Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d

Abstract

Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension $d$ in terms of (generalized) hypergeometric functions ${}_2{F}_1$ and $F_1$. Values at asymptotic or exceptional kinematic points as well as expansions around the singular points at $d=4+2n$, $n$ non-negative integers, may be derived from the representations easily. The Feynman integrals studied here may be used as building blocks for the calculation of one-loop and higher-loop scalar and tensor amplitudes. From the recursion relation presented, higher n-point functions may be obtained in a straightforward manner.

Comments: 9 pages, talk presented by TR at workshop "Matter To The Deepest", XLI International Conference on Recent Developments in Physics of Fundamental Interactions (MTTD 2017), September 3-8, 2017, Podlesice, Poland, to appear in the proceedings