Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions

TL;DR

This paper explicitly connects off-shell cubic interactions with on-shell three-point amplitudes in four dimensions, clarifying their relationship and deriving covariant forms of parity-odd vertices.

Contribution

It provides the first explicit link between off-shell cubic interactions and on-shell three-point amplitudes, including covariant forms of parity-odd vertices.

Findings

Established the relation between cubic interactions and three-point amplitudes

Derived covariant forms of all parity-odd massless vertices

Clarified differences and similarities in their constructions

Abstract

We make an explicit link between the cubic interactions of off-shell fields and the on-shell three-point amplitudes in four dimensions. Both the cubic interactions and the on-shell three-point amplitudes had been independently classified in the literature, but their relation has not been made explicit. The aim of this note is to provide such a relation and discuss similarities and differences of their constructions. For the completeness of our analysis, we also derive the covariant form of all parity-odd massless vertices.