Revisiting the top-quark pair production at future e + e − colliders* * Supported in part by the Natural Science Foundation of China (12175025, 12147102, 12265011), by the Projects of Guizhou Provincial Department (YQK[2023]016, ZK[2023]141, [2020]1Y027, GZMUZK[2022]PT01)

In this study, we reanalyze the top-quark pair production at next-to-next-to-leading order (NNLO) in quantum chromodynamics (QCD) at future colliders using the Principle of Maximum Conformality (PMC) method. The PMC renormalization scales in are determined by absorbing the non-conformal β terms by recursively using the Renormalization Group Equation (RGE). Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energy , the determined PMC scale is far smaller than the and increases with the , yielding the correct physical behavior for the top-quark pair production process. Moreover, the convergence of the pQCD series for the top-quark pair production is greatly improved owing to the elimination of the renormalon divergence. For a typical collision energy of GeV, the PMC scale is GeV; the QCD correction factor K for conventional results is , where the first error is caused by varying the scale and the second error is from the top-quark mass GeV. After applying the PMC, the renormalization scale uncertainty is eliminated, and the QCD correction factor K is improved to , where the error is from the top-quark mass GeV. The PMC improved predictions for the top-quark pair production are helpful for detailed studies of the properties of the top-quark at future colliders.