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arXiv 2106.05296hep-ph
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计算费曼积分的半解析方法用于$\overline{\rm MS}$ -极夸克质量关系的四圈修正

A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{\rm MS}$-pole quark mass relation

Matteo Fael, Fabian Lange, Kay Schönwald, Matthias Steinhauser

摘要:

我们描述了一种方法来数值计算多回路积分,取决于一个无量纲参数$x$和尺寸$d$,在整个运动范围的$x$。该方法是基于微分方程,其中,然而,不需要任何特殊的形式,和一系列的扩展周围的奇异点和定期。这种方法提供的结果非常适合快速数值计算和足够精确的唯象应用。我们将这种方法应用到四圈壳积分和计算八色结构的系数函数之间的关系的重夸克的质量定义在$\overline{\rm MS}$和壳计划允许第二个非零夸克质量。我们还得到了这八个系数函数的调和多项式和迭代积分的解析结果。这允许验证数值准确性。

英文摘要:

We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter $x$ and the dimension $d$, in the whole kinematic range of $x$. The method is based on differential equations, which, however, do not require any special form, and series expansions around singular and regular points. This method provides results well suited for fast numerical evaluation and sufficiently precise for phenomenological applications. We apply the approach to four-loop on-shell integrals and compute the coefficient function of eight colour structures in the relation between the mass of a heavy quark defined in the $\overline{\rm MS}$ and the on-shell scheme allowing for a second non-zero quark mass. We also obtain analytic results for these eight coefficient functions in terms of harmonic polylogarithms and iterated integrals. This allows for a validation of the numerical accuracy.

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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