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 $d$ in terms of(generalized) hypergeometric functions $_2F_1$ and $F_1$. Values at asymptoticor exceptional kinematic points as well as expansions around the singularpoints at $d=4+2n$, $n$ non-negative integers, may be derived from therepresentations easily. The Feynman integrals studied here may be used asbuilding blocks for the calculation of one-loop and higher-loop scalar andtensor amplitudes. From the recursion relation presented, higher n-pointfunctions may be obtained in a straightforward manner.