Singularities of Feynman integrals
Centre for High Energy Physics, Indian Institute of Science, 560012, Bangalore, Karnataka, India
2 Statistics and Mathematics Department, Indian Statistical Institute, Bangalore, 560059, Bangalore, Karnataka, India
Accepted: 27 December 2023
Published online: 24 January 2024
In this paper, we study the singularities of Feynman integrals by compactifying the integration domain as well as the ambient space of these integrals, by embedding them in higher-dimensional space. In this compactified space, the singularities occur due to the meeting of compactified propagators at non-general position. The present analysis, which had been previously used only for the singularities of second type, is used to study other kinds of singularities viz threshold, pseudo-threshold and anomalous threshold singularities. We study various one-loop and two-loop examples and obtain their singularities. We also present observations based on results obtained, that allow us to determine whether the singularities lie on the physical sheet or not for some simple cases. Thus, this work at the frontier of our knowledge of Feynman integral calculus sheds insight into the analytic structure.
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