Classical 3-loop 2-body diagrams

Abstract

As part of the study of the two-body problem in Einstein's gravity, the fourth post-Newtonian order (4PN) of the two-body effective action is being computed presently by both effective field theory (EFT) methods and others. Diagrams with 3 (or 4) classical loops appear to be a significant obstacle. In this paper we develop a method to compute such 3-loop diagrams and demonstrate it through a specific diagram. We reduce the classical diagrams through shrinking the body worldlines to a form more familiar in Quantum Field Theory. A key ingredient in the evaluation is the Integration By Parts method for Feynman integrals.

15 pages, 6 figures. v2: updated references and credit. v3: added calculation and a minor correction

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Cited by in corpus (7)

• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Effective field theory methods to model compact binaries
• N${}^3$LO gravitational spin-orbit coupling at order $G^4$
• Renormalizing Love: tidal effects at the third post-Newtonian order
• Gravitoelectric dynamical tides at second post-Newtonian order
• Radiating Love: adiabatic tidal fluxes and modes up to next-to-next-to-leading post-Newtonian order
• Symmetries of Feynman integrals and the Integration By Parts method