Next-to-leading-order relativistic and QCD corrections to prompt pair photoproduction at future colliders

Within the framework of nonrelativistic-QCD factorization, we calculate both the next-to-leading-order relativistic and QCD corrections to prompt $J\mathrm{/}\psi$ pair production, with feeddown from $\psi (2S)$ mesons, via photon-photon collisions at future $e^{+}{e}^{-}$ colliders including the Future Circular Lepton Collider (FCC-ee), the Circular Electron Positron Collider (CEPC), and the Compact Linear Collider (CLIC). We present total cross sections and distributions in single $J\mathrm{/}\psi$ transverse momentum and rapidity, and in $J\mathrm{/}\psi$ pair invariant mass. The relativistic and QCD corrections both turn out to be large and negative. Yet, the production rates are large enough for useful experimental studies.