Landau singularities and higher-order polynomial roots

Jacob L. Bourjaily, Cristian Vergu, Matt Von Hippel

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Landau's work on the singularities of Feynman diagrams suggests that they can only be of three types: either poles, logarithmic divergences, or the roots of quadratic polynomials. On the other hand, many Feynman integrals exist whose singularities involve arbitrarily higher-order polynomial roots. We investigate this apparent paradox using concrete examples involving cube roots and roots of a degree-eight polynomial in four dimensions and roots of a degree-six polynomial in two dimensions and suggest that these higher-order singularities can only be approached via kinematic limits of higher codimension than one, thus evading Landau's argument.

Original languageEnglish (US)
Article number085021
JournalPhysical Review D
Volume108
Issue number8
DOIs
StatePublished - Oct 15 2023

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

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