# Cubic Term in Higgs Boson

the_pulp
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!

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

the_pulp
Ok, thanks!

kurros
Dickfore
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:
$$\varphi = (v + \rho) \, e^{i \, \chi}$$

kurros
Oh, yeah fair enough.