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Foffa, S., Mastrolia, P., Sturani, R., Sturm, C., & Bobadilla, W. J. T. (2019). Static Two-Body Potential at Fifth Post-Newtonian Order. Phys. Rev. Lett., 122(24), 241605–6pp.
Abstract: We determine the gravitational interaction between two compact bodies up to the sixth power in Newton's constant, G(N), in the static limit. This result is achieved within the effective field theory approach to general relativity, and exploits a manifest factorization property of static diagrams which allows us to derive static post Newtonian (PN) contributions of (2n + 1) order in terms of lower order ones. We recompute in this fashion the 1PN and 3PN static potential, and present the novel 5PN contribution.
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Foffa, S., Sturani, R., & Torres Bobadilla, W. J. (2021). Efficient resummation of high post-Newtonian contributions to the binding energy. J. High Energy Phys., 02(2), 165–18pp.
Abstract: A factorisation property of Feynman diagrams in the context the Effective Field Theory approach to the compact binary problem has been recently employed to efficiently determine the static sector of the potential at fifth post-Newtonian (5PN) order. We extend this procedure to the case of non-static diagrams and we use it to fix, by means of elementary algebraic manipulations, the value of more than one thousand diagrams at 5PN order, that is a substantial fraction of the diagrams needed to fully determine the dynamics at 5PN. This procedure addresses the redundancy problem that plagues the computation of the binding energy with respect to more “efficient” observables like the scattering angle, thus making the EFT approach in harmonic gauge at least as scalable as the others methods.
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