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  • Open Access

Momentum expansions in finite-density perturbative calculations

Mika Nurmela* and Juuso Österman†

  • Department of Physics and Helsinki Institute of Physics, P.O. Box 64, FI-00014 University of Helsinki, Finland

  • *Contact author: mika.nurmela@helsinki.fi
  • †Contact author: juuso.s.osterman@helsinki.fi
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Phys. Rev. D 112, 096016 – Published 12 November, 2025

DOI: https://doi.org/10.1103/f3ln-3sf8

Abstract

Complex-valued Feynman integrals in the imaginary time formalism and zero-temperature limit suffer from particular types of infrared divergences that cannot be regulated by integration dimension alone. Related problems leading to integration-order-dependent results are even further pronounced in the presence of additional scales such as external momenta. This plays a noticeable role in systems featuring fermionic degrees of freedom such as cold quantum chromodynamics, where loop integrals are complexified by chemical potential(s). Working in the limit of vanishing temperature, we utilize novel complex-valued extensions to bubble Feynman integrals and study momentum expansions of fermionic loop integrals. The expansions are then used to illustrate the mechanisms of manifested discrepancies between orders of integration, associated with the residue theorem. Finally, we address the issues by introducing a representation avoiding the observed ambiguity and briefly overview classes of integrals insensitive to problems from external momenta.

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See Also

Augmenting the residue theorem with boundary terms in finite-density calculations

Tyler Gorda, Juuso Österman, and Saga Säppi
Phys. Rev. D 106, 105026 (2022)

Article Text

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Phys. Rev. D 112, 096016– Published 12 November, 2025
  • Received 25 August 2025
  • Accepted 19 October 2025
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