What are all the possible direct interactions between bosons in Standard Model?

Question

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 $g \rightarrow gg$.

For that you would need to consider all the interaction terms in the standard model Lagrangian which involve the bosonic fields. — twisted manifold, Jan 15 '20 at 00:50

Cosmas Zachos · Accepted Answer · 2020-01-16T17:55:53.853

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?

What are all the possible direct interactions between bosons in Standard Model?

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