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arXiv 1606.06754hep-ph
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$\overline{\rm MS}$ -QCD和一般SU $(N)$规范群中最多四圈的壳层夸克质量关系

$\overline{\rm MS}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group

Peter Marquard, Alexander V. Smirnov, Vladimir A. Smirnov, Matthias Steinhauser, David Wellmann

摘要:

本文计算了修正的最小减法和在壳方案中定义的重夸克质量之间的关系。详细的结果,所有系数的SU $(N_c)$颜色因子。对一般的QCD规范参数进行了四圈壳层积分的约化。大约380个主积分中的一些是解析计算的,其他的是基于Mellin-Barnes表示的高数值精度,其余的是在{ \tt FIESTA}的帮助下数值计算的。我们详细讨论了四回路主积分的精确数值计算。对粲夸克、底夸克和顶夸克,给出了各种短程质量与$\overline{\rm MS}$夸克质量之间的关系,并将其精度提高到次领先阶.我们讨论了重整化和因式分解尺度的依赖性。

英文摘要:

In this paper we compute the relation between heavy quark masses defined in the modified minimal subtraction and on-shell scheme. Detailed results are presented for all coefficients of the SU$(N_c)$ colour factors. The reduction of the four-loop on-shell integrals is performed for a general QCD gauge parameter. Some of the about 380 master integrals are computed analytically, others with high numerical precision based on Mellin-Barnes representations, and the rest numerically with the help of {\tt FIESTA}. We discuss in detail the precise numerical evaluation of the four-loop master integrals. Updated relations between various short-distance masses and the $\overline{\rm MS}$ quark mass to next-to-next-to-next-to-leading order accuracy are provided for the charm, bottom and top quark. We discuss the dependence on the renormalization and factorization scale.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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