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<p>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 <i>ε</i>-dependent apparent singularities. We introduce an appropriate ansatz which allows us to bring such cases into an <i>ε</i>-factorized form. As a proof of principle, we apply it to the integral at hand.</p>

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Calabi-Yau Feynman integrals in gravity: ε-factorized form for apparent singularities

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月28日

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  • Hjalte Frellesvig,
  • Roger Morales,
  • Sebastian Pögel,
  • Stefan Weinzierl,
  • Matthias Wilhelm

摘要

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