Massive two--loop integrals in renormalizable theories

Abstract

We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy numerical integration, similar to a method proposed previously for treating diagrams without numerators. We reduce all possible tensor structures to a small set of scalar integrals, for which we provide integral representations in terms of four basic functions. The algebraic part is suitable for implementing in a computer program for the automatic generation and evaluation of Feynman graphs. The numerical part is essentially the same as in the case of Feynman diagrams without numerators.