Quadpack computation of Feynman loop integrals

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• 作者：Elise de Doncker^a ; ^{elise.dedoncker@wmich.edu}  ; [Author Vitae] ; Junpei Fujimoto^b ; ^{junpei.fujimoto@kek.jp}  ; [Author Vitae] ; Nobuyuki Hamaguchi^c ; ^{nobuyuki.hamaguchi.xr@hitachi.com}  ; [Author Vitae] ; Tadashi Ishikawa^b ; ^{tadashi.ishikawa@kek.jp}  ; [Author Vitae] ; Yoshimasa Kurihara^b ; ^{yoshimasa.kurihara@kek.jp}  ; [Author Vitae] ; Yoshimitsu Shimizu^b ; ^{yoshimitsu.shimizu@kek.jp}  ; [Author Vitae] ; Fukuko Yuasa^b ; ^{fukuko.yuasa@kek.jp}  ; [Author Vitae]
• 关键词：30E15 ; 41A55 ; 41A58 ; 41A60 ; 65B05 ; 65B15 ; 65D20 ; 65D30 ; 65D32 ; 65Z05 ; 68N30 ; 68W01
• 刊名：Journal of Computational Science
• 出版年：2012
• 出版时间：May, 2012
• 年：2012
• 卷：3
• 期：3
• 页码：102-112
• 全文大小：733 K

文摘

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.