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Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov

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arxiv 2405.17255 v2 pith:CBAZTO6V submitted 2024-05-27 hep-th gr-qc

Hjalte Frellesvig , Roger Morales , Matthias Wilhelm This is my paper · ORCID
classification hep-thgr-qc
keywords geometriespost-minkowskianbaikovdiagramsdynamicsfeynmanfullloop-by-loop
verification ladder T0 review T1 audit T2 compute T3 formal
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We use the loop-by-loop Baikov representation to investigate the geometries in Feynman integrals contributing to the classical dynamics of a black-hole two-body system in the post-Minkowskian expansion of general relativity. These geometries determine the spaces of functions to which the corresponding Feynman diagrams evaluate. As a proof of principle, we provide a full classification of the geometries appearing up to three loops, i.e. fourth post-Minkowskian order, for all diagrams relevant to the conservative as well as the dissipative dynamics, finding full agreement with the literature. Moreover, we show that the non-planar top topology at four loops, which is the most complicated sector with respect to integration-by-parts identities, has an algebraic leading singularity and thus can only depend on non-trivial geometries through its subsectors.

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Cited by 3 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. Calabi-Yau Feynman integrals in gravity: $\varepsilon$-factorized form for apparent singularities

    hep-th 2024-12 conditional novelty 7.0 of 10

    An extended ansatz for canonical differential equations handles epsilon-dependent apparent singularities and yields an epsilon-factorized form for the four-loop Calabi-Yau Feynman integral relevant to 5PM black-hole s...

  3. Special Fano geometry from Feynman integrals

    hep-th 2024-12 conditional novelty 5.0 of 10

    Special Fano varieties, which include Calabi-Yau spaces as the Q=1 case, arise from the Symanzik polynomials of several families of Feynman integrals.

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