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

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arxiv 2412.12057 v2 pith:KJCABKCO submitted 2024-12-16 hep-th gr-qchep-ph

Hjalte Frellesvig , Roger Morales , Sebastian Pögel , Stefan Weinzierl , Matthias Wilhelm This is my paper · ORCID
classification hep-thgr-qchep-ph
keywords calabi-yaufeynmanintegralvarepsilonapparentfactorizedformgravity
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abstract

We study a recently identified four-loop Feynman integral that contains a three-dimensional Calabi-Yau geometry and contributes to the scattering of black holes in classical gravity at fifth post-Minkowskian and second self-force order (5PM 2SF) in the conservative sector. In contrast to previously studied Calabi-Yau Feynman integrals, the higher-order differential equation that this integral satisfies in dimensional regularization exhibits $\varepsilon$-dependent apparent singularities. We introduce an appropriate ansatz which allows us to bring such cases into an $\varepsilon$-factorized form. As a proof of principle, we apply it to the integral at hand.

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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. Analytic result of a three-loop integral family in the Higgs decay to four massive bottom quarks

    hep-ph 2026-07 accept novelty 6.5 of 10

    Analytic master-integral results through O(ε²) are obtained for a three-loop family containing elliptic and K3 geometries by building and solving a mixed-sector ε-factorized differential equation.

  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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