Extrapolation Algorithms for Infrared Divergent Integrals

Elise de Doncker; Junpei Fujimoto; Nobuyuki Hamaguchi; Tadashi Ishikawa; Yoshimasa Kurihara; Marko Ljucovic; Yoshimitsu Shimizu; Fukuko Yuasa

arXiv · 1110.3587

Extrapolation Algorithms for Infrared Divergent Integrals

Elise de Doncker·Junpei Fujimoto·Nobuyuki Hamaguchi·Tadashi Ishikawa·Yoshimasa Kurihara·Marko Ljucovic·Yoshimitsu Shimizu·Fukuko Yuasa

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Abstract

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.

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Elise de Doncker, Junpei Fujimoto, Nobuyuki Hamaguchi, Tadashi Ishikawa, Yoshimasa Kurihara, Marko Ljucovic, Yoshimitsu Shimizu, Fukuko Yuasa. 2011-10-17. Extrapolation Algorithms for Infrared Divergent Integrals. https://arxiv.org/abs/1110.3587

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