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

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.