Other ways to break the Higgs symmetry group

In summary: VeV)?I don't know what "other stuff" you are talking about. Or how this relates to the original question.
  • #1
jtlz
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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?
 
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  • #2
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.
 
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  • #3
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).
 
  • #4
Vanadium 50 said:
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..
 
  • #5
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)?
 
  • #6
Orodruin said:
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?
 
  • #7
I don't know what "other stuff" you are talking about. Or how this relates to the original question.
 
  • #8
Vanadium 50 said:
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.
 
  • #9
By the way. In BSM. What other field has nonzero VeV at low energy (MeV scale)?
 
  • #10
Vanadium 50 said:
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
 
  • #11
jtlz said:
By the way. In BSM. What other field has nonzero VeV at low energy (MeV scale)?
That would depend on the BSM theory.
 
  • #12
Orodruin said:
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?
 
  • #13
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.
 
  • #14
Orodruin said:
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)??
 
  • #15
jtlz said:
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”.
 
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  • #16
Orodruin said:
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.
 
  • #17
Orodruin said:
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.
 

Related to Other ways to break the Higgs symmetry group

1. What is the Higgs symmetry group?

The Higgs symmetry group, also known as the Higgs mechanism, is a theoretical concept in particle physics that explains the origin of mass in certain elementary particles. It involves the spontaneous breaking of a fundamental symmetry in the universe, known as the electroweak symmetry, which gives rise to the Higgs field.

2. How does the Higgs symmetry group contribute to our understanding of the universe?

The Higgs symmetry group is an essential component of the Standard Model of particle physics, which is the most comprehensive theory we have to describe the fundamental particles and forces in the universe. It helps us understand how particles acquire mass and how the forces between them interact.

3. What are some ways to break the Higgs symmetry group?

One way is through the use of a Higgs field, which is a quantum field that permeates the universe and interacts with certain particles to give them mass. Another way is through the discovery of new particles or interactions that could alter the symmetry of the Higgs field, leading to a breakdown of the symmetry group.

4. Are there any experimental methods for studying other ways to break the Higgs symmetry group?

Yes, there are many ongoing experimental efforts to study the Higgs symmetry group and its potential breaking. These include experiments at particle accelerators such as the Large Hadron Collider, as well as astrophysical observations and theoretical calculations.

5. Why is it important to study other ways to break the Higgs symmetry group?

Studying other ways to break the Higgs symmetry group can help us gain a deeper understanding of the fundamental nature of the universe. It could also potentially lead to the discovery of new particles or interactions that could revolutionize our understanding of physics and the universe as a whole.

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