Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach

TL;DR

This paper computes the conservative dynamics of non-spinning binary systems to third Post-Minkowskian order using an effective field theory approach, employing scattering angles and amplitude techniques, and confirms agreement with previous results.

Contribution

It introduces a novel EFT-based method to derive third-order Post-Minkowskian dynamics using scattering angles and amplitude bootstrap techniques.

Findings

Derived the third Post-Minkowskian Hamiltonian for binaries.

Computed scattering angles to ${ m O}(G^3)$ via Feynman diagrams.

Confirmed consistency with prior results by Bern et al.

Abstract

We derive the conservative dynamics of non-spinning binaries to third Post-Minkowskian order, using the Effective Field Theory (EFT) approach introduced in [2006.01184] together with the Boundary-to-Bound dictionary developed in [1910.03008, 1911.09130]. The main ingredient is the scattering angle, which we compute to ${\cal O}(G^3)$ via Feynman diagrams. Adapting to the EFT framework powerful tools from the amplitudes program, we show how the associated (master) integrals are bootstrapped to all orders in velocities via differential equations. Remarkably, the boundary conditions can be reduced to the same integrals that appear in the EFT with Post-Newtonian sources. For the sake of comparison, we reconstruct the Hamiltonian and the classical limit of the scattering amplitude. Our results are in perfect agreement with those in Bern et al. [1901.04424, 1908.01493].