Was Electroweak Symmetry Breaking in the Early Universe Controversial?

[Hornbein]

According to Sabine Hossenfelder in the extremely early Universe nothing had mass because the electroweak symmetry was not yet broken so there was no Higgs field. Am I correct in thinking this is not controversial?

https://youtu.be/9-jIplX6Wjw?t=638

 

[Drakkith]

I think it would be accurate to say that nothing had rest mass derived from the interaction with the Higgs field. Other sources of mass may have existed. Alas I'm no expert in this area, so don't that with a grain of salt.

 

[malawi_glenn]

Hadrons would have mass even if quarks were massless.

 

[malawi_glenn]

But if you could have hadronization in the early universie with massless quarks... I do not know

 

[Vanadium 50]

I see the Mentors have been doing some stealth deleting again - naughty, naughty!

I an going to assume that Hosenfelder got it right and this isn't another "please explain this Youtube video for me" thread. Above a very high temperature - many, many terakekvins - the SM takes on a simpler form. Insteda of W's, Z's and photons, you have w's and B's. Lefft-handed fermions interact as left-handed fermions before they have had a chance to become right-handed. In short, symmetries that are broken at room temperature become approximate and later very good as the temperature goes up.

It is generally believes that in the SM, there is neither a first order nor second order phase transition involved. It is more like the difference between a block of quartz and a pile of sand - very different properties, but just not a phase transition.

In short, there was a time when this was a better description than the preesent-day one.

A completely separate question is how would a Higgs-less world look. I know Chris Quigg was writing a paper on that, but don;t know where or even if it got published. WE argued about this a bit - there's some freedom in which assumptions you make. I would say that there is that the baryons still get some mass, tehy form a condensate that gives the W mass, which in turn transmits a tiny mass to the fermions. The pions - now 36 of them - have their masses driven close to zero because they are Goldstones, and probably become lighter than the electron. o you get giant atoms but no chemistry.

 

[PeterDonis]

in the extremely early Universe nothing had mass because the electroweak symmetry was not yet broken so there was no Higgs field. Am I correct in thinking this is not controversial?

The part about all of the Standard Model fields being massless before electroweak symmetry breaking is not controversial.

I'm not sure the statement that "there was no Higgs field" is correct in that regime, though. My understanding is that the Higgs field was there, it just had not acquired a nonzero vacuum expectation value (it does that when electroweak symmetry breaking happens), and without a nonzero VEV for the Higgs field the interactions that give mass to various SM fields do not happen. (Also, the term "Higgs field" is something of a misnomer; there are, as I understand it, actually four Higgs degrees of freedom in the high energy SM, not one. Three of the four get "eaten" in electroweak symmetry breaking in the process of giving mass to the electroweak bosons, which become the W+, W-, and Z that we observe now. The fourth becomes the "Higgs field" whose particle manifestations have been detected in the LHC.)

 

[PeterDonis]

But if you could habe hadronization in the early universie with massless quarks... I do not know

I think that's rather a moot point since at high energies quarks are asymptotically free anyway.

 

[Vanadium 50]

The part about all of the Standard Model fields being massless before electroweak symmetry breaking is not controversial.

Well, if by "before" you mean "without", I agree.

If by "before" you mean that there was a time when the Higgs field did not have a vev, I do not believe you get that in the SM. What you get is that the vev is small compared to the temperature. There is also the subtlety that the W gets a mass of about 30 MeV from QCD, so even if there were no Higgs, it would not be massless.

 

[PeterDonis]

if by "before" you mean "without", I agree.

I mean at energies well above the electroweak symmetry breaking energy.

If by "before" you mean that there was a time when the Higgs field did not have a vev, I do not believe you get that in the SM. What you get is that the vev is small compared to the temperature.

I don't think that's correct. With a "Mexican hat" potential for the Higgs field, at energies well above the electroweak symmetry breaking energy, the Higgs field has no vev because it's not anywhere near its vacuum state; all of its degrees of freedom are excited to high energy (just like all of the other SM fields).

As the energy drops below the electroweak symmetry breaking energy, the Higgs field has to pick a particular direction in which to roll down the Mexican hat from its top (which is at a field value of $\phi = 0$ but has a higher potential energy than the trough) to the trough at its bottom. That picking of a particular direction is electroweak symmetry breaking. The field ends up at some particular point in the trough, and any such point has a nonzero value $\phi \neq 0$ for the field; that value is the nonzero vev of the Higgs field ("vacuum" because the field is in its vacuum, i.e., ground state).

 

[Vanadium 50]

With a "Mexican hat" potential for the Higgs field, at energies well above the electroweak symmetry breaking energy, the Higgs field has no vev because it's not anywhere near its vacuum stat

That's a statement that EWESB is irrelevant, not that it doesn't exist. This scale is millions of times greater than the electron mass, so yes, the electron mass is not relevant. But the electron does not become massless.

It can in BSM theories, but not in the SM.

If you like, with a wine bottle potential. as you fill the bottle, the punt on the bottom becomes less and less important, but it is stiill there.

 

[PeterDonis]

the electron does not become massless.

If you are claiming that the electron (and indeed all SM fields) is not massless at energy scales above the electroweak symmetry breaking scale, that appears to me to contradict pretty much every source I have read on electroweak symmetry breaking.

For example, see section 2.2 of this paper, which describes the Weinberg-Salam model of the electroweak interaction:

https://arxiv.org/pdf/hep-ph/9901280.pdf

As the paper notes, in the Lagrangian of the SM above the electroweak symmetry breaking energy scale, there are no mass terms for any of the fields at all. Not just that they don't happen to be there: they are forbidden to be there by gauge invariance.

Once electroweak symmetry breaking has occurred, meaning once the energy scale has dropped well below the electroweak symmetry breaking energy scale and the Higgs field has had to choose a particular "direction" as I described and has acquired a vev, the W and Z gauge bosons acquire mass by "eating" three of the Higgs degrees of freedom (the paper describes it this way in the text after equation 29). The fermions acquire mass via Yukawa couplings to the remaining Higgs degree of freedom.

I describe the above as "acquire mass" because the couplings in question can't even be written down if electroweak symmetry breaking has not occurred; they depend on the process of the Higgs field choosing a particular "direction" as it rolls down the Mexican hat potential (in standard electroweak theory this "direction" becomes encoded in the Weinberg angle) having already happened. In our universe, that process happened as the universe cooled below the electroweak symmetry breaking energy.

 

[vanhees71]

But if you could have hadronization in the early universie with massless quarks... I do not know

The quarks and gluons in a quark-gluon plasma (QGP), i.e., the effective degrees of freedom leading to the correct equation of state and thus thermodynamic properties are far from being massless. The QGP is rather a very "sloshy liquid" than an ideal gas of massless quarks and gluons, as can be seen from lattice-QCD calculations of the thermodynamic quantities (pressure, entropy, energy density, free-energy density,...).

 

[vanhees71]

The part about all of the Standard Model fields being massless before electroweak symmetry breaking is not controversial.

I'm not sure the statement that "there was no Higgs field" is correct in that regime, though. My understanding is that the Higgs field was there, it just had not acquired a nonzero vacuum expectation value (it does that when electroweak symmetry breaking happens), and without a nonzero VEV for the Higgs field the interactions that give mass to various SM fields do not happen. (Also, the term "Higgs field" is something of a misnomer; there are, as I understand it, actually four Higgs degrees of freedom in the high energy SM, not one. Three of the four get "eaten" in electroweak symmetry breaking in the process of giving mass to the electroweak bosons, which become the W+, W-, and Z that we observe now. The fourth becomes the "Higgs field" whose particle manifestations have been detected in the LHC.)

The fields are always there within a QFT. The question is, in which state they are. In the Anderson-Higgs phase the Higgs field has a non-vanishing expectation value. That's the case at low temperatures (particularly in the vacuum), and there the particles get mass via the coupling to the Higgs-field (vacuum) expectation value. Note that this is not spontaneous symmetry breaking, although almost all textbooks sloppily call it so, because what "would be broken" is a local gauge symmetry. Particularly the vacuum is not degenerate, and in the Anderson-Higgs phase there are no Goldstone bosons. The corresponding "would-be-Goldstone-degerees of freedom" are "eaten up" by the gauge fields (here the $\text{SU}(2)_{\text{flavor}} \times \text{U}_{\text{Y}}$) is "Higgsed" to $\text{U}(1)_{\text{em}}$, i.e., 3 out of the 4 gauge fields become massive, the W- and Z-bosons, and 1 stays massless, the photon). Indeed in the minimal-Higgs-doublet model (a $\text{SU}(2)_{\text{flavor}}$ doublet, i.e., 4 real field-degrees of freedom), one spin-0 Higgs boson stays in the physical spectrum.

One should note that at finite temperature you deal with effective degrees of freedom, sometimes describable as "quasi particles". The quarks and gluons in the quark-gluon plasma, e.g., are rather quite broad massive quasiparticles than massless particles due to the strong interaction. One should also be aware that about 98% of the mass of the matter around is is due to the strong interaction/confinement and mostly due to the trace anomaly and to a small extent also the formation of a quark condensate, leading to spontaneous breaking of the approximate chiral symmetry of the light-quark sector of QCD, which leads to the mass split between chiral-partner hadrons, while the bulk of the mass is due to the trace anomaly, i.e., gluon degrees of freedom. As is now pretty clear from heavy-ion collision experiments and theory (particularly dileptons) the chiral symmetry is realized by models like the chiral-doubler models, where in the effective hadronic theory for every hadron field there must be another chiral-partner field with a generic mass term for both which does not drop in the chiral-symmetry restoration at higher temperatures and/or densities, i.e., at the chiral crossover or phase, depending on the baryo-chemical potential, transition the masses don't vanish ("dropping-mass scenario") but rather the spectral functions of the chiral-partner hadrons get degenerate, becoming usually broad continuum-like states close to the deconfinement transition.

 

[Vanadium 50]

I thought for sure we would get the word "sphaleron" into a B-level thread!

 

[ohwilleke]

According to Sabine Hossenfelder in the extremely early Universe nothing had mass because the electroweak symmetry was not yet broken so there was no Higgs field. Am I correct in thinking this is not controversial?

https://youtu.be/9-jIplX6Wjw?t=638

Some of the previous discussion got very technical for a B-level thread. I'm going to attempt to boil it down more simply.

At high energies, which can be calculated to quite a bit of precision in the Standard Model, all of the particles in the Standard Model (i.e. quarks and leptons and W bosons and Z bosons) cease to get rest mass from the Higgs field.

At energies quite a bit lower than that, temperatures are still too hot for composite particles made of quarks and gluons (which carry the strong force) to hold together.

Instead, these particles form what is called a "quark gluon plasma" which is a big mush of quarks and gluons.

In contrast, at lower energies quarks and gluons "confined" in small lumps called "hadrons" that are bound by the strong force with only a few primary quarks each (called valence quarks). Hadrons also have a "sea" of other short-lived or "virtual" particles that pop into and out of existence, however, which is how things which aren't primary components of a proton, for example, can pop out of a proton-proton collision at high energies.

Sabine is oversimplifying (or being oversimplified in paraphrase) in saying that nothing had mass.

No fundamental particles had "rest mass" but the universe still would have had vast amounts of mass-energy at that point (mass is equivalent to energy for gravitational purposes) with sources other than particle rest masses. Also, some particles have a trivial portion of their mass that is due not to its Higgs field interactions, but to other sources (such as the strong force component of the W boson mass).

A bunch of quark-gluon plasma, for example, would have a finite, well defined gravitational mass and would require the application of force to move in space-time with change in velocity (a.k.a. acceleration) equal to the amount of force divided by the mass to be moved.

Figuring out how all this would have played out, however, is not easy.

This is because all of the Standard Model laws of physics are affected by energy scale, not just the Higgs field. For example, the strength of the strong force, the weak force, and electromagnetic force are all different at very high energies than they are a energies comparable to the part of the universe in which we live now, which has been at this low energy state for the vast majority of the 13.8 billion years of the universe.

Between the energy scale of our era and the energy scale of electroweak symmetry breaking, electromagnetism gets stronger, while the strong force gets weaker.

It also isn't just a matter of tweaking the strength of forces and other constants of the Standard Model. Electroweak symmetry breaking involves a phase-like change in the set of allowed particles that exist in the universe, at least on the force carrying fundamental boson side. The familiar set of particles (to physicists) of W bosons, Z bosons, photons, and the Higgs boson are replaced by a different pre-electroweak symmetry breaking set of possible particles. The predominant assumption is that the Standard Model fermions had come into existence via baryogenesis and leptongenesis before electroweak symmetry breaking, and that before that point there were
the three W vector bosons and one B vector boson, none of which had rest mass. These different carrier bosons also jumble the version concepts of electromagnetism and the weak force, in addition to the Higgs field, as the distinct forces we know them to be in our era.

In the history of the universe, this is believed to have happened shortly after the Big Bang, when the universe was at a temperature 159.5±1.5 GeV a.k.a. approximately 10¹⁵ Kelvin (assuming the Standard Model of particle physics).

This is all taking place starting a billionth of a second before the Big Bang and ending a 100,000th of a second after the Big Bang, when the observable universe (assuming spherical symmetry) had a radius similar in order of magnitude to the size of the inner solar system. It is close to the boundary between solid scientific prediction and educated scientific guesswork and speculation.

Anyway, that's what should happen if the universe behaves at high energies as a straight extrapolation of the laws of physics we have devised that at tested experimentally up to the energy scales of the Large Hadron Collider.

We don't have any particularly good reason for something different that what the laws of physics predict should happen at that scale to occur. But we also have no direct empirical evidence that can confirm that this is what happens either. The temperatures at this point are many orders of magnitude higher than anything we have directly observed.

We also don't have a consensus theory about how quarks, electrons, muons, tau leptons, and neutrinos (collectively the "Standard Model fermions"), came into being in the first place. The process by which this happened is called baryogenesis (for quarks) and leptogenesis (for electrons, muons, tau leptons, and neutrinos), and we don't know how, when, or why any of these things happened, although we can narrow down the "when" part to an extremely small window of time at or after the Big Bang.

 

[Vanadium 50]

At high energies, which can be calculated to quite a bit of precision in the Standard Model, all of the particles in the Standard Model (i.e. quarks and leptons and W bosons and Z bosons) cease to get rest mass from the Higgs field.

Not true.

Electroweak symmetry breaking involves a phase-like change

"Phase change" is a term in physics. "Phase-like change" is not. In the SM, there is no phase change, either 1st or 2nd order.

Sabine is oversimplifying

That I will believe.

 

[PeterDonis]

Not true.

I'm still not convinced about this. See my post #11.

 

[Vanadium 50]

If you fill a wine bottle, the punt becomes less and less relevant, but it never goes away.

If you run the RGEs using the SM parameters, you do not every reach a spot where everything is massless. (Even Wikipedia says this) Of course, if you add BSM physics you can get other answers - likely any answer you want.

A phase transition has an order parameter as well as an order (first and second). It's not enough to say "thinks look different above this temperature). So, what's the roder parameter? What's the critical temperature? What's the order of the phase transition? Wine bottle and Mexican hats aren't the actual math.

Take you pick.

 

[PeterDonis]

If you run the RGEs using the SM parameters, you do not every reach a spot where everything is massless.

How does this relate to what is said in the paper and section I referenced in post #11?

 

[Vanadium 50]

As I understand it, for some values of m(H), m(t) etc. there would have been a phase transition, and this was unclear a few decades ago. However, with better measurements, we cam calculate where the phase transition occurs and the answer is
nowhere". (Assuming only SM fields)

 

[vanhees71]

Reference?

 

[Vanadium 50]

This is from https://doi.org/10.1016/j.physletb.2012.08.024 which, while a decade old. outlines the arguments well:

In that time, the data point has moved down and to the right, i.e. further into the green. Three reasons for that:

• Higgs mas has gone up a bit
• Top mass has gone down a bit
• Connection between the theoretical and measured top mass has shifted down, so the top quark mass parameter (e.g. pole., MSBar) is even lighter for a given measurement.

Note that this is a necessary but not sufficient condition for a phase transition in the early universe: you can't have a transition if there is only one phase, but if you have two that doesn't mean you have gone from one to the other,

 

[PeterDonis]

This is from https://doi.org/10.1016/j.physletb.2012.08.024 which, while a decade old. outlines the arguments well

It summarizes the state of knowledge regarding absolute stability of the electroweak vacuum. But we're talking about electroweak symmetry breaking. They're not the same thing.

From what I can gather from the paper (and from references 4, 5, and 6, which seem to be the key theoretical papers referenced), "stability of the electroweak vacuum" means that the quartic coupling constant $\lambda$ in the Higgs sector Lagrangian remains positive. But that in no way rules out electroweak symmetry breaking; indeed, $\lambda > 0$ is required for the electroweak symmetry breaking mechanism to be used to account for the masses of SM particles. But that just puts me right back to what I said in post #11. If what I said there is wrong, I still do not understand why.

 

[Vanadium 50]

Like I said - necessary but not sufficient. The first step isb to show that there are two phases differing by a phase transition, and this shows what is known about that. As a starting point, you can't tunnel into a state that doesn't exist.

I'm done here -

1. I have shown the problem with the wine bottle analogy
2. I pointed people to Wikipedia, which is not always the best source, but the references can be judged accordingly.
3. I pointed people to an article which outlines the issues, and explained what has changed since then.
4. I asked pertinent questions about the counter-proposal, in particular, "If it is a phase transition, what order and what is the order parameter?" These have been unanswered.
5. Disagreeing with the mentor participating in this thread often results in very active moderation. No thanks.

 

[PeterDonis]

The first step is to show that there are two phases differing by a phase transition

The first step to what? Are you saying that if there is no phase transition, electroweak symmetry breaking doesn't exist? I don't understand your position.

you can't tunnel into a state that doesn't exist

I don't see what this has to do with anything I've asked.

I have shown the problem with the wine bottle analogy

I don't see how. The Higgs field does not "fill up" the potential. The potential is a term in the Lagrangian.

I pointed people to Wikipedia, which is not always the best source, but the references can be judged accordingly.
I pointed people to an article which outlines the issues, and explained what has changed since then.

And I've followed up with questions which you haven't answered.

I asked pertinent questions about the counter-proposal, in particular, "If it is a phase transition, what order and what is the order parameter?" These have been unanswered.

I haven't claimed there was a phase transition. (Or that there wasn't, for that matter.) As you can see from the above, I'm still trying to understand what "there was no phase transition" even means as far as electroweak symmetry breaking is concerned.

Disagreeing with the mentor participating in this thread often results in very active moderation. No thanks.

Oh, please. We're all grownups here. You've been here long enough to know that we don't moderate people for substantive contributions. If you are simply unable or unwilling to give any further information, you can say so and that's fine. But hiding behind "I'm afraid I'll be moderated" on a subject like this is beneath you.

 

[PeterDonis]

Wine bottle and Mexican hats aren't the actual math.

Ok, fine, let's talk about the actual math. The actual math is, heuristically, that there are two ways to write down the SM Lagrangian (some papers call them two different "gauges"):

(1) You can write down a Lagrangian that, in the electroweak sector, includes the left-handed fermions and four gauge bosons, $W^1$, $W^2$, $W^3$, and $B$, and the Higgs, which is a complex scalar SU(2) doublet (so four degrees of freedom). There are no mass terms for any of these fields. There are also right-handed fermion fields but there are no terms coupling them to left-handed fermion fields.

(2) You can write down a Lagrangian that, in the weak sector, includes both left-handed and right-handed fermions and four gauge bosons, which are now $W^+$, $W^-$, $Z$, and the photon. The three weak bosons now have masses because they have "eaten" three of the four Higgs degrees of freedom. The fourth Higgs degree of freedom appears in Yukawa interactions between the left-handed and right-handed fermions, which behave just like Dirac mass terms for those fermions. The coupling constant in these Yukawa terms is proportional to the Higgs vacuum expectation value. The coupling constants in the weak boson interaction terms include the Weinberg angle, which describes the specific "direction" (in the abstract space of the Higgs potential) in which the electroweak symmetry was broken.

Now mathematically, (1) and (2) are equivalent, in the sense that we can mathematically transform one into the other no matter what the energy scale is. But at high energies, (2) is physically meaningless, because the Higgs does not have a nonzero vacuum expectation value. In fact, the adjective "vacuum" here is misleading; it's just an expectation value for the fourth Higgs degree of freedom, and at high energies, it's zero, because at high energies, all of the possible "directions" for the Weinberg angle are equally likely. And that means that at high energies, only (1) above is physically relevant, and in (1) above, all of the fields are massless. Not "almost massless"; not "massless except for a small correction due to the shape of the Higgs potential". They are massless, period.

Only at low energies, after electroweak symmetry breaking takes place as the universe cools, do we have a specific value for the Weinberg angle that in turn drives a specific nonzero expectation value for the Higgs field (because now only one "direction" is physically relevant). And so only at low energies does it even make sense to talk about the Yukawa interactions that give masses to the fermions, and the "eating" of the three Higgs degrees of freedom that gives masses to the weak gauge bosons. Those interactions are only present when the Higgs has a nonzero expectation value, and it only has that at low energies, after electroweak symmetry breaking takes place.

The above is just a more expanded version of what I wrote in the last paragraph of post #11. Yes, it's a heuristic description, but as far as I can tell from everything I've read (including what I've read in the papers you have referenced in this thread), it is a valid description of electroweak symmetry breaking and the behavior of the masses of the SM fields. Note, also, what I have not said in the above: I have not said that the transition from the high energy to the low energy regime, electroweak symmetry breaking, requires an actual phase transition, of first or second or any other order. I don't know if it does or not. I don't see why it would have to. But at any rate I am not claiming that it does.

Is it possible that the above heuristic description is wrong? Of course. But if so, I would like to understand why, and nothing that you have said or referenced in this thread has helped, because none of it addresses the key point I made above, about the effects that give masses to the SM fields only making physical sense at low energies, where a specific value has been picked out for the Weinberg angle and a specific nonzero expectation value has been picked out for the Higgs field.

 

[PeterDonis]

The actual math is, heuristically, that there are two ways to write down the SM Lagrangian

This paper describes the math in much more detail:

https://cds.cern.ch/record/984122/files/p1.pdf

Sections 5.2 and 5.3 in particular discuss rewriting the Lagrangian and obtaining mass terms for the gauge bosons and fermions.

 

[PeterDonis]

Moderator's note: Thread level changed to "I".

 

[vanhees71]

The order parrameter is the expectation value of the Higgs field, and it's a phase transition, although it's not "symmetry restoration" of local gauge symmetry, which cannot be sponteneously broken due to Elitzur's theorem. It's rarely accurately discussed in the literture, because the hand-waving arguments with "spontaneously broken gauge symmetry" (rather than the better notion of "hidden gauge symmetry" or "Higgsed gauge symmetry") work so well. Here are very good lecture notes, setting the record straight (including a chapter on ew. theory at finite temperature):

https://static.uni-graz.at/fileadmin/_Persoenliche_Webseite/maas_axel/ew2021.pdf