Higgs Boson and the Missing Cubic Term in the Standard Model

[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]

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

 

[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.