Revisiting the top-quark pair production at futuree⁺e⁻colliders

Abstract：

In this study, we reanalyze the top-quark pair production at next-to-next-to-leading order (NNLO) in quantum chromodynamics (QCD) at future $ e^+e^- $ colliders using the Principle of Maximum Conformality (PMC) method. The PMC renormalization scales in $ \alpha_s $ are determined by absorbing the non-conformal βterms by recursively using the Renormalization Group Equation (RGE). Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energy $ \mu_r=\sqrt{s} $ , the determined PMC scale $ Q_\star $ is far smaller than the $ \sqrt{s} $ and increases with the $ \sqrt{s} $ , 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 $ \sqrt{s}=500 $ GeV, the PMC scale is $ Q_\star=107 $ GeV; the QCD correction factor Kfor conventional results is $ K\sim1+0.1244^{+0.0102+0.0012}_{-0.0087-0.0011}+0.0184^{-0.0086+0.0002}_{+0.0061-0.0003} $ , where the first error is caused by varying the scale $ \mu_r\in[\sqrt{s}/2, 2\sqrt{s}] $ and the second error is from the top-quark mass $ \Delta{m_t}=\pm0.7 $ GeV. After applying the PMC, the renormalization scale uncertainty is eliminated, and the QCD correction factor Kis improved to $ K\sim 1+0.1507^{+0.0015}_{-0.0015}-0.0057^{+0.0001}_{-0.0000} $ , where the error is from the top-quark mass $ \Delta{m_t}=\pm0.7 $ 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 $ e^+e^- $ colliders.