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

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arxiv 2007.04977 v2 pith:U23YC7E2 submitted 2020-07-09 hep-th gr-qc

Gregor Kälin , Zhengwen Liu , Rafael A. Porto This is my paper · ORCID
classification hep-thgr-qc
keywords approachconservativedynamicseffectivefieldintegralsorderpost-minkowskian
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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].

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order

    hep-th 2026-01 conditional novelty 7.0 of 10

    The conservative black-hole scattering angle at fifth post-Minkowskian and second self-force order is computed in terms of K3 periods, but contains a coefficient fixed only by an ad hoc 'γ-3' prescription.

  2. Local-in-Time Conservative Binary Dynamics at Fifth Post-Minkowskian and First Self-Force Orders

    hep-th 2025-06 conditional novelty 7.0 of 10

    The authors isolate the nonlocal tail part of the 5PM/1SF scattering angle and reconstruct a local-in-time Hamiltonian for generic bound orbits.

  3. First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order

    hep-th 2025-02 conditional novelty 7.0 of 10

    The O(G^3) conservative and radiation-reaction classical observables for spinning black-hole scattering are extended to quartic order in spin, with all-order-in-spin radiation reaction beyond the aligned-spin limit.

  4. Scattering of a point mass by a Schwarzschild black hole: radiated energy and angular momentum

    gr-qc 2025-07 conditional novelty 6.0 of 10

    The 5PM-1SF radiated energy and the complete 4PM-1SF radiated angular momentum to 7PN order are derived for a point mass scattering off a Schwarzschild black hole, along with the resulting 5PM radiation-reacted scatte...

  5. Manifest symplecticity in classical scattering

    hep-th 2025-11 conditional novelty 4.0 of 10

    The on-shell action and the exponential scattering generator differ as functions, but the on-shell action of the true Hamiltonian equals the on-shell action of the generator treated as a unit-time effective Hamiltonian.

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