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

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. – redhood Jan 15 at 0:50

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?