Extrapolation Algorithms for Infrared Divergent Integrals

This paper describes applications of extrapolation for the computation of coefficients in an expansion of infrared divergent integrals. An extrapolation procedure is performed with respect to a parameter introduced by dimensional regularization. While this treats typical IR singularities at the boun...

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Bibliographic Details
Published inarXiv.org
Main Authors de Doncker, Elise, Fujimoto, Junpei, Hamaguchi, Nobuyuki, Ishikawa, Tadashi, Kurihara, Yoshimasa, Ljucovic, Marko, Shimizu, Yoshimitsu, Yuasa, Fukuko
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.10.2011
Subjects
Algorithms
Boundaries
Extrapolation
Integrals
Regularization
Singularities
Thermal expansion
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Summary:This paper describes applications of extrapolation for the computation of coefficients in an expansion of infrared divergent integrals. An extrapolation procedure is performed with respect to a parameter introduced by dimensional regularization. While this treats typical IR singularities at the boundaries of the integration domain, special care needs to be taken in cases where the integrand is singular in the interior of the domain as well as on the boundaries. A double extrapolation is devised for a class of massless vertex integrals. Quadruple precision results are presented, demonstrating high accuracy. The computations are supported by the use of general adaptive integration programs from the QUADPACK package, in iterated integrations with highly singular integrand functions.
ISSN:2331-8422