Six-loop gravitational interactions at the sixth post-Newtonian order

TL;DR

This paper calculates the sixth post-Newtonian order gravitational interaction between two compact objects using a novel six-loop Feynman diagram approach within effective field theory, providing a key missing piece for precise two-body dynamics.

Contribution

First computation of six-loop Feynman diagrams for gravitational interactions at sixth post-Newtonian order in the static limit within effective field theory.

Findings

Six-loop diagrams evaluated for the first time.

Result is finite in three dimensions.

Provides essential component for two-body gravitational dynamics at sixth PN order.

Abstract

We compute the gravitational interaction of two coalescing compact objects at sixth post-Newtonian order in the static limit, employing the diagrammatic approach within the effective field theory framework of General Relativity. The calculation requires the evaluation of six-loop Feynman diagrams that are mapped onto two-point integrals with a gauge-theory-like structure, which are computed here for the first time. The resulting seventh-order contribution in Newton's constant is finite in three space dimensions. This result provides the most technically demanding missing ingredient for the determination of the conservative dynamics of the gravitational two-body system at sixth post-Newtonian order.