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

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 $\epsilon$-dependent apparent singularities. We introduce an appropriate ansatz which allows us to bring such cases into an $\epsilon$-factorized form. As a proof of principle, we apply it to the integral at hand.

45 pages, 3 Figures, one ancillary file in Mathematica format; v2: corresponds to published version

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Cited by in corpus (6)

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• SOFIA: Singularities of Feynman Integrals Automatized
• Classification of Feynman integral geometries for black-hole scattering at 5PM order
• Canonical differential equations and intersection matrices
• The spectrum of Feynman-integral geometries at two loops
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