Cubic Term in Higgs Boson

  • Thread starter the_pulp
  • Start date
  • #1
195
7

Main Question or Discussion Point

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!
 

Answers and Replies

  • #2
2,967
5
The higgs field is a complex field. How do you propose to include a cubic term and leave the Lagrangian u(1) invariant?
 
  • #3
195
7
Ok, thanks!
 
  • #4
453
15
  • #5
2,967
5
But that's after we had shifted the field by its VEV, if I'm not mistaken. That occurs even for:
[tex]
\mathcal{L}_{4} = \frac{\lambda}{2} \, \left( \vert \varphi \vert^2 - v^2 \right)^2
[/tex]
if you make the subst:
[tex]
\varphi = (v + \rho) \, e^{i \, \chi}
[/tex]
 
  • #6
453
15
Oh, yeah fair enough.
 

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