In this paper, we present an improved analysis of the top-quark pair production via the process near the threshold region up to next-to-next-to-next-to-leading order (NLO) QCD corrections. Near the threshold region, the top-quark velocity tends to zero, leading to Coulomb singularity. To achieve a reasonable prediction in the threshold region, we reconstruct the analytical expression for the Coulomb-terms up to NLO accuracy by using the PSLQ algorithm, whose numerical values agree well with the previous NLO-level calculations. It is found that the NLO series still has sizable renormalization scale dependence, and to improve the precision of the series, we apply the Principle of Maximum Conformality to eliminate such scale dependence. After that, the Coulomb part is resummed into a Sommerfeld-Gamow-Sakharov factor, which finally leads to a much more reasonable behavior near the threshold region.

中文翻译：

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通过阈值区域附近的 e+e− 湮灭直至 N3LO QCD 校正来重新分析顶夸克对的产生

在本文中，我们通过阈值区域附近的过程直至下一个到下一个前导顺序（NLO）QCD 校正，对顶夸克对产生进行了改进的分析。在阈值区域附近，顶夸克速度趋于零，导致库仑奇点。为了在阈值区域实现合理的预测，我们使用PSLQ算法重建了达到NLO精度的库仑项解析表达式，其数值与之前的NLO级计算非常吻合。发现NLO级数仍然存在相当大的重正化尺度依赖性，为了提高级数的精度，我们应用最大共形原理来消除这种尺度依赖性。之后，库仑部分恢复为索末菲-伽莫夫-萨哈罗夫因子，最终导致阈值区域附近更加合理的行为。