Automatic numerical integration methods for Feynman integrals through 3-loop

16th International workshop on Advanced Computing and Analysis Techniques in physics research

物理学;计算机科学

De Doncker, E.^1 ; Yuasa, F.^2 ; Kato, K.^3 ; Ishikawa, T.^2 ; Olagbemi, O.^1

Department of Computer Science, Western Michigan University, Kalamazoo

MI

49008, United States^1

High Energy Accelerator Research Organization (KEK), Oho 1-1, Tsukuba, Ibaraki

305-0801, Japan^2

Department of Physics, Kogakuin University, Shinjuku, Tokyo

163-8677, Japan^3

关键词: Automatic adaptive;    Boundary singularities;    Feynman loop diagrams;    Message passing interface;    Multivariate integration;    Multivariate techniques;    Numerical integration methods;    Numerical integrations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/608/1/012071/pdf
DOI  :  10.1088/1742-6596/608/1/012071

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.