The $B_c$ meson pair, including pairs of both pseudoscalar states and vector states, productions in high energy photon-photon interaction are investigated at the next-to-leading order (NLO) accuracy in the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism. The corresponding cross sections at the future $e^+e^-$ colliders with $sqrt{s}=250$ GeV and $500$ GeV are evaluated. Numerical result indicates that the inclusion of the NLO corrections shall greatly suppress the scale dependence and enhance the prediction reliability. In addition to the phenomenological meaning, the NLO QCD calculation of this process subjects to certain technical issues, which are elucidated in details and might be applicable to other relevant investigations.
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