Past exam of the particle and nuclear physics course of the University of Cambridge / 2022 / Section A / 3 / c / Solution

There are five vertex types:

The quartic terms arise from the square of the quadratic-field piece of the non-Abelian gauge field strength. Every electroweak quartic gauge boson self-interaction contains a $W^{+}{W}^{-}$ pair. The absence of a fundamental purely neutral quartic vertex does not forbid amplitudes such as light-by-light scattering: those can be generated by loop diagrams, rather than by a single fundamental interaction vertex.