Evaluating Feynman integrals by the hypergeometry

doi:10.1016/j.nuclphysb.2018.01.001

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	Evaluating Feynman integrals by the hypergeometry
	Feng, TF ; Chang, CH ; Chen, JB ; Gu, ZH ; Zhang, HB
刊名	NUCLEAR PHYSICS B
	2018
卷号	927 页码:516-549
关键词	DIFFERENTIAL-EQUATIONS METHOD DIAGRAMS RENORMALIZATION REDUCTION ALGORITHM MASSES BOSON LHC
ISSN号	0550-3213
DOI	10.1016/j.nuclphysb.2018.01.001
英文摘要	The 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.
学科主题	Physics
语种	英语
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/22967]
专题	理论物理研究所_理论物理所1978-2010年知识产出
作者单位	1.Hebei Univ, Dept Phys, Baoding 071002, Peoples R China 2.Chinese Acad Sci, Inst Theoret Phys, Key Lab Theoret Phys, Beijing 100190, Peoples R China 3.CCAST, World Lab, POB 8730, Beijing 100190, Peoples R China 4.Taiyuan Univ Technol, Dept Phys, Taiyuan 030024, Shanxi, Peoples R China 5.Univ Chinese Acad Sci, Sch Phys Sci, Beijing 100049, Peoples R China 6.[Feng, Tai-Fu 7.Gu, Zhi-Hua
推荐引用方式 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.