Kite diagram through Symmetries of Feynman Integrals

TL;DR

This paper applies the Symmetries of Feynman Integrals (SFI) method to analyze the kite diagram, revealing new symmetries and reduction techniques that simplify complex two-loop integrals with arbitrary masses.

Contribution

The paper extends the SFI method to the kite diagram, identifying a parameter space locus where integrals simplify significantly, generalizing previous massless results.

Findings

Identified a symmetry group for the kite diagram.

Reduced complex integrals to simpler forms on a specific parameter locus.

Generalized massless case results to arbitrary masses.

Abstract

The Symmetries of Feynman Integrals (SFI) is a method for evaluating Feynman Integrals which exposes a novel continuous group associated with the diagram which depends only on its topology and acts on its parameters. Using this method we study the kite diagram, a two-loop diagram with two external legs, with arbitrary masses and spacetime dimension. Generically, this method reduces a Feynman integral into a line integral over simpler diagrams. We identify a locus in parameter space where the integral further reduces to a mere linear combination of simpler diagrams, thereby maximally generalizing the known massless case.