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arXiv · 2206.08402

Cutkosky's Theorem for Massive One-Loop Feynman Integrals -- Part 1

Maximilian Mühlbauer
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Abstract

We formulate and prove Cutkosky's Theorem regarding the discontinuity of Feynman integrals in the massive one-loop case up to the involved intersection index. This is done by applying the techniques to treat singular integrals developed in \cite{app-iso}. We write one-loop integrals as an integral of a holomorphic family of holomorphic forms over a compact cycle. Then, we determine at which points simple pinches occur and explicitly compute a representative of the corresponding vanishing sphere. This also yields an algorithm to compute the Landau surface of a one-loop graph without explicitly solving the Landau equations. We also discuss the bubble, triangle and box graph in detail.

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Maximilian Mühlbauer. 2022-06-16. Cutkosky's Theorem for Massive One-Loop Feynman Integrals -- Part 1. https://doi.org/10.1007/s11005-022-01612-4

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