# On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems

## TL;DR

This paper clarifies the origins of ambiguities in the Post-Newtonian expansion for binary systems, showing that effective field theory methods can resolve IR divergence issues at 4PN order without extra data.

## Contribution

It demonstrates that IR divergences in the Post-Newtonian framework can be addressed using EFT techniques, specifically zero-bin subtraction, eliminating the need for additional matching calculations.

## Key findings

- IR divergences at 4PN order can be resolved with zero-bin subtraction
- Ambiguity parameters are linked to finite size effects appearing at 5PN
- EFT formalism clarifies the origin of divergences and ambiguities

## Abstract

We discuss the source of the apparent ambiguities arising in the calculation of the dynamics of binary black holes within the Post-Newtonian framework. Divergences appear in both the near and far zone calculations, and may be of either ultraviolet (UV) or infrared (IR) nature. The effective field theory (EFT) formalism elucidates the origin of the singularities which may introduce apparent ambiguities. In particular, the only (physical) 'ambiguity parameters' that necessitate a matching calculation correspond to unknown finite size effects, which first appear at fifth Post-Newtonian (5PN) order for non-spinning bodies. We demonstrate that the ambiguities linked to IR divergences in the near zone, that plague the recent derivations of the binding energy at 4PN order, both in the ADM and 'Fokker-action' approach, can be resolved by implementing the so-called 'zero-bin' subtraction in the EFT framework. The procedure yields ambiguity-free results without the need of additional information beyond the PN expansion.