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

Based on the non-relativistic quantum chromodynamics factorization framework, we study the inclusive $J\mathrm{/}\psi$ photoproduction at the future high energy $e^{+}{e}^{-}$ collider, International Linear Collider(ILC), where the initial photons come from the back-scattering of laser and electron (positron). The intermediate states, $c\bar{c}$$({}^3\text{\hspace{0.17em}⁣}{S}_1^{[\mathbf{\text{1}}]}$,${}^1\text{\hspace{0.17em}⁣}{S}_0^{[\mathbf{\text{8}}]}$,${}^3\text{\hspace{0.17em}⁣}{S}_1^{[\mathbf{\text{8}}]}$,${}^3\text{\hspace{0.17em}⁣}{P}_{0,1,2}^{[\mathbf{\text{8}}]})$, and resolved photoproduction processes are considered. Numerical results show that the cross section of $J\mathrm{/}\psi$ photoproduction at the ILC could be very large, and the single resolved process via $c\bar{c}({}^1\text{\hspace{0.17em}⁣}{S}_0^{[\mathbf{\text{8}}]})$ intermediate state dominates primarily the production. We also present various kinematic distributions for $J\mathrm{/}\psi$ photoproduction. Combining the high luminosity of the collision, $J\mathrm{/}\psi$ photoproduction at the ILC shall provide a good platform to test the NRQCD factorization.