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  • Open Access

Geometric singularities of Feynman integrals

Martin Helmer1,* and Felix Tellander2,†

  • *Contact author: martin.helmer@swansea.ac.uk
  • †Contact author: felix@tellander.se
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Phys. Rev. D 112, 065019 – Published 23 September, 2025

DOI: https://doi.org/10.1103/l234-l557

Abstract

We provide a new method to calculate the full microlocal description of the singularities of Feynman integrals. This is done by associating a unique constructible function to the system of partial differential equations (PDEs) annihilating the integral and from this function the singularities can directly be read-off. This function can be constructed explicitly even if the system of PDEs is unknown and describes both the location of the singularities and the number of (generalized) master integrals on them. Our framework is flexible enough to perform the calculation in any of the Lee-Pomeransky, Feynman, or momentum representations.

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Phys. Rev. D 112, 065019– Published 23 September, 2025
  • Received 9 June 2025
  • Accepted 25 August 2025
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