Next-to-leading-order relativistic and QCD corrections to prompt <inline-formula><tex-math id="M1">\begin{document}$ {\boldsymbol J/\boldsymbol\psi} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2024-0121_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2024-0121_M1.png"/></alternatives></inline-formula> pair photoproduction at future <inline-formula><tex-math id="M2">\begin{document}${\boldsymbol e^{\bf +}\boldsymbol e^{\bf -}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2024-0121_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2024-0121_M2.png"/></alternatives></inline-formula> colliders

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