Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals

Abstract

We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment of Landau singularities, we develop an algorithm for classifying and computing them using techniques from computational algebraic geometry. We introduce an algebraic variety called the principal Landau determinant, which captures the singularities even in the presence of massless particles or UV/IR divergences. We illustrate this for 114 example diagrams, including a cutting-edge 2-loop 5-point non-planar QCD process with multiple mass scales. The algorithms introduced in this work are implemented in the open-source Julia package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.

7 pages, title change to match the published version

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Cited by in corpus (12)

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• Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar{t}+$jet production at leading colour
• SOFIA: Singularities of Feynman Integrals Automatized
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Differential equations for tree--level cosmological correlators with massive states
• Disperon QED
• Integrated Unitarity for Scattering Amplitudes
• Box Singularity Conditions in Box Diagrams of Decay Processes