Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant

TL;DR

This paper advances the effective field theory approach to the gravitational two-body problem by calculating the conservative dynamics at fourth post-Newtonian order and fifth order in the Newton constant, using multi-loop diagram techniques.

Contribution

It provides the first EFT-based computation of the 4-loop contributions to the 4th post-Newtonian order, confirming previous results with a novel diagrammatic approach.

Findings

Confirmed previous results for certain terms using EFT methods.

Developed a diagrammatic approach for 4-loop amplitude calculations.

Extended the EFT framework to higher-order gravitational dynamics.

Abstract

Working within the post-Newtonian (PN) approximation to General Relativity, we use the effective field theory (EFT) framework to study the conservative dynamics of the two-body motion at fourth PN order, at fifth order in the Newton constant. This is one of the missing pieces preventing the computation of the full Lagrangian at fourth PN order using EFT methods. We exploit the analogy between diagrams in the EFT gravitational theory and 2-point functions in massless gauge theory, to address the calculation of 4-loop amplitudes by means of standard multi-loop diagrammatic techniques. For those terms which can be directly compared, our result confirms the findings of previous studies, performed using different methods.