Electroweak spontaneous symmetry breaking is much harder for me to understand than the gluon-quark plasma phase transition. In the latter the physical laws remain the same and gluons and quarks just bind together below a temperature threshold because the free energy describing its thermodynamic properties presents a new single global minimum.

However, at the EWSSB the fundamental physical laws describing particle interactions (our Standard Model of particle physics) change at that phase transition. I used to think that it was just an artifact to explain the EW interactions but since the Higgs boson has been discovered and a systematic exploration of the Higgs sector is taking place at CERN, EWSSB needs to be taken seriously.

Now I wonder if there is more to the EWSSB than meets the eye. More precisely, could dark matter and dark energy be explained by this phase transition?

1.- I think that it is reasonable to consider that the electroweak spontaneous symmetry breaking was a true thermodynamic phase transition.

2.- I also think that it is also reasonable to assume that it was a "first order phase transition".

3.- I think it is also posible/probable that the isospinor scalar field (Higgs field), could have presented two different global minima, one with a zero VEV and another with a nonzero VEV when the phase transition began. Usually, first order phase transitions ocurr because a new global minimum of the free energy of the thermodynamical system appears in addition to the already existing one. These two global minima allow two different phases with different physical properties to coexist, at least for a while. As far as I know, as long as the thermodynamical system undergoing the first order phase transitions, presents two different free energy global minima, the two phases coexist everywhere, at least in the thermodynamical limit.

Nucleation and domain expansion start only later (if they do), when one of 
the minima becomes local and the remaining one stays global. The phase 
belonging to the global minimum nucleates and expands at the expenses of the 
one belonging to the local minima. The picture can become more complicated 
if the transition process from being a global minimum to becoming a local  
one is very fast (water supercooling would be an example).

4.- If the Higgs field still had the two global minima at present times (or a global one and a supercooled local one separated by a large free energy barrier), I think that we would have two different sets of elementary particles with different physical properties. The true gauge charges and mass values in these two sets of particles would be:

a) Color, weak isospin, weak hypercharge and zero masses. (Higgs field 

b) Color, weak isospin and EM charge and non-zero massess. (Higgs field 
VEV > 0).

5.- If we had the two sets of elementary particles, their interactions could be very, very weak (it is just an assumption). I take for granted that they would, at least, interact gravitationally.

6.- If all this were possible, could this explain dark matter and/or dark energy?

For example, the long-range weak forces (in the massless sector) between 
particles with the same Y_w and I^3_w could lead to large-scale repulsive 
effects (see Quantum Field Theory 2nd Edition by Lewis E. Ryder, page 306 
and references therein) that could, perhaps, explain the accelerated 
expansion of the universe.

I apologyze in advance for posting this question in such an odd way. However, it is the only way that I have been able to express what I had in mind.

I also realize that it is paradoxical (I suppose that many will find it laughable) thinking about two sets of elementary particles abiding different physical laws, so, please do not be too harsh with me. I can follow the maths of EWSSB but when I think about the physical process (fundamental physical laws that, suddenly change/evolve? gradually change/evolve?) I feel that either there is something that I am definitely not getting right or the dynamical process of symmetry breaking is very poorly understood.

I have written the sixth point, posing a single question and rephrased everything else because, to be honest, this is the reason why I started thinking about the EW-SSB. I have been wondering for a while if a massless Higgs Standard Model that coexisted with our Standard Model could produce a set of "almost non interacting particles" that could explain the dark components of the Lambda-CDM cosmological model.

Common sense tells me that the answer is no. I am not naive enough to think that all this is likely to be right. But it should be possible (maybe even easy) to check that the whole idea is wrong because I assume that the physics of a zero mass Higgs Standard Model can be either worked out or, even better, perhaps someone has already done it. Since I have not been able to find that information and I am unable to work it out by myself, I decided to post this question.

If such a model (zero mass Higgs Standard Model) has already been developed, please, do let me know. A link would be MUCH appreciated.

  • $\begingroup$ People will wonder what you mean by "coexist". From physicsforums.com/threads/… it seems like you mean that they would exist in adjacent spatial domains? $\endgroup$ – Mitchell Porter Oct 18 '17 at 18:39
  • $\begingroup$ @MitchellPorter Yes, the term "phase coexistence" usually refers to adjacent spatial domains. $\endgroup$ – tparker Oct 18 '17 at 18:43
  • $\begingroup$ Closely related, possible duplicate: physics.stackexchange.com/q/343532 $\endgroup$ – tparker Oct 18 '17 at 18:43
  • $\begingroup$ Yes, the two questions are very similar indeed. $\endgroup$ – Carlos L. Janer Oct 18 '17 at 18:47
  • $\begingroup$ I am not even sure that "phase coexistence" must refer to adjacent spatial domains. The free energy function is nonanalitic in phase transitions. At any given place (in a container with boiling water) you may find either water or vapor droplets. So I was wonderig if the two sets of particles could coexist in space-time while the transition was taking place. What I'd like to know if this would be possible and if it were, would there be any kind of interaction between the two sets of particles? $\endgroup$ – Carlos L. Janer Oct 18 '17 at 19:05

Lattice calculations carried out in the 90's have shown pretty definitively that the electroweak phase transition is a smooth crossover (it is NOT a sharp phase transition), see, for example https://arxiv.org/abs/hep-lat/9809045 . This was known even before the Higgs was discovered, because the Higgs mass corresponding to the second order endpoint of the first order transition at low $m_H$ is $m_H(crit)\simeq 75$ GeV, below the lower bound for $m_H$ extracted from precision electroweak data at LEP. Now, of course, we know that there does indeed appear to be only a single Higgs with $m_H\simeq 125$ GeV. Extended models with extra Higgses that give a first order transition may not be totally dead, but they are getting very convoluted.

I should mention why people care about this: In order for electroweak baryogenesis to work we need to satisfy the Sakharov criteria, and one of them is that we need an non-equilibrium process. In a first order transition we can have super cooling and bubble nucleation, but in a smooth crossover the system is never very far from equilibrium. So the fact that the transition is smooth was one of the facts that killed EW baryogenesis.

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  • $\begingroup$ Do you know if the free energy density is smooth but not analytic at the transition, as with the Kosterlitz-Thouless transition, or whether it actually remains analytic and there is no transition at all? I don't see how a system above and below the critical temperatures could possibly be in the same phase, as they have different symmetry groups. $\endgroup$ – tparker Oct 19 '17 at 2:42
  • $\begingroup$ Doesn't, say, the mass of the electron (or almost any other particle) count as an order parameter which changes non-analytically from identically zero above the critical temperature to nonzero below it? $\endgroup$ – tparker Oct 19 '17 at 2:45
  • $\begingroup$ You are only "breaking" gauge symmetries, which cannot be broken (can only be Higgsed), and have no local order parameters. $\endgroup$ – Thomas Oct 19 '17 at 2:52
  • $\begingroup$ What about the massive particle masses? They may not be an "order parameter" in the traditional sense, but they're a locally measurable quantity which tells you which phase you're in. $\endgroup$ – tparker Oct 19 '17 at 2:56
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    $\begingroup$ This means, for example, that the electron has a screening mass in the EW plasma, which continuously evolves into the mass in the broken phase. $\endgroup$ – Thomas Oct 19 '17 at 3:08

While people address the headline question ("Electroweak spontaneous symmetry breaking, a true first order phase transition?"), let me say something about the subsidiary questions.

3 - "is it conceivable that the isospinor scalar field (Higgs field), could have presented two different global minima, one with a zero VEV and another with a nonzero VEV?"

Under certain conditions, the SM electroweak sector does have a second minimum, but it's not at zero VEV, it's at a much greater nonzero field value. Zero VEV only happens at temperatures so ultra-high that the Higgs field has no opportunity to find its minimum.

4-5 - I will rephrase as: if you had adjacent domains that were in different phases and with different particle spectra, could the particles from the different domains interact, and how would they do so?

In a theory with a more complicated phase structure than the standard model, and with stable domain walls, you might find that excitations in the domain wall serve as the interface between the physics of the two domains.

However, the standard model does not seem to have that sort of phase structure. It is said here (thanks to "king vitamin" of physicsforums.com for this reference), page 52, that in the single-minimum standard model, you simply don't get domain walls; and meanwhile, in the regime where the standard model has a second, true minimum at very high scales, the resulting domain walls simply decay rapidly.

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  • $\begingroup$ In condensed matter physics, first order phase transitions allow both phases to coexist everywhere as long as the free energy has two equal global minima. Nucleation and bubble expansion begins when one of them becomes a local minimum and the other a global one. I'm wondering what would have happened if the first situation (two global minima) could have lasted for a long time. $\endgroup$ – Carlos L. Janer Oct 20 '17 at 16:52

My understanding is that the question of whether the electroweak transition was first- or second-order is not entirely settled, but the evidence currently seems to indicate that it was weakly first-order: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.45.2933. In this case there presumably would indeed have been phase coexistence across different regions of space for some very short time period as the universe cooled through the critical temperature. I asked about this process's phenomenology at What did electroweak symmetry breaking actually look like?, but did not receive any answers.

Edit: Apparently this answer is probably incorrect. I'm only leaving it up because I think there's some interesting discussion in the comments.

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  • $\begingroup$ I think your references are out of date. In light of $m_h \simeq 125\,\text{GeV}$ and thus $\lambda$, and precise measurements of $m_t$ and thus the top Yukawa, I believe SM EWSB is thought to be a second-order phase transition. $\endgroup$ – innisfree Oct 18 '17 at 22:27
  • $\begingroup$ @innisfree If you have a reference, I'm happy to change my answer $\endgroup$ – tparker Oct 18 '17 at 22:42
  • $\begingroup$ See e.g. table 1 in arxiv.org/pdf/1206.2942.pdf and refs therein. A first-order transition requires $m_h \lesssim 80\,\text{GeV}$, so it's been known that it can't be first-order since LEP at least (2000 or so). $\endgroup$ – innisfree Oct 18 '17 at 22:48
  • $\begingroup$ I think your ref was assuming a rather light Higgs boson, 60 GeV is mentioned in the figures. $\endgroup$ – innisfree Oct 18 '17 at 22:50
  • $\begingroup$ @innisfree Interesting, thank you. Do you understand what they mean by "cross over transition" in their statement "The scaling behavior of χ with lattice volume can be used to determine whether the [electroweak] transition is first order, second order, or cross over. For $M_h \gg M_h^C \approx 75$ GeV, as implied by collider searches for the Higgs, the transition appears to be a cross over transition" on the bottom of page 11? $\endgroup$ – tparker Oct 18 '17 at 23:36

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