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arXiv 2011.11655hep-ph
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重夸克的$\overline{\mathrm{MS}}$与运动质量的关系

On the relation between the $\overline{\mathrm{MS}}$ and the kinetic mass of heavy quarks

Matteo Fael, Kay Schönwald, Matthias Steinhauser

摘要:

本文计算了三圈重夸克的极质量与运动质量之间的关系。利用已知的极与$\overline{\rm MS}$质量之间的关系,我们得到了精确的$\overline{\rm MS}$与动力学质量之间的转换关系.通过涉及一个重夸克接近阈值的散射谱函数的时刻定义的动力学质量。这需要计算前向散射振幅的虚部,直到三个环路阶。详细讨论了主积分的展开过程和归约过程。对于后者的分析结果提供。我们将结果应用于粲夸克和底夸克质量。在后一种情况下,我们计算并包括有限的夸克质量的影响。此外,我们确定了大$β_0$结果的转换公式在四个循环的顺序。对于底夸克,我们估计$\overline{\rm MS}$和动力学质量之间的转换的不确定性约为15 MeV,这是一个改进的因素相比,两个两到三个圈的公式。提高精度是至关重要的Cabibbo-Kobayashi-Maskawa矩阵元素$|V_{cb}|$在Belle II的提取。

英文摘要:

We compute the relation between the pole mass and the kinetic mass of a heavy quark to three loops. Using the known relation between the pole and the $\overline{\rm MS}$ mass we obtain precise conversion relations between the $\overline{\rm MS}$ and kinetic masses. The kinetic mass is defined via the moments of the spectral function for the scattering involving a heavy quark close to threshold. This requires the computation of the imaginary part of a forward scattering amplitude up to three-loop order. We discuss in detail the expansion procedure and the reduction to master integrals. For the latter analytic results are provided. We apply our result both to charm and bottom quark masses. In the latter case we compute and include finite charm quark mass effects. Furthermore, we determine the large-$β_0$ result for the conversion formula at four-loop order. For the bottom quark we estimate the uncertainty in the conversion between the $\overline{\rm MS}$ and kinetic masses to about 15 MeV which is an improvement by a factor two to three as compared to the two-loop formula. The improved precision is crucial for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ at Belle II.

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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