= Solution
There are \b[five vertex types]:
$$
\boxed{gggg,\quad W^+W^-W^+W^-,\quad
W^+W^-ZZ,\quad W^+W^-Z\gamma,\quad W^+W^-\gamma\gamma.}
$$
\Image[/past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2022-gauge-quartic-vertices.png]
{title=The five fundamental quartic gauge-boson 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>.
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