## Cubic Term in Higgs Boson

Why does the standard model have a higgs boson quadratic and a cuartic term but it does not have a cubic term? is there any problem if it happens to have a cubic term?

Thanks!
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 The higgs field is a complex field. How do you propose to include a cubic term and leave the Lagrangian u(1) invariant?
 Ok, thanks!

## Cubic Term in Higgs Boson

Apparently you CAN have a cubic term in there if you do some extra trickery that I don't really understand: http://arxiv.org/pdf/1208.5180.pdf
 But that's after we had shifted the field by its VEV, if I'm not mistaken. That occurs even for: $$\mathcal{L}_{4} = \frac{\lambda}{2} \, \left( \vert \varphi \vert^2 - v^2 \right)^2$$ if you make the subst: $$\varphi = (v + \rho) \, e^{i \, \chi}$$
 Oh, yeah fair enough.