# Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian

## TL;DR

This paper derives the missing G^3 and G^4 contributions to the conservative two-body dynamics at fourth post-Newtonian order using an effective field theory approach, providing a regularized Lagrangian consistent with prior results.

## Contribution

It presents the first calculation of the G^3 and G^4 sectors at 4PN order within the EFT framework, completing the conservative dynamics at this level.

## Key findings

- Derived the G^3 and G^4 sectors at 4PN order.
- Constructed a regularized Lagrangian consistent with previous methods.
- Validated results against existing computations.

## Abstract

Within the framework of the effective field theory approach to the post-Newtonian approximation to General Relativity, we report the so far missing G^3 and G^4 sectors of the conservative two body dynamics at fourth perturbative order for non-spinning compact objects. Following the standard procedure, the exchange of gravitational interaction is integrated out to obtain a systematic expansion in terms of Feynman graphs. Building on this result and on previously obtained ones, we are able to write the local-in-time regularized Lagrangian at fourth post-Newtonian order, which is in agreement with results previously computed with other methods.