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Feng, TF; Chang, CH; Chen, JB; Gu, ZH; Zhang, HB
Evaluating Feynman integrals by the hypergeometry
Source PublicationNUCLEAR PHYSICS B
AbstractThe hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B-0 and massless C-0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams. (c) 2018 The Authors. Published by Elsevier B.V.
Subject AreaPhysics
MOST Discipline CataloguePhysics, Particles & Fields
Indexed BySCIE
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Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.[Feng, Tai-Fu
2.Gu, Zhi-Hua
3.Hebei Univ, Dept Phys, Baoding 071002, Peoples R China
4.Chinese Acad Sci, Inst Theoret Phys, Key Lab Theoret Phys, Beijing 100190, Peoples R China
5.CCAST, World Lab, POB 8730, Beijing 100190, Peoples R China
6.Univ Chinese Acad Sci, Sch Phys Sci, Beijing 100049, Peoples R China
7.Taiyuan Univ Technol, Dept Phys, Taiyuan 030024, Shanxi, Peoples R China
Recommended Citation
GB/T 7714
Feng, TF,Chang, CH,Chen, JB,et al. Evaluating Feynman integrals by the hypergeometry[J]. NUCLEAR PHYSICS B,2018,927:516-549.
APA Feng, TF,Chang, CH,Chen, JB,Gu, ZH,&Zhang, HB.(2018).Evaluating Feynman integrals by the hypergeometry.NUCLEAR PHYSICS B,927,516-549.
MLA Feng, TF,et al."Evaluating Feynman integrals by the hypergeometry".NUCLEAR PHYSICS B 927(2018):516-549.
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