Quadpack computation of Feynman loop integrals |
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| Authors: | Elise de Doncker Junpei Fujimoto Nobuyuki Hamaguchi Tadashi Ishikawa Yoshimasa Kurihara Yoshimitsu Shimizu Fukuko Yuasa |
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| Institution: | 1. Department of Computer Science, Western Michigan University, 1903 West Michigan Avenue, Kalamazoo, MI 49008, United States;2. High Energy Accelerator Research Organization (KEK), 1-1 OHO Tsukuba, Ibaraki 305-0801, Japan;3. Hitachi ICT Business Services, Ltd., Totsuka-ku, Yokohama, Japan;1. Virtual Plants, INRIA Sophia-antipolis, France;2. CIRAD/UMR AGAP, Avenue Agropolis, TA 40/02, 34398Montpellier, France;3. Parietal project-team, INRIA Saclay-île de France, France;4. CEA/Neurospin bât 145, 91191 Gif-Sur-Yvette, France;5. Simula Research Laboratory, P.O. Box 134 NO-1325 Lysaker, Norway;6. Department of Informatics, University of Oslo, P.O. Box 1080 Blinder, NO-0316, Norway;1. Physics Department, Razi University, Kermanshah 67149, Iran;2. Physics Department, University of Sistan and Baluchestan, Zahedan, Iran;1. School of Physics, University of Chinese Academy of Sciences, YuQuan Road 19A, Beijing 100049, China;2. CAS Center for Excellence in Particle Physics, Beijing 100049, China;1. Division of Science, Penn State University Berks, Reading, PA 19610, USA;2. Department of Physics, SERC, Temple University, Philadelphia, PA 19122, USA;3. Theory Center, Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, USA |
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| Abstract: | The paper addresses a numerical computation of Feynman loop integrals, which are computed by an extrapolation to the limit as a parameter in the integrand tends to zero. An important objective is to achieve an automatic computation which is effective for a wide range of instances. Singular or near singular integrand behavior is handled via an adaptive partitioning of the domain, implemented in an iterated/repeated multivariate integration method. Integrand singularities possibly introduced via infrared (IR) divergence at the boundaries of the integration domain are addressed using a version of the Dqags algorithm from the integration package Quadpack, which uses an adaptive strategy combined with extrapolation. The latter is justified for a large class of problems by the underlying asymptotic expansions of the integration error. For IR divergent problems, an extrapolation scheme is presented based on dimensional regularization. |
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