Cohen-Macaulay Property of Feynman Integrals

The connection between Feynman integrals and GKZ $A$-hypergeometric systems has been a topic of recent interest with advances in mathematical techniques computational tools opening new possibilities; this paper we continue to explore connection. To each such hypergeometric system there is an associated toric ideal, prove that the latter Cohen-Macaulay property for two large families integrals. This implies, example, both number independent solutions dynamical singularities are space-time dimension generalized propagator powers. Furthermore, particular, it means process finding series representation these fully algorithmic.