Scattering Equations and Feynman Diagrams

TL;DR

This paper establishes a direct correspondence between Feynman diagrams and the scattering equation formalism, revealing a graph-theoretic link that extends to string theory integrands in scalar field theories.

Contribution

It introduces a novel graph-theoretic approach connecting Feynman diagrams with scattering equations and string theory integrands, generalizing to scalar theories with arbitrary interactions.

Findings

Matching between Feynman diagrams and scattering equation measures

Extension to scalar theories with p-point interactions

Link to string theory integrands through graph theory

Abstract

We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in $\phi^3$-theory. We also discuss the generalization to general scalar field theories with $\phi^p$ interactions, corresponding to polygonal graphs involving vertices of order $p$. Finally, we describe how the same graph-theoretic language can be used to provide the precise link between individual Feynman diagrams and string theory integrands.