Other ways to break the Higgs symmetry group

[jtlz]

Our standard model breaks the Higgs Su(2) electroweak symmetry via the Higgs mechanism.

In official beyond the standard models. May I know the different lists of models where the Higgs field can be part of larger symmetry group like SU(10) and different ways to break it?

 

[Orodruin]

I do not think you can find a complete list of posibilities. What you need is a scalar transforming under a representation of the unified group that, when the larger symmetry group is broken, contains an irrep transforming like the SM Higgs under the SM gauge groups, i.e., colourless SU(2) doublet with appropriate hypercharge.

 

[Vanadium 50]

I believe there is an infinite number of such groups: SU(n) breaks to SU(n - 2) x SU(2) x U(1). So, for example, SU(8) will break to SU(3) x SU(3) x SU(2) x U(1).

 

[Haelfix]

I believe there is an infinite number of such groups: SU(n) breaks to SU(n - 2) x SU(2) x U(1). So, for example, SU(8) will break to SU(3) x SU(3) x SU(2) x U(1).

Yes, there should be an infinite class as currently stated. Of course one could (and should) place additional restrictions on the nature of the group on physical grounds. For instance that there exists suitable complex (chiral) representations, and that restricts it to E6, SO(4n+2) and SU(n). From there you could place additional constraints, like for instance the absence of anomalies or say asymptotic freedom..

 

[jtlz]

The standard Higgs field was tasked to give masses to particles..

So it can be confusing when you try to attribute the Higgs field to do other stuff besides giving mass.. maybe there should be other terms for it?

What exact properties of the Higgs field which made it versatile enough to do other stuff or general vacuum housekeeping (besides giving mass)?

 

[jtlz]

I do not think you can find a complete list of posibilities. What you need is a scalar transforming under a representation of the unified group that, when the larger symmetry group is broken, contains an irrep transforming like the SM Higgs under the SM gauge groups, i.e., colourless SU(2) doublet with appropriate hypercharge.

I need an example.
Mathematically.. I know one can't introduce the mass-energy terms in the wave equation because gauge invariance, symmetry with respect to local U(1) and SU(2) transformations is destroyed. Hence the Higgs field were introduced as counter terms or compensating terms when one added the mass terms to the equations so it reflects a hidden gauge symmetry. This is standard higgs physics.

Now when one introduces GUT.. the higgs complex doublet SU(2) can still be found after the larger group symmetry breaks. No problem about this.

But there seems to be this separate concept where instead of GUT.. the higgs field itself has higher symmetry group like SU(10). Can anyone explain this portion?

 

[Vanadium 50]

I don't know what "other stuff" you are talking about. Or how this relates to the original question.

 

[jtlz]

I don't know what "other stuff" you are talking about. Or how this relates to the original question.

We sent our replies at same time so don't miss my reply to Orodruin. Some beyond standard models are using the superconductor part of the Higgs field to do other tasks besides the standard idea of the higgs field as compensating terms to retain the gauge symmetry when one introduces the mass terms. I'd like a list of such BSM ideas of using the higgs field for its superconducting properties.

 

[jtlz]

By the way. In BSM. What other field has nonzero VeV at low energy (MeV scale)?

 

[jtlz]

I don't know what "other stuff" you are talking about. Or how this relates to the original question.

The "other stuff" seem to be Abelian Higgs model versus the non-Abelian Higgs Model. There seems to be many Higgs model. Which of them has higher than SU(2) symmetry group?

https://arxiv.org/pdf/hep-ph/9504278.pdf

 

[Orodruin]

By the way. In BSM. What other field has nonzero VeV at low energy (MeV scale)?

That would depend on the BSM theory.

 

[jtlz]

That would depend on the BSM theory.

Can you give example of BSM where other fields besides the Higgs field has nonzero VeV at low energy?

 

[Orodruin]

Essentially any theory with a larger symmetry group than the SM one. The typical thing is to break it down to the SM groups through a vev of a scalar field in some representation.

 

[jtlz]

Essentially any theory with a larger symmetry group than the SM one. The typical thing is to break it down to the SM groups through a vev of a scalar field in some representation.

But any theory with a larger symmetry group than the SM one will have very high energy (GUT scale).. here the vev is zero.

What actual example of larger symmetry group that is low energy (that can have nonzero vev)??

 

[Orodruin]

But any theory with a larger symmetry group than the SM one will have very high energy (GUT scale).. here the vev is zero.

No this is wrong. The point with a higher symmetry group that is broken at low energies is exactly that. This is true of the SM gauge group as well. At low energies the remaining symmetry of the electroweak group is the EM U(1). In the same way you must break the higher symmetry before you get to low energies. A theory in itself does not ”have an energy”.

 

[jtlz]

No this is wrong. The point with a higher symmetry group that is broken at low energies is exactly that. This is true of the SM gauge group as well. At low energies the remaining symmetry of the electroweak group is the EM U(1). In the same way you must break the higher symmetry before you get to low energies. A theory in itself does not ”have an energy”.

What? Let's take an example. Before the SU(2) x U(1) was broken, the electroweak is above 100GeV and has zero vev. After it was broken, we have separate weak and EM U(1). So when a force is in higher symmetry group, the force has higher energy scale. I was asking what example of another force/field besides the higgs field whose higher symmetry group was broken and has nonzero vev.

You said "Essentially any theory with a larger symmetry group than the SM one".. but again when a force has higher symmetry group than the SM one, for example the GUT field has higher symmetry and has zero vev. Please use actual example. Thanks.

 

[jtlz]

No this is wrong. The point with a higher symmetry group that is broken at low energies is exactly that. This is true of the SM gauge group as well. At low energies the remaining symmetry of the electroweak group is the EM U(1). In the same way you must break the higher symmetry before you get to low energies. A theory in itself does not ”have an energy”.

I got your point. I was asking what exact field of that BSM larger symmetry group can have nonzero vev at low energy.. besides the Higgs field.. I need actual example of such BSM model.