The Diagrammatic Coaction and Cuts of the Double Box

TL;DR

This paper explores the diagrammatic coaction of the fully massless double box Feynman diagram, using differential equations and hypergeometric functions to formulate its cuts and analytic structure.

Contribution

It extends the diagrammatic coaction framework to the fully massless double box diagram using hypergeometric functions and homology techniques.

Findings

Formulated the coaction on cuts of the double box in closed form

Applied differential equations to analyze the diagrammatic coaction

Connected hypergeometric functions with the coaction structure

Abstract

The diagrammatic coaction encodes the analytic structure of Feynman integrals by mapping any given Feynman diagram into a tensor product of diagrams defined by contractions and cuts of the original diagram. Feynman integrals evaluate to generalized hypergeometric functions in dimensional regularization. Establishing the coaction on this type of functions has helped formulating and checking the diagrammatic coaction of certain two-loop integrals. In this talk we study its application on the fully massless double box diagram. We make use of differential equation techniques, which, together with the properties of homology and cohomology theory of the resulting hypergeometric functions, allow us to formulate the coaction on a range of cuts of the double box in closed form.