Other ways to break the Higgs symmetry group

  • I
  • Thread starter jtlz
  • Start date
  • #1
jtlz
107
4
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?
 

Answers and Replies

  • #2
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
20,004
10,650
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.
 
  • #3
Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
29,604
15,059
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
Haelfix
Science Advisor
1,964
232
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
jtlz
107
4
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
jtlz
107
4
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
Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
29,604
15,059
I don't know what "other stuff" you are talking about. Or how this relates to the original question.
 
  • #8
jtlz
107
4
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
jtlz
107
4
By the way. In BSM. What other field has nonzero VeV at low energy (MeV scale)?
 
  • #10
jtlz
107
4
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
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
20,004
10,650
By the way. In BSM. What other field has nonzero VeV at low energy (MeV scale)?
That would depend on the BSM theory.
 
  • #12
jtlz
107
4
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
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
20,004
10,650
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
jtlz
107
4
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
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
20,004
10,650
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”.
 
  • #16
jtlz
107
4
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
jtlz
107
4
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.
 

Suggested for: Other ways to break the Higgs symmetry group

Replies
3
Views
612
Replies
8
Views
719
Replies
3
Views
752
Replies
5
Views
473
Replies
16
Views
747
Replies
2
Views
663
Replies
6
Views
655
  • Last Post
Replies
1
Views
810
  • Last Post
Replies
3
Views
705
  • Last Post
Replies
5
Views
1K
Top