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Feynman graph polynomials
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The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.
Forward citations
Cited by 5 Pith papers
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Hepp's bound for Feynman graphs and matroids
The Hepp bound, a rational matroid invariant from tropicalizing the Feynman period integral, provably respects all known graph period symmetries and correlates strongly with actual periods.
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The paper develops reduction operators from resonance in GKZ systems to contract edges in Feynman graphs for one-loop, sunrise, and banana graphs, closing differential equation systems to master integrals.
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Electroweak double-box integrals for Moller scattering
Presents epsilon-factorised master integrals, boundary values, and numerical routines for the planar and non-planar electroweak double-box families relevant to NNLO Moller scattering.
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Feynman Fox integrals in the physical region
A recipe is given that expresses physical-region Feynman integrals as Fox functions on vertical Mellin-Barnes contours with the correct cut structure, but the claimed imaginary-part correctness is not yet verified.
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Unitarity Cuts, t-channel Divergences and the KLN Theorem for Unstable Particles
Authors formulate prescriptions for KLN cancellations of t-channel divergences in an unstable-particle model, showing scheme-independent results and steps toward finite inclusive observables.
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