# What is q (the charge) in higgs mechanism?

1. Aug 2, 2012

### ariel97

what is "q" (the charge) in higgs mechanism?

hi,

does anybody know what kind of charge the "q" stand for in the higgs mechanism?

I mean the mechanism between the weak force mediators: W & Z, and the higgs boson, which leads to them acquiring mass.

I've learnt about it from the text book by David Griffiths "Introduction to Elementary Particles". There in section 10.9 (2nd addition) or 11.9 (1st addition) he introduces the "q" along with the covariant derivative (first stage by Weyl to transform the Lagrangian into an invariant under local phase transformasions), which leads me to consider it being the charge of the weak force, as was the case with implemnting Weyl's procedure for QED & for QCD. However, in those cases the Interaction was electromagneic or strong respectively, while in the Higgs Mechanism the interaction is of the kind needed to grant mass to the weak force mediators, and NOT a weak force interaction at all.

That's why I have a huge problem figuring out what "q" really stands for.

thanks in advance to anyone who might help, and thanks for spendind the time reading my question.

Shalom,
A.

2. Aug 2, 2012

### Bill_K

Re: what is "q" (the charge) in higgs mechanism?

ariel97, I don't know what Griffiths calls q, but the masses of W and Z are MW = ½vg, MZ = ½v√(g2 + g'2) where v is the vacuum value of the Higgs field, v = 246 GeV, and g, g' are the coupling constants that appear in the covariant derivative: ∂μ + ig(½τ·Wμ) - ig'(½Bμ)

Last edited: Aug 2, 2012
3. Aug 2, 2012

### muppet

Re: what is "q" (the charge) in higgs mechanism?

Hi ariel97,

What's happening here is that he's presenting the "Higgs mechanism" not as it appears in the Standard model, but in a simplified model- a complex scalar field with a U(1) gauge symmetry (i.e. the freedom to make local phase redefinitions of the field). This is the same gauge symmetry as quantum electrodynamics, so the model- without symmetry breaking- is sometimes called "scalar QED". q here would correspond to the electric charge of the field in this model, and the gauge boson that gains a mass would be a "photon".

In the electroweak sector of the standard model, the real-world Higgs breaks a more complicated gauge symmetry- SU(2)xU(1), where the U(1) isn't the electromagnetism gauge group, but its charge is instead called "hypercharge". The real Higgs has a hypercharge, and is complex doublet of the SU(2) symmetry, but has no electric charge, which is why the real photon is still massless; the U(1) of electromagnetism is a subgroup of the SU(2)xU(1) that remains unbroken.

I don't know of a better introductory explanation of all of this than in these lecture notes:
http://hep.ph.liv.ac.uk/~tara/lectures/sm_signer.ps

Hope that helps.

4. Aug 5, 2012

### ariel97

Re: what is "q" (the charge) in higgs mechanism?

thank you both so much for replying

muppet: my computer doesn't recognize the file type, and doesn't know which program to use to open it. I don't recognize the ending ".ps" either. If u can tell me how to open it I'd appreciate it.

I know the author simplifies the theory, but yet I think we can expect the simplified model to be consistent with the actuall generalization of the theory in the standard model. It can't contradict in any way the broader theory, can it? so I'm trying to figure out what in accordance with the parallelism, what role is played by "q", following his on stages.

Bill_K: thank you, that's my reason for suspecting it might be the weak force charge, as it also appears in the mass term for the mediators of the weak force, in this theory, and the coupling constants are related to the charge relavant to the interaction it is used to describe. so thanks again.

5. Aug 5, 2012