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Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals

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arxiv 2311.14669 v2 pith:IUCSJ33M submitted 2023-11-24 hep-th hep-ph

Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals

classification hep-th hep-ph
keywords singularitiesalgebraiclandaucomputationalfeynmangeometryintegralsalgorithm
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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/.

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Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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