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

TL;DR

This paper advances the five-loop level of the conservative two-body Hamiltonian in general relativity by computing the 5PN potential contributions using an effective field theory and dimensional regularization framework in harmonic coordinates. It presents a pole-containing expression for the 5PN potential, then constructs a canonical transformation to obtain a pole-free Hamiltonian and incorporates part of the non-local tail terms, achieving consistency with existing EOB results in several ν-power sectors. The work also extracts the π^2 contributions to the yet-unknown constants \bar{d}_5 and a_6 from circular-orbit observables and demonstrates broad agreement with the literature for multiple observables, while identifying remaining discrepancies in purely rational tail-term pieces. Overall, the study provides ab initio 5PN insights, clarifies the merging of potential and tail terms, and strengthens the connection between EFT-based calculations and the EOB approach, with implications for high-precision gravitational-wave modelling.

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.