Automatic numerical integration methods for Feynman integrals through 3-loop

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 ParI...

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Bibliographic Details
Published in:Journal of physics. Conference series 2015-05, Vol.608 (1), p.12071
Main Authors: de Doncker, E, Yuasa, F, Kato, K, Ishikawa, T, Olagbemi, O
Format: Article
Language:English
Subjects:
Algorithms
Extrapolation
Integrals
Message passing
Multivariate analysis
Numerical integration
Numerical methods
Physics
Regularization
Singularities
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Summary: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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/608/1/012071