本文计算非 Coulomb 重夸克势对阈值附近顶夸克对 S 波 Green 函数的 NNNLO 三阶修正，并讨论有限宽度、极点重求和和势减除质量方案。
摘要：
我们详细阐述了由 Coulomb 势以外的重夸克势对 S 波 Green 函数产生三阶修正的方法与计算。本文结果与 next-to-next-to-next-to-leading（NNNLO，次次次领头阶）的顶-反顶阈值产生过程以及由高矩求和规则确定底夸克质量相关，并已用于此前相应的出版物中。除三阶计算外，我们还详细讨论了为顶夸克阈值获得可靠三阶结果所必需的三项改进：有限宽度效应、极点重求和，以及 potential-subtracted（势减除）质量方案的实施。文中对残余标度依赖性以及顶夸克产生截面各种贡献的大小进行了详细数值分析。任意主量子数 n 的重夸克偶素态的 S 波能级和原点波函数收录于附录中。
英文摘要：
We provide a detailed account of the methods and calculations for the third-order corrections to the S-wave Green function from heavy-quark potentials other than the Coulomb potential. The results of this paper are relevant to the top-antitop threshold production process in next-to-next-to-next-to-leading (NNNLO) order and to the determination of the bottom-quark mass from high-moment sum rules, and have been employed in corresponding previous publications. Further to the third-order calculation, we discuss in detail three refinements necessary to obtain reliable third-order results for the top threshold: finite-width effects, pole resummation, and the implementation of the potential-subtracted mass scheme. A detailed numerical analysis of residual scale dependence and the size of various contributions to the top production cross section is provided. The S-wave energy levels and wave functions at the origin for heavy quarkonium states of arbitrary principal quantum number $n$ are collected in an appendix.
P-wave contribution to third-order top-quark pair production near threshold
次领先阶（NLO）P波库仑格林函数在阈值附近对e+ e碰撞中的顶对产生有三阶贡献。在本文中，我们计算的非线性光学P波格林函数的尺寸正则化，要求与非共振生产的W+ W- b \bar{b}的最终状态的一致组合，并提出了一个唯象分析的P波的贡献。我们进一步简要地讨论夸克生产阈值附近和顶部对生产的伽马-伽马碰撞，没有S波的贡献是本，P-波，从而构成了主导生产过程。
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Threshold Resummation of Drell-Yan type colorless processes at LHC
RWTH Aachen University（亚琛工业大学）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Physical Research Laboratory（物理研究实验室）；Indian Institute of Technology Guwahati（古瓦哈提印度理工学院）；Durham University（杜伦大学）
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