General partial-wave expansion for arbitrary tree-level topologies

Establish a general partial-wave expansion for arbitrary tree-level Feynman-diagram topologies, beyond the half-ladder and Mercedes-Benz diagrams, including a general angular parametrization and a classification of the special functions required to resolve all internal spins and vertex structures.

Background

The main construction in the paper applies to half-ladder diagrams, while the authors also briefly examine the six-point Mercedes-Benz topology. They suggest that a general tree-level diagram should admit a basis obtained by imposing angular-momentum eigenvalue equations in the rest frames of its internal particles.

The unresolved part is whether such a universal object exists and, if so, how to formulate its angular variables and special functions for arbitrary topologies. This would extend the formalism from the specific half-ladder geometry to general tree-level scattering diagrams.