Can a W+ boson couple to a W- boson?

[c++guru]

Can a W+ boson couple to a W- boson? Say, if a Higgs decays into a W+ and a W-, what would be the Lagrangian density for this interaction? How would you evaluate such a first order diagram?

 

[Orodruin]

Such interactions appear in the Lagrangian after electroweak symmetry breaking and are generally proportional to the Higgs vev. The origin is the covariant derivative terms of the Higgs field. They would be treated in perturbation theory just as any other interaction term.

Note that the Higgs (125 GeV) is too light to decay into two on-shell Ws (80 GeV) and thus at least one of the Ws has to be off-shell.

 

[mfb]

In addition to the Higgs decay/production, you can also have those in ZWW, ZZWW, WWWW couplings.

 

[ChrisVer]

and the Lagrangian density of this interaction (W- W+ and others) can comes from the:
$\mathcal{L} = - \frac{1}{4} F_{\mu \nu}^b F^{\mu \nu}_b$
which for non-abelian gauge group theories will give you interactions of fields with themselves (not only the kinetic terms).
The interactions of bosons with the Higgs scalar come from the Higg's potential term which contains: $D_{\mu} \phi D^{\mu} \phi^*$, where the gauge boson fields exist in the covariant derivatives $D_{\mu}$ (as connections)