On Feynman graphs, matroids, and GKZ-systems

We show in several important cases that the $A$-hypergeometric system attached to a Feynman diagram in Lee–Pomeransky form, obtained by viewing the momenta and the nonzero masses as indeterminates, has a normal underlying semigroup. This continues a quest initiated by Klausen, and studied by Helmer and Tellander. In the process we identify several relevant matroids related to the situation and explore their relationships.