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The $\gamma+\gamma\rightarrow J/\psi+c+\bar{c}$ inclusive process is anextremely important subprocess in $J/\psi$ production via photon-photonscattering, like at LEP\uppercase\expandafter{\romannumeral2} or various typesfuture electron-positron colliders. In this work we perform thenext-to-leading(NLO) QCD corrections to this process in the framework ofnon-relativistic QCD(NRQCD) factorization formalism, the first NLO calculationfor two projectiles to 3-body quarkonium inclusive production process. Bysetting the center-of-mass energy at LEP\uppercase\expandafter{\romannumeral2},the $\sqrt{s}=197$ GeV, we conduct analyses of the $p_t^2$ distribution andtotal cross section of this process at the NLO accuracy. It turns out that thetotal cross section is moderately enhanced by the NLO correction with a $K$factor of about 1.46, and hence the discrepancy between DELPHI data andcolor-singlet(CS) calculation is reduced while the color-octet(CO)contributions are still inevitable at this order. At the future CircularElectron-Positron Collider(CEPC), the NLO corrections are found to be moresignificant, with a $K$ factor of about 1.76.

NLO QCD Corrections for $J/\psi+ c + \bar{c}$ Production in Photon-Photon Collision