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Six-Loop Gravitational Interactions at the Sixth Post-Newtonian Order

Giacomo Brunello1, Manoj K. Mandal2,3, Pierpaolo Mastrolia2,3, Raj Patil4,5, Matteo Pegorin2,3,4, Jonathan Ronca2,3, Sid Smith2,3,6, Jan Steinhoff4, and William J. Torres Bobadilla7

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Phys. Rev. Lett. 137, 111401 – Published 9 September, 2026

DOI: https://doi.org/10.1103/c2r3-cqtf

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.

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Outline

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Phys. Rev. Lett. 137, 111401– Published 9 September, 2026
  • Received 12 January 2026
  • Revised 10 July 2026
  • Accepted 5 August 2026
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