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Based on the non-relativistic quantum chromodynamics factorization framework,we study the inclusive $J/\psi$ photoproduction at the future high energy$e^+e^-$ collider, International Linear Collider(ILC), where the initialphotons come from the back-scattering of laser and electron (positron). Theintermediate states,$c\bar{c}$$({}^3\!S_1^{[\textbf{1}]}$,${}^1\!S_0^{[\textbf{8}]}$,${}^3\!S_1^{[\textbf{8}]}$,${}^3\!P_{0,1,2}^{[\textbf{8}]})$,and resolved photoproduction processes are considered. Numerical results showthat the cross section of $J/\psi$ photoproduction at the ILC could be verylarge, and the single resolved process via $c\bar{c}({}^1\!S_0^{[\textbf{8}]})$intermediate state dominates primarily the production. We also present variouskinematic distributions for $J/\psi$ photoproduction. Combining the highluminosity of the collision, $J/\psi$ photoproduction at the ILC shall providea good platform to test the NRQCD factorization.

Inclusive $J/\psi$ photoproduction at the ILC within the framework of non-relativistic QCD