The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions

TL;DR

This paper computes the fifth-order post-Newtonian gravitational potential for binary systems using an effective field theory approach, including tail effects and regularization, advancing precision in gravitational dynamics modeling.

Contribution

It provides a first-principles calculation of the fifth-order potential contributions, including tail effects, within an effective field theory framework for binary systems.

Findings

Calculation of potential contributions at 5PN order

Inclusion of tail and non-local effects

Comparison with existing literature results

Abstract

We calculate the potential contributions of the motion of binary mass systems in gravity to the fifth post--Newtonian order ab initio using coupling and velocity expansions within an effective field theory approach based on Feynman amplitudes starting with harmonic coordinates and using dimensional regularization. Furthermore, the singular and logarithmic tail contributions are calculated. We also consider the non--local tail contributions. Further steps towards the complete calculation are discussed and first comparisons are given to results in the literature.