Analytic results for the massive sunrise integral in the context of an alternative perturbative calculational method

Abstract

An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such a perturbative amplitude is related to many important physical process treated in the Standard Model context. The background of this investigation is an alternative strategy to handle the divergences typical for perturbative solutions of quantum field theory. Since its proposition, the mentioned method was exhaustively used to calculate and manipulate one-loop Feynman integrals with a great success. However, the great advances in precision of experimental data collected in particle physics colliders have pushed up theoretical physicists to improve their predictions through multi-loop calculations. In this paper, we describe the main steps required to perform two-loop calculations within the context of the referred method. We show that the same rules used for one-loop calculations are enough to deal with two-loop graphs as well. Analytic results for the sunrise graph are obtained in terms of elliptic multiple polylogarithms as well as a numerical analysis is provided.