One loop integration with hypergeometric series by using recursion relations

15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research

物理学;计算机科学

Watanabe, Norihisa^1 ; Kaneko, Toshiaki^1

High Energy Accelerator Research Organization (KEK), Computing Research Center, 1-1, O-ho, Ibaraki 305-0801 Tsukuba, Japan^1

关键词: D-dimensional spaces;    Hypergeometric functions;    Hypergeometric series;    Numerical results;    Point functions;    Power series expansions;    Recursion relations;    Three-point function;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/523/1/012063/pdf
DOI  :  10.1088/1742-6596/523/1/012063

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

General one-loop integrals with arbitrary mass and kinematical parameters in d-dimensional space-time are studied. By using Bernstein theorem, a recursion relation is obtained which connects (n + 1)-point to n-point functions. In solving this recursion relation, we have shown that one-loop integrals are expressed by a newly defined hypergeometric function, which is a special case of Aomoto-Gelfand hypergeometric functions. We have also obtained coefficients of power series expansion around 4-dimensional space-time for two-, three- and four-point functions. The numerical results are compared with LoopTools for the case of two- and three-point functions as examples.