Cubic Term in Higgs Boson

1. Aug 27, 2012

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!

2. Aug 27, 2012

Dickfore

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

3. Aug 28, 2012

the_pulp

Ok, thanks!

4. Aug 29, 2012

kurros

5. Aug 29, 2012

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

6. Aug 29, 2012

kurros

Oh, yeah fair enough.