Scalar One-loop Vertex Integrals as Meromorphic Functions of Space-time Dimension d

摘要

Representations are derived for the basic scalar one-loop vertex Feynmanintegrals as meromorphic functions of the space-time dimension d interms of (generalized) hypergeometric functions 2F1 and F1. Values atasymptotic or exceptional kinematic points as well as expansions aroundthe singular points at d = 4+2n, n being non-negative integers, may be derivedfrom the representations easily. The Feynman integrals studied heremay be used as building blocks for the calculation of one-loop and higherloopscalar and tensor amplitudes. From the recursion relation presented,higher n-point functions may be obtained in a straightforward manner.