Spanning forest polynomials and the transcendental weight of Feynman graphs

TL;DR

This paper develops combinatorial methods using spanning forest polynomials to predict the transcendental weight of Feynman integrals in $\

Contribution

It introduces new graph operations that preserve weight and identifies subgraphs that reduce transcendental weight, advancing understanding of Feynman integral complexity.

Findings

Operations on graphs that preserve transcendental weight

Criteria for subgraphs that decrease weight

Enhanced ability to predict integral complexity

Abstract

We give combinatorial criteria for predicting the transcendental weight of Feynman integrals of certain graphs in $\phi^4$ theory. By studying spanning forest polynomials, we obtain operations on graphs which are weight-preserving, and a list of subgraphs which induce a drop in the transcendental weight.