Conservative (failed)-tail effects at the fifth post-Newtonian order

TL;DR

This paper investigates the tail and 'failed' tail effects in the conservative dynamics of compact binary systems at 5PN order, using the Fokker Lagrangian method, aiming to resolve existing discrepancies.

Contribution

It provides a new computation of the 'failed' tail sector at 5PN order, potentially resolving discrepancies in the literature and confirming previous tail sector results.

Findings

Tail sector results match previous EFT computations

New 'failed' tail sector computation offers insights for resolving discrepancies

Methodology employs Fokker Lagrangian with dimensional regularization

Abstract

This work deals with the tail and ``failed'' tail sectors of the conservative dynamics for compact binary systems at the 5PN order. We employ the Fokker Lagrangian method with dimensional regularization, and our results for the tail sector are perfectly consistent with the previous EFT computations. As for the ``failed'' tail sector, we have good hopes that this new computation will help solving the current discrepancy in the literature.