Calculating the static gravitational two-body potential to fifth post-Newtonian order with Feynman diagrams

TL;DR

This paper presents a novel calculation of the static gravitational two-body potential up to fifth post-Newtonian order using Feynman diagrams, revealing a factorization property of odd PN diagrams.

Contribution

It introduces a new method leveraging factorization properties to compute high-order post-Newtonian terms in gravitational potentials.

Findings

Successfully calculated up to fifth PN order

Identified factorization property in odd PN diagrams

Demonstrated calculations at first and third PN order

Abstract

We discuss the first-time calculation of the static gravitational two-body potential up to fifth post-Newtonian(PN) order. The results are achieved through a manifest factorization property of the odd PN diagrams. The factorization property is illustrated also at first and third PN order.