We study a rational matroid invariant, obtained as the tropicalization of the Feynman period integral. It equals the volume of the polar of the matroid polytope and we give efficient formulas for its computation. This invariant is proven to respect all known identities of Feynman integrals for graphs. We observe a strong correlation between the tropical and transcendental integrals, which yields a method to approximate unknown Feynman periods.
Cite this article
Erik Panzer, Hepp’s bound for Feynman graphs and matroids. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 10 (2023), no. 1, pp. 31–119DOI 10.4171/AIHPD/126