Electroweak spontaneous symmetry breaking

[Carlos L. Janer]

This is a question that I have tried to pose several times without any success but, anyway, I would like to try again for the very last time.

Asume for a moment that EW-SSB (electroweak spontaneous symmetry breaking) actually happened in our early universe. Imagine that our Standard Model of particle physics is the way it is NOW just because the temperature dropped below a critical value. I ASSUME (and I may very well be wrong) that, above this temperature (critical T), in an earlier universe, the relevant charges should be the weak isospin, the weak hipercharge and color. I also think that the isospinor VEV should be 0 and, therefore, all leptons, quarks and interaction bosons should be massless.

I also ASSUME that we can can make quantitative predictions using the more symmetric model of particle physics at
temperatures just above critical T (just before the EW-SSB phase transition took place), although I am much less confident about this assumption.

I would be very grateful if someone could help me.

 

[king vitamin]

This all seems right. I should mention that the "mass" of a particle is technically not temperature dependent (it is defined at zero temperature), but it's true that you can write an effective theory at a given temperature and the "mass" calculated in that theory goes to zero at high temperature, so it's not too bad of a language.

What is your question?

 

[Carlos L. Janer]

This all seems right. I should mention that the "mass" of a particle is technically not temperature dependent (it is defined at zero temperature), but it's true that you can write an effective theory at a given temperature and the "mass" calculated in that theory goes to zero at high temperature, so it's not too bad of a language.

What is your question?

OK, first of all thanks for the post. I have several questions in mind:

1.- How would the universe be expanding now if no EW-SSB had taken place?

2.- Is it conceivable that the phase transtion (PHT) were first order, so that two different global minima could coexist?

3.- Imagine that we live in an universe where the Higgs scalar field has developped two local minima, one with a 0 VEV and another one with a non-zero VEV. These local minima extend through the whole space-time and some particles have been trapped in the first one and some others in the second one. I know this sounds crazy but imagine, for a second, that it had happened.

¿Would these two sets of particles interact between each other?

 

[Orodruin]

How would the universe be expanding now if no EW-SSB had taken place?

This is a rather weird question to answer because it does not really say anything about your presumptions. In the SM, electroweak symmetry breaks and in order to answer this question appropriately you will therefore have to specify what model you would put in its place. Why would EWSB not take place in your universe?

Is it conceivable that the phase transtion (PHT) were first order, so that two different global minima could coexist?

What do you mean by "coexist"? You cannot have a field that has two different values in the same point. You could have a field that takes different values in different points. In that case, the regions of the true vacuum would start expanding essentially at the speed of light. For really small regions of true vacuum, the expansion could be overcome by the surface tension of the region separating the vacua. The region will then contract back to the false vacuum.

Imagine that we live in an universe where the Higgs scalar field has developped two local minima, one with a 0 VEV and another one with a non-zero VEV. These local minima extend through the whole space-time and some particles have been trapped in the first one and some others in the second one. I know this sounds crazy but imagine, for a second, that it had happened.

Again, you seem to misunderstand what the Higgs vacuum is. The Higgs field is a single field and cannot take different vevs in the same point. Other fields are not "trapped" in this vev, they are interacting with it, giving them an effective mass.

 

[Carlos L. Janer]

What do you mean by "coexist"? You cannot have a field that has two different values in the same point. You could have a field that takes different values in different points. In that case, the regions of the true vacuum would start expanding essentially at the speed of light. For really small regions of true vacuum, the expansion could be overcome by the surface tension of the region separating the vacua. The region will then contract back to the false vacuum.

Thank you for your answer. In condensed matter physics you do have two different phases with different physical properties that coexist in first order phase transitions because the free energy has two different global minima (everywhere). The difference between the two phases disappears only when you change the conditions to reach the critical point. That is exactly what I am asking: is such a situation conceivable in particle physics? You are clearly telling me that it is not.

Again, you seem to misunderstand what the Higgs vacuum is. The Higgs field is a single field and cannot take different vevs in the same point. Other fields are not "trapped" in this vev, they are interacting with it, giving them an effective mass.

OK, I understand what you mean. However, the field seems to have a whole continuum of equivalent minima VEVs and, for reasons that I do not understand, the universe seems to have picked up exactly the same one everywhere because we do not perceive any domain walls. That is literally killing me. Where am I not thinking straight?

 

[king vitamin]

I don't know how to answer your question about expansion, because the relation between QFT and cosmological expansion is not well-understood.

2.- Is it conceivable that the phase transtion (PHT) were first order, so that two different global minima could coexist?

Yes, in fact cosmologists are fairly sure that the electroweak phase transition was first-order (but that's not totally conclusive). The nature of the phase transition depends both on the temperature and the value of the T=0 the Higgs mass, and there is a point in the phase diagram with a critical point in the 3D Ising universality class, but most people estimate that the first-order scenario is more probable.

However, the field seems to have a whole continuum of equivalent minima VEVs and, for reason that I do not understand, the universe seems to have picked up exactly the same one everywhere because we do not perceive any domain walls. That is literally killing me.

This is a very good question, one that I have asked before. The Higgs is in an SU(2) doublet so you can think of it living on a three-sphere. Then you classify possible topological defects by homotopy groups (hopefully you're somewhat familiar with this analysis). This automatically means you can have no line defects, no vortices, and no monopoles. But you can consider textures where the Higgs VEV reaches a constant at spatial infinity, but undergoes a twist in the interior (I'd call this a skyrmion). But from the TASI lectures of Carrol and Trodden:

"Thus, the electroweak model does not lead to walls, strings, or monopoles. It does lead to what we called "texture," which deserves further comment. In a theory where pi3(M) is nontrivial but the other groups vanish, we can always map three-dimensional space smoothly into the vacuum manifold; there will not be a defect where the field climbs out of M. However, if we consider field configurations which approach a unique value at spatial infinity, they will fall into homotopy classes characterized by elements of pi3(M); configurations with nonzero winding will be textures. If the symmetry is global, such configurations will necessarily contain gradient energies from the scalar fields. The energy perturbations caused by global textures were, along with cosmic strings, formerly popular as a possible origin of structure formation in the universe [124, 125]; the predictions of these theories are inconsistent with the sharp acoustic peaks observed in the CMB, so such models are no longer considered viable."

I'm not totally sure if this rules out skyrmions in general, or merely as explanations for cosmological structure formation.

 

[Carlos L. Janer]

This is a very good question, one that I have asked before. The Higgs is in an SU(2) doublet so you can think of it living on a three-sphere. Then you classify possible topological defects by homotopy groups (hopefully you're somewhat familiar with this analysis). This automatically means you can have no line defects, no vortices, and no monopoles. But you can consider textures where the Higgs VEV reaches a constant at spatial infinity, but undergoes a twist in the interior (I'd call this a skyrmion). But from the TASI lectures of Carrol and Trodden:

"Thus, the electroweak model does not lead to walls, strings, or monopoles. It does lead to what we called "texture," which deserves further comment. In a theory where pi3(M) is nontrivial but the other groups vanish, we can always map three-dimensional space smoothly into the vacuum manifold; there will not be a defect where the field climbs out of M. However, if we consider field configurations which approach a unique value at spatial infinity, they will fall into homotopy classes characterized by elements of pi3(M); configurations with nonzero winding will be textures. If the symmetry is global, such configurations will necessarily contain gradient energies from the scalar fields. The energy perturbations caused by global textures were, along with cosmic strings, formerly popular as a possible origin of structure formation in the universe [124, 125]; the predictions of these theories are inconsistent with the sharp acoustic peaks observed in the CMB, so such models are no longer considered viable."

I'm not totally sure if this rules out skyrmions in general, or merely as explanations for cosmological structure formation.

Thank you very much for your answer. I cannot say that I fully understand it, but I will in due time. I am not yet familiar with topological QFT.

 

[Carlos L. Janer]

I don't know how to answer your question about expansion, because the relation between QFT and cosmological expansion is not well-understood.

I was kind of hoping that there could be some sort of repulsive interaction among the elementary particles, but it is just a hunch based on nothing, really. Not worth thinking much about it.

 

[Vanadium 50]

That is literally killing me.

I don't think that is correct.

I was kind of hoping

This is a personal theory. As I said in another context a mere 21 hours ago, "you're creating your own mental model of how the universe works, and are unhappy that nature isn't following that. There's really no reason why it should."

 

[Carlos L. Janer]

This is a personal theory. As I said in another context a mere 21 hours ago, "you're creating your own mental model of how the universe works, and are unhappy that nature isn't following that. There's really no reason why it should."

Do you think a hunch is a bad thing to have? How do you work, then? I am not unhappy about anything, on the contrary, I am happy that I can let go of an idea that has been bugging for a while and, moreover, I feel gratitude towards the persons that have helped me to reach that conclusion. What is wrong with it?

This is clearly off-topic, but so is your remark and you are supposed to play the role of an "exemplary figure".

 

[Vanadium 50]

Oh, for heaven's sake. It's not my fault that you posted what you did, and being an "exemplary figure" does not prohibit me from calling out nonsense when I see it. "Exemplary figure" my tushy.

 

[jim mcnamara]

This thread became derailed. Closing now.