Relations between some analytic representations of one-loop scalar integrals

TL;DR

This paper compares various analytic expressions for one-loop scalar integrals in quantum field theory, demonstrating their equivalence through direct and path-integral methods.

Contribution

It introduces a comprehensive comparison and proof of equivalence among different parametrized analytic forms of one-loop scalar integrals.

Findings

Different analytic representations are equivalent.

Path-integral methods confirm the equivalence.

Provides a unified understanding of scalar integrals.

Abstract

We compare several parametrized analytic expressions for an arbitrary off-shell one-loop $n$-point function in scalar field theory in $D$-dimensional space-time, and show their equivalence both directly and through path-integral methods.