How can the Higgs boson be detected if its VEV costs no energy?

[DrDu]

In what sense is the higgs particle expected to be discovered at the LHC?
I mean, the Higgs field has a non-vanishing vacuum expectation value, so it costs no energy to absorb or emit a higgs boson.Hence what is meant when saying that the expected mass is about 126 GeV?
I suppose one is looking for some excited state or something?

 

[fzero]

It's not an excited state. The physical Higgs field is the degree of freedom as seen in the classical vacuum state that breaks the electroweak symmetry. The $SU(2)$ doublet $H$ is an expansion around the false vacuum at $\langle H \rangle =0$. The true vacuum is an expansion around $\langle H^0\rangle =\upsilon$, for which we write

$$H = \begin{pmatrix} H^+ \\ \upsilon + h \end{pmatrix}.$$

$H^\pm$ are the degree of freedom that gets "eaten" to generate mass for the EW gauge bosons, while $h$ is the massive Higgs scalar being investigated. The mass of $h$ is set in terms of the parameters of the Higgs potential once you expand using the parametrization above.

 

[DrDu]

Ok, I see. Thank you!

 

[Bill_K]

In other words, yes the Higgs boson is an excited state of the Higgs field.