Effective field theory calculation of conservative binary dynamics at third post-Newtonian order

TL;DR

This paper uses effective field theory and automation to calculate the conservative dynamics of non-spinning binary systems at third post-Newtonian order, improving computational efficiency and paving the way for higher-order analyses.

Contribution

It introduces an automated Mathematica-based method to compute third post-Newtonian order dynamics, enhancing traditional calculation techniques.

Findings

Reproduces third post-Newtonian order conservative dynamics for spin-less binaries.

Automates Feynman amplitude calculations using Mathematica.

Facilitates future higher-order gravitational computations.

Abstract

We reproduce the two-body gravitational conservative dynamics at third post-Newtonian order for spin-less sources by using the effective field theory methods for the gravitationally bound two-body system, proposed by Goldberger and Rothstein. This result has been obtained by automatizing the computation of Feynman amplitudes within a Mathematica algorithm, paving the way for higher-order computations not yet performed by traditional methods.