Fun with higher-loop Feynman diagrams

TL;DR

This paper reviews recent advances in calculating fully massive vacuum Feynman integrals at five loops, highlighting classification, evaluation, and new expansion results around four dimensions.

Contribution

It introduces new methods and results for five-loop vacuum integrals, advancing computational techniques in quantum field theory.

Findings

New five-loop vacuum integral evaluations

Expanded results around four dimensions

Improved algorithms for classifying Feynman integrals

Abstract

We review recent progress that we have achieved in evaluating the class of fully massive vacuum integrals at five loops. After discussing topics that arise in classification, evaluation and algorithmic codification of this specific set of Feynman integrals, we present some selected new results for their expansions around $4-2\varepsilon$ dimensions.