$ production in electron-ion collisions

Within the framework of non-relativistic QCD (NRQCD) effective field theory, we study the leptoproduction of $J\mathrm{/}\psi$ at next-to-leading order in perturbative QCD for both unpolarized and polarized electron-ion collisions. We demonstrate that the $J\mathrm{/}\psi$-tagged deep inelastic scattering in the future Electron-Ion Collider can be served as a golden channel for the reasons including constraining NRQCD long distance matrix elements, probing the nuclear gluon distribution functions, as well as investigating the gluon helicity distribution inside a longitudinal polarized proton.