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Finite Integrals from Feynman Polytopes

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arxiv 2410.18014 v1 pith:OKIV57EE submitted 2024-10-23 hep-th hep-ph

Leonardo de la Cruz , David A. Kosower , Pavel P. Novichkov This is my paper
classification hep-thhep-ph
keywords approachintegralsfeynmanfiniteconjecturegeometricgraphnumerators
verification ladder T0 review T1 audit T2 compute T3 formal
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We investigate a geometric approach to determining the complete set of numerators giving rise to finite Feynman integrals. Our approach proceeds graph by graph, and makes use of the Newton polytope associated to the integral's Symanzik polynomials. It relies on a theorem by Berkesch, Forsg{\aa}rd, and Passare on the convergence of Euler--Mellin integrals, which include Feynman integrals. We conjecture that a necessary in addition to a sufficient condition is that all parameter-space monomials lie in the interior of the polytope. We present an algorithm for finding all finite numerators based on this conjecture. In a variety of examples, we find agreement between the results obtained using the geometric approach, and a Landau-analysis approach developed by Gambuti, Tancredi, and two of the authors.

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Cited by 3 Pith papers

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

  1. Pseudo-Evanescent Feynman Integrals from Local Subtraction

    hep-th 2026-05 conditional novelty 7.0 of 10

    Local subtraction reduces pseudo-evanescent Feynman integrals to products of one-loop integrals or one-fold integrals, with the finite part of the two-loop all-plus five-point amplitude arising solely from ultraviolet...

  2. Fano and Reflexive Polytopes from Feynman Integrals

    hep-th 2025-12 unverdicted novelty 6.0 of 10

    Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.

  3. Finite Massless Pentaboxes

    hep-ph 2026-06 unverdicted novelty 5.0 of 10

    Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.

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