Higgs Field with SB but without Higgs Boson?

[arivero]

Hi,

I was searching for some example of a theory where all the components of the higgs field are "eaten" by the vector gauge fields and no Higgs boson is left. I have just checked Georgi-Glashow SO(3) --> U(1), but they use a triplet Higgs so at the end again a Higgs Boson does appear.

Is it a generic result that you always will have a Higgs Boson?

 

[Vanadium 50]

If you have a massless photon you will.

 

[arivero]

If you have a massless photon you will.

So, is it possible, say, to produce a completely broken version of the Georgi-Glashow model, without photon but then also without Higgs Boson?

And realy, I am not sure of the connection between "massless photon" and "higgs boson". The number of Higgs Bosons getting mass after symmetry breaking is not equal to the number of unbroken symmetries, isn't it? For instance I could break with a two-doublets higgs field, and I would get five massive bosons.

 

[Vanadium 50]

You need to insert complete gauge multiplets. If you leave a "space" for the photon, you will have a leftover degree of freedom. You can always have more.

 

[arivero]

You need to insert complete gauge multiplets. If you leave a "space" for the photon, you will have a leftover degree of freedom. You can always have more.

Yeah, I see it in the standard model. But 1) is is true for any breaing G ---> U(1), for any gauge group G, that we always will have a leftover? and 2) are there "leftovers" if we completely break the gauge group?

 

[ChrisVer]

I think you can if you procceed in breaking the (since you are working with SU[N] ) remaining U(1) too...

 

[arivero]

I should try :-) Davelock (not sure if this is his nick here in PF) asked me some days ago about role for the third mass in the SU(2)xU(1) breaking. I mean, when the vacuum takes a value <v>, we define a coupling g0 and a angle of Weinberg th, so that mass of Z is g0 v / 2, and mass of W is g0 cos th v /2, and then it is a very obvious thing to ask if the quantity g0 sin th v/2 could have a physical incarnation too.

 

[ChrisVer]

I am not sure...but the sinθ_w is as much meaningful as the cosθ_w... and the definition of Weinberg's angle comes from the ratio M_w over M_z... So what's the "physical" meaning of that?

 

[arivero]

I am not sure...but the sinθ_w is as much meaningful as the cosθ_w... and the definition of Weinberg's angle comes from the ratio M_w over M_z... So what's the "physical" meaning of that?

Well, not exactly. The theoretical success of GWS model is its prediction that M_w over M_z is equal to the angle. The definition of the angle is really that it produces separately the constants of SU(2) and U(1) from an unique constant "g0". If you add other breaking mechanism beyond doublet you can still recover the low energy phenomenology but the prediction of M_w over M_z changes. The "rho parameter" and all such stuff... there was usually a pretty detailed description in the Particle Data Group reviews.