\begin{document}$ e^+e^- $\end{document} colliders using the Principle of Maximum Conformality (PMC) method. The PMC renormalization scales in \begin{document}$ \alpha_s $\end{document} are determined by absorbing the non-conformal β terms by recursively using the Renormalization Group Equation (RGE). Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energy \begin{document}$ \mu_r=\sqrt{s} $\end{document}, the determined PMC scale \begin{document}$ Q_\star $\end{document} is far smaller than the \begin{document}$ \sqrt{s} $\end{document} and increases with the \begin{document}$ \sqrt{s} $\end{document}, yielding the correct physical behavior for the top-quark pair production process. Moreover, the convergence of the pQCD series for the top-quark pair production is greatly improved owing to the elimination of the renormalon divergence. For a typical collision energy of \begin{document}$ \sqrt{s}=500 $\end{document} GeV, the PMC scale is \begin{document}$ Q_\star=107 $\end{document} GeV; the QCD correction factor K for conventional results is \begin{document}$ K\sim1+0.1244^{+0.0102+0.0012}_{-0.0087-0.0011}+0.0184^{-0.0086+0.0002}_{+0.0061-0.0003} $\end{document}, where the first error is caused by varying the scale \begin{document}$ \mu_r\in[\sqrt{s}/2, 2\sqrt{s}] $\end{document} and the second error is from the top-quark mass \begin{document}$ \Delta{m_t}=\pm0.7 $\end{document} GeV. After applying the PMC, the renormalization scale uncertainty is eliminated, and the QCD correction factor K is improved to \begin{document}$ K\sim 1+0.1507^{+0.0015}_{-0.0015}-0.0057^{+0.0001}_{-0.0000} $\end{document}, where the error is from the top-quark mass \begin{document}$ \Delta{m_t}=\pm0.7 $\end{document} GeV. The PMC improved predictions for the top-quark pair production are helpful for detailed studies of the properties of the top-quark at future \begin{document}$ e^+e^- $\end{document} colliders."> Revisiting the top-quark pair production at future <i>e</i><sup>+</sup><i>e</i><sup>−</sup> colliders -
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