$\overline{\rm MS}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
$\overline{\rm MS}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
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DOI：
10.1103/physrevd.94.074025
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发表时间：
2016-06
影响因子：
5
通讯作者：
P. Marquard;A. Smirnov;V. Smirnov;M. Steinhauser;David Wellmann
中科院分区：
文献类型：
--
作者：
P. Marquard;A. Smirnov;V. Smirnov;M. Steinhauser;David Wellmann
我们计算了修正的最小减法和在壳层方案中定义的重夸克质量之间的关系。给出了$\mathrm{SU}（{N}_{c}）$色因子的所有系数的详细结果。对一般的QCD规范参数进行了四圈壳层积分的约化。总共有大约380个主积分。其中一些是解析计算的，另一些是使用Mellin-Barnes表示的高数值精度，其余的是在FIESTA的帮助下进行数值计算的。我们详细讨论了四回路主积分的精确数值计算。更新的各种短距离质量和夸克质量之间的关系，以下一个到领先的顺序的准确性提供的魅力，底和顶夸克。我们讨论了重整化和因式分解尺度的依赖性。
We compute the relation between heavy quark masses defined in the modified minimal subtraction and the on-shell schemes. Detailed results are presented for all coefficients of the $\mathrm{SU}({N}_{c})$ color factors. The reduction of the four-loop on-shell integrals is performed for a general QCD gauge parameter. Altogether there are about 380 master integrals. Some of them are computed analytically, others with high numerical precision using Mellin-Barnes representations, and the rest numerically with the help of FIESTA. We discuss in detail the precise numerical evaluation of the four-loop master integrals. Updated relations between various short-distance masses and the $\overline{\mathrm{MS}}$ quark mass to next-to-next-to-next-to-leading order accuracy are provided for the charm, bottom and top quarks. We discuss the dependence on the renormalization and factorization scale.