Hepp's bound for Feynman graphs and matroids

Understand

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.