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arXiv 1909.08015hep-ph
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计算五圈QED对电子反常磁矩的贡献:无轻子圈的图形

Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops

Sergey Volkov

摘要:

本文叙述了作者在超级计算机上计算了QED对电子反常磁矩的部分贡献。计算部分包括所有不含轻子圈的5圈QED费曼图。计算结果$7.668(159)$与T. Aoyama,T. Kinoshita和M. 2018年的Nio。差异是关于$4.8σ$的。计算给出了该值的第一个独立检查。本文揭示了精细结构常数预测的一个转变。所开发的计算方法是基于(a)一个减法程序,用于消除所有的紫外和红外发散费曼参数空间之前的积分;(b)一个非自适应蒙特卡罗积分,使用的概率密度函数,分别为每个费曼图使用其组合结构构建。本文简要介绍了该方法(与以前的论文相应的参考)。本文给出了9个规范不变类对整个集合分裂的贡献值。此外,不含轻子圈的所有5圈图的整个集合被分成807个子集,以便(在将来)将计算值与通过其他方法获得的值进行比较。这些详细结果见补充材料。此外,补充材料包含3213个费曼图中每个图的贡献值。这些值的“振荡”性质进行了讨论。描述了实现的技术细节。

英文摘要:

This paper describes a computation of a part of the QED contribution to the electron anomalous magnetic moment that was performed by the author with the help of a supercomputer. The computed part includes all 5-loop QED Feynman graphs without lepton loops. The calculation has led to the result $A_1^{(10)}[\text{no lepton loops}]=6.793(90)$ that is slightly different than the value $7.668(159)$ presented by T. Aoyama, T. Kinoshita, and M. Nio in 2018. The discrepancy is about $4.8σ$. The computation gives the first independent check for that value. A shift in the fine-structure constant prediction is revealed in the paper. The developed calculation method is based on (a) a subtraction procedure for removing all ultraviolet and infrared divergences in Feynman parametric space before integration; (b) a nonadaptive Monte Carlo integration that uses the probability density functions that are constructed for each Feynman graph individually using its combinatorial structure. The method is described briefly in the paper (with the corresponding references to the previous papers). The values for the contributions of nine gauge-invariant classes splitting the whole set are presented in the paper. Moreover, the whole set of all 5-loop graphs without lepton loops is split into 807 subsets for comparison (in the future) of the calculated values with the values obtained by another methods. These detailed results are presented in the supplemental materials. Also, the supplemental materials contain the contribution values for each of 3213 individual Feynman graphs. An "oscillating" nature of these values is discussed. Technical details of the realization are described.

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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