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For the bosons $g$, $\gamma$, $Z$, $W$, $H$ in the standard model, what are all of the possible direct interactions between them?

Some of the interactions I can think of are $H \rightarrow ZZ$, $HH \rightarrow WW$, $HH \rightarrow ZZ$ and $g \rightarrow gg$.

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    $\begingroup$ For that you would need to consider all the interaction terms in the standard model Lagrangian which involve the bosonic fields. $\endgroup$
    – twisted manifold
    Jan 15, 2020 at 0:50

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Go to the gauge and Higgs kinetic & potential terms of the EW model and read off the vertices: The fun should be the actual strengths of the couplings, which I should not spoil by revealing it to you. (To check your work, go to Appendix B of Li & Cheng).

  • Gluons only couple to themselves, among the bosons, so you have cubic and quartic terms for them--renormalizability will allow for nothing else.

So, in the remainder EW sector, you have

  • Cubics: γWW; ZWW; HWW; HZZ; HHH;
  • Quartics: γγWW; WWZZ; HHHH; ZZZZ; HHZZ; HHWW; WWWW; ZHWW; γHWW; γZWW .

Reassure yourself you appreciate which terms each comes from. If it looked haphazard, it is only because I skipped the coupling strengths, which reveal the method in the model's madness.

The most interesting ones, in my view, come from the covariant completions of the Higgs doublet "kinetic" terms.

  • Extra credit: Can you intuit why there are no γγZ, γZZ (duh!), ZZZ, ZHH and ZHHH terms?
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