On $c_2$ invariants of 4-regular Feynman graphs

Abstract

The obstruction for application of effective techniques like denominator reduction for the computation of the $c_2$ invariant of Feynman graphs in general is the absence of a 3-valent vertex for the initial steps. In this paper such a formula for a 4-valent vertex is derived. The formula allows to compute the $c_2$ invariant of new graphs, for instance, 4-regular graphs with small loop number.

22 pages, 2 figures

References in corpus (3)

• A K3 in phi4
• On one example and one counterexample in counting rational points on graph hypersurfaces
• Spanning forest polynomials and the transcendental weight of Feynman graphs