Triangle diagram, Distance Geometry and Symmetries of Feynman Integrals

Abstract: We study the most general triangle diagram through the Symmetries of Feynman Integrals (SFI) approach. The SFI equation system is obtained and presented in a simple basis. The system is solved providing a novel derivation of an essentially known expression. We stress a description of the underlying geometry in terms of the Distance Geometry of a tetrahedron discussed by Davydychev-Delbourgo [1], a tetrahedron which is the dual on-shell diagram. In addition, the singular locus is identified and the diagram's value on the locus's two components is expressed as a linear combination of descendant bubble diagrams. The massless triangle and the associated magic connection are revisited.