Efficient resummation of high post-Newtonian contributions to the binding energy

TL;DR

This paper extends a factorization technique within the Effective Field Theory framework to efficiently compute high-order post-Newtonian contributions to the binding energy of compact binaries, significantly reducing computational complexity.

Contribution

It generalizes the factorization method to non-static diagrams at 5PN order, fixing over a thousand diagrams algebraically, enhancing scalability of EFT calculations.

Findings

Successfully fixed over a thousand diagrams at 5PN order.

Extended the factorization approach to non-static diagrams.

Improved scalability of EFT computations for binary dynamics.

Abstract

A factorisation property of Feynman diagrams in the context the Effective Field Theory approach to the compact binary problem has been recently employed to efficiently determine the static sector of the potential at fifth post-Newtonian (5PN) order. We extend this procedure to the case of non-static diagrams and we use it to fix, by means of elementary algebraic manipulations, the value of more than one thousand diagrams at 5PN order, that is a substantial fraction of the diagrams needed to fully determine the dynamics at 5PN. This procedure addresses the redundancy problem that plagues the computation of the binding energy with respect to more "efficient" observables like the scattering angle, thus making the EFT approach in harmonic gauge at least as scalable as the others methods.