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?