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

TL;DR

This paper presents an analytic approach to calculating the two-loop sunrise Feynman integral using an alternative perturbative method, extending previous one-loop techniques and providing explicit results in terms of elliptic polylogarithms.

Contribution

It introduces a novel application of an existing perturbative method to two-loop integrals, demonstrating its effectiveness beyond one-loop calculations.

Findings

Analytic expressions for the two-loop sunrise integral in terms of elliptic multiple polylogarithms.

Validation of the method's applicability to multi-loop Feynman integrals.

Numerical analysis supporting the analytic results.

Abstract

An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such perturbative amplitude is related with many important physical process treated in the standard model context. The background of this investigation is an alternative strategy to handle with the divergences typical of 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-loops calculations. In the present job, we describe the main steps required to perform two-loops 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-loops 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.