Classical 3-loop 2-body diagrams

TL;DR

This paper develops a method to compute complex 3-loop classical diagrams in the context of Einstein's gravity, aiding the calculation of the 4PN two-body effective action using quantum field theory techniques.

Contribution

It introduces a novel approach to evaluate 3-loop classical diagrams by reducing them to familiar QFT forms and applying Integration By Parts methods.

Findings

Successfully demonstrated the method on a specific diagram.

Provides a framework for tackling higher-order loop diagrams in gravitational two-body problems.

Facilitates progress in precise gravitational modeling at the 4PN order.

Abstract

As part of the study of the two-body problem in Einstein's gravity, the fourth post-Newtonian order (4PN) of the two-body effective action is being computed presently by both effective field theory (EFT) methods and others. Diagrams with 3 (or 4) classical loops appear to be a significant obstacle. In this paper we develop a method to compute such 3-loop diagrams and demonstrate it through a specific diagram. We reduce the classical diagrams through shrinking the body worldlines to a form more familiar in Quantum Field Theory. A key ingredient in the evaluation is the Integration By Parts method for Feynman integrals.