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  • Letter
  • Open Access

Multipoint fishnet Feynman diagrams: Sequential splitting

Francesco Aprile1 and Enrico Olivucci2

  • 1Departamento de Física Teórica and IPARCOS, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
  • 2Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

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Phys. Rev. D 108, L121902 – Published 21 December, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L121902

Abstract

We study fishnet Feynman diagrams defined by a certain triangulation of a planar n-gon, with massless scalars propagating along and across the cuts. Our solution theory uses the technique of separation of variables, in combination with the theory of symmetric polynomials and Mellin space. The n-point split-ladders are solved by a recursion where all building blocks are made fully explicit. In particular, we find an elegant formula for the coefficient functions of the light-cone leading logs. When the diagram grows into a fishnet, we obtain new results exploiting a Cauchy identity decomposition of the measure over separated variables. This leads to an elementary proof of the Basso-Dixon formula at 4-points, while at n-points it provides a natural operator product expansion-like stratification of the diagram. Finally, we propose an independent approach based on “stampede” combinatorics to study the light-cone behavior of the diagrams as the partition function of a certain vertex model.

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References (44)

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Phys. Rev. D 108, L121902– Published 21 December, 2023
  • Received 20 September 2023
  • Accepted 27 November 2023
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