Regularization of Feynman 4-Loop Integrals with Numerical Integration and Extrapolation
Regularization of Feynman 4-Loop Integrals with Numerical Integration and Extrapolation
复制标题
利用数值积分和外推法对费曼 4 环积分进行正则化
DOI：
10.1007/978-3-031-10562-3_28
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Yuasa F.
中科院分区：
文献类型：
--
作者：
de Doncker E.;Yuasa F.
在本文中，我们继续我们最近的工作评估数值近似的一组4圈自能积分所需的高阶微扰理论的计算。结果是由维正则化参数的Laurent展开给出的，其中与时空维相关：虽然文献中以解析形式给出了无质量内部线图的首阶系数，但我们使用数值方法和现代计算技术获得了它们。以类似的方式，我们得出的结果，图与大量的线。基于复合格规则的循环积分的计算的SIMD（单指令，多数据）性质使其自身适合于高效的GPU实现。我们进一步应用双指数数值积分分层的消息传递接口（MPI）并行平台。积分序列的限制（正则化参数趋于零）的数值实现使用线性和非线性外推程序。数值结果表明，该方法的通用性，并显示出一定的鲁棒性方面的序列参数的选择。
In this paper we continue our recent work on evaluating numerical approximations for a set of 4-loop self-energy integrals required in the computation of higher orders in perturbation theory. The results are given by a Laurent expansion in the dimensional regularization parameter,whereis related to the space-time dimension asAlthough the leading-order coefficients for the diagrams with massless internal lines are given in analytic form in the literature, we obtain them using a numerical approach and with modern computational techniques. In a similar manner, we derive results for diagrams with massive lines. The SIMD (Single Instruction, Multiple Data) nature of the computation of loop integrals based on composite lattice rules lends itself to an efficient GPU implementation. We further apply double exponential numerical integration layered over the message passing interface (MPI) parallel platform. Limits of integral sequences (as the regularization parameter tends to zero) are implemented numerically using linear and nonlinear extrapolation procedures. Numerical results are given to illustrate the versatility of the methods and show some robustness with regard to the selection of sequence parameters.