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arXiv · 2208.12765

Landau Singularities and Higher-Order Roots

Jacob L. Bourjaily·Cristian Vergu·Matt von Hippel
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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 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 co-dimension than one, thus evading Landau's argument.

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Jacob L. Bourjaily, Cristian Vergu, Matt von Hippel. 2023-10-20. Landau Singularities and Higher-Order Roots. https://arxiv.org/abs/2208.12765

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