What was matter like during the GUT and Electroweak Epochs?

[Comradez]

Hi all,

I was reading about the history of the early universe today, and there were some things that I did not understand. In particular, I do not understand the concept of "spontaneous symmetry breaking." After reading the Mexican Hat analogy many times, here is my best understanding of it:

At higher temperatures, certain physical processes have multiple possible outcomes. For example, imagine a Uranium-235 nucleus having an equal chance of decaying into two different kinds of nucleus (I know that this particular example is not real; this is just a metaphor). However, once the temperature of the early universe cooled to a certain level, certain physical processes (like the strong and weak forces) became more constrained(?) in how they operated, favoring one type of outcome over another in reaction to some stimulus whereas formerly both or multiple outcomes from that stimulus had been possible.

If that was the situation, then I could fathom it. I still wouldn't understand why exactly the stuff behaved differently at different details, but I'm familiar with other substances behaving differently at different temperatures (like water ice), so it would at least be fathomable. But so far, no presentations that I have watched or read have been able to bridge the gap between metaphors like the Mexican Hat one and a non-trivial explanation of spontaneous symmetry breaking that I can understand.

I understand the concept of a substance's *state* being asymmetrical. For example, if a column is sitting up straight, knocking it over to the right or left (i.e. displacing the position of the head of the column to the right or left) would be equally easy. However, if the column has already started falling over to the left, then suddenly the task of displacing the head of the column to the right or left is asymmetrical; pushing it further to the left is easier than arresting its fall to the left and pushing it to the right. However, to me this example seems to only pertain to the physical state of the system. The underlying forces or laws of motion themselves have not changed their operation or become asymmetrical.

What does it even mean to have several forces "coupled" together? What really happened when the strong force became "uncoupled" from the electroweak force, and please try to explain it like you would to a kindergartner, without math or reference to "gauge symmetries" (unless you can explain those to a kindergartner as well!) I'm looking for a physical metaphor, not a wall of math and symbols please. I have spent about six hours trying to understand what that SU(2)xU(1) stuff is all about, and it has gotten me nowhere! Lie groups? Manifolds? Lagrangians? I'm sorry...

In other words, I'm interested in the following questions:
1. What did matter "look like" during the electroweak epoch? (My guess is that matter would not have "looked like" anything in the electromagnetic spectrum because photons didn't exist yet. So, if "look" is the wrong question, then maybe I can ask: what forms did matter come in at that point? Was it a "quark-gluon plasma"? And, aside from this plasma being very hot and presumably wanting to stick to itself, were there any other notable characteristics of it?) What about even earlier, during the hypothesized "GUT" epoch? I ask these questions not just out of idle philosophizing, but because I am led to understand that our supercolliders are increasingly able to replicate, for short nanoseconds, these temperatures of the early universe, and thus these conditions are in principle reproducible and could have practical applications someday.

2. Did matter exert an attractive force on itself yet? My understanding is that gravity was already a separate force that existed, but apparently matter didn't have mass yet because matter wasn't yet being clamped onto by the Higgs field to give it mass...so presumably there was no tendency yet for the universe's ongoing expansion to decelerate yet even in the slightest due to the lack of matter having mass and thus being affected by gravity or inertia. (And if matter did not yet have inertia, then what was keeping matter from flying apart infinitely fast at that point?

 

[nikkkom]

Hi all,

I was reading about the history of the early universe today, and there were some things that I did not understand. In particular, I do not understand the concept of "spontaneous symmetry breaking."

Higgs field has a non-zero vacuum expectation value. When conditions are such that average energies ("temperature") are lower than this value, it makes sense to write Higgs field as H0+h, where H0 is this expectation value, and h is a small deviation from H0.

When average energies are much higher than H0, it makes sense to just use "zero-based" Higgs field, without beaking it into a sum of two parts.

When you use Higgs field in the first form in your equations, you get "spontaneously broken" picture. When you use the second form, you get unbroken picture.

Theoretically, both pictures are valid for any conditions. However, choice of a non-suitable form (say, if you would try to use "unbroken" formulas for todays "cold" Universe) will make your calculations intractable. You will immediately run into divergent results.

 

[nikkkom]

1. What did matter "look like" during the electroweak epoch? (My guess is that matter would not have "looked like" anything in the electromagnetic spectrum because photons didn't exist yet. So, if "look" is the wrong question, then maybe I can ask: what forms did matter come in at that point?

With temperatures >300GeV, the most natural way of looking at SM interactions is as follows:
* color force works the same as today, however, plasma is so dense and particles collide so often that "hadrons" as separate clumps do not exist, it's a "quark-gluon plasma" with about the same density everywhere;
* there is a "weak hypercharge" force which is similar to electromagnetism: it has an uncharged spin-1 B boson which carries the interaction, and all quarks and leptons have +- charges under it. See https://en.wikipedia.org/wiki/Weak_hypercharge
* there is a "weak isospin" force. It has three spin-1 bosons, W1, W2 and W3. You can think about it as being somewhat similar to the color force, but only with two colors instead of three: "up" and "down". Exchange of W1 and W2 particles carries "up/down"-ness with them: quarks and leptons change their "up/down"-ness when they do that. W3 particle does not change "up/down"-ness. Weak isospin force is attractive but not strong enough to have confinement property. See https://en.wikipedia.org/wiki/Weak_isospin
* electromagnetism does not exist as a separate force;
* all fermions are massless;
* with these high energies, particles easily generate new Higgs bosons in collisions.

 

[Comradez]

Theoretically, both pictures are valid for any conditions. However, choice of a non-suitable form (say, if you would try to use "unbroken" formulas for todays "cold" Universe) will make your calculations intractable. You will immediately run into divergent results.

Thank you for your response! Although I don't think I really understood your post. It sounds to me like you are saying that, when energies from sources other than the Higgs field are very high, they dwarf the effect of the Higgs field by comparison and make the calculation of that minor deviation term of the Higgs field unnecessary in a practical sense. Although, wouldn't the nonzero vacuum expectation value of the Higgs field still have its effect of giving masses to the gauge bosons nonetheless? Obviously I am missing something.

Also, it seems strange to me to call both ways of representing the Higgs field "valid" in the context of a cold universe if one way provides tractable calculations and the other does not. Why not just say that physical reality behaves according to one set of laws in one context and a different set of laws in a different context? Or why not simply insist on never including the h deviation term if it apparently creates intractable or inconsistent mathematics? Wouldn't that invalidate this approach in all cases if it is mathematically inconsistent in any situation?

If this way of representing the Higgs field doesn't give sensible answers in a certain context, then how exactly can it be "valid"? For example, if I am calculating the specific heat needed to melt a volume of ice, and I come up with a nonsensical answer, I wouldn't insist that this way of calculating it is valid albeit suboptimal, or insist that in this unique situation the laws of thermodynamics themselves in physical reality broke some conservation law. I'd simply say that I messed up and am not describing or calculating the state correctly.

With temperatures >300GeV, the most natural way of looking at SM interactions is as follows:
* color force works the same as today, however, plasma is so dense and particles collide so often that "hadrons" as separate clumps do not exist, it's a "quark-gluon plasma" with about the same density everywhere;
* there is a "weak hypercharge" force which is similar to electromagnetism: it has an uncharged spin-1 B boson which carries the interaction, and all quarks and leptons have +- charges under it. See https://en.wikipedia.org/wiki/Weak_hypercharge
* there is a "weak isospin" force. It has three spin-1 bosons, W1, W2 and W3. You can think about it as being somewhat similar to the color force, but only with two colors instead of three: "up" and "down". Exchange of W1 and W2 particles carries "up/down"-ness with them: quarks and leptons change their "up/down"-ness when they do that. W3 particle does not change "up/down"-ness. Weak isospin force is attractive but not strong enough to have confinement property. See https://en.wikipedia.org/wiki/Weak_isospin
* electromagnetism does not exist as a separate force;
* all fermions are massless;
* with these high energies, particles easily generate new Higgs bosons in collisions.

Thank you, this response helped. Although, regarding the "weak hypercharge" force, when you say that it is similar to electromagnetism, do you mean that it would also have had attractive and repulsive effects on its constituent bits of matter depending on their hypercharges? And how would this spin-1 boson be different from the photon?

 

[nikkkom]

Thank you, this response helped. Although, regarding the "weak hypercharge" force, when you say that it is similar to electromagnetism, do you mean that it would also have had attractive and repulsive effects on its constituent bits of matter depending on their hypercharges?

Yes. As you see in Weak_hypercharge wiki article, each quark and lepton has a weak hypercharge (some are positive, others are negative). It works just like electric charge.

And how would this spin-1 boson be different from the photon?

Yes: unlike photon, B-boson interacts with Higgs field.

 

[nikkkom]

Thank you for your response! Although I don't think I really understood your post. It sounds to me like you are saying that, when energies from sources other than the Higgs field are very high, they dwarf the effect of the Higgs field

No. In the plasma that is in thermal equilibrium, each degree of freedom carries excitations with the same average energy. With temperatures >300GeV, Higgs field vacuum expectation value is smaller that this energy, thermal Higgs field excitations will be larger than it. In the "H0+h" decomposition, h can no longer be seen as small, and the whole reason for using such decomposition disappears.

 

[nikkkom]

Or why not simply insist on never including the h deviation term if it apparently creates intractable or inconsistent mathematics? Wouldn't that invalidate this approach in all cases if it is mathematically inconsistent in any situation?

QFT math is _in general_ quite difficult, and it takes a lot of very difficult work to make it give mathematically consistent predictions in all cases.

You probably heard about "Perturbative Quantum Field Theory". This is QFT restricted to the case where perturbations (deviations from the vacuum expectation value) are small. And this is basically _the only_ kind of QFT which we so far managed to make mathematically consistent! (People do work on making math work for large fields as well, for one, QCD needs that).

"Simply" using Higgs field representation which does not let you work with it so that the perturbations are small is anything but simple.

 

[Comradez]

No. In the plasma that is in thermal equilibrium, each degree of freedom carries excitations with the same average energy. With temperatures >300GeV, Higgs field vacuum expectation value is smaller that this energy, thermal Higgs field excitations will be larger than it. In the "H0+h" decomposition, h can no longer be seen as small, and the whole reason for using such decomposition disappears.

But I still don't understand...wouldn't you want to use the decomposition when h is large? When you don't use the decomposition, are you just treating the energy of the Higgs field at that point as if it is H0 and just throwing away whatever h would be (in which case this would be most inaccurate when h is large)? Clearly I'm not understanding something.

So perhaps I should back up a bit.

My understanding of quantum field theories is that they hypothesize that there are fields in every point in space for the electromagnetic force, strong force, weak force, and Higgs mechanism, and that each of these fields has a quantum state (energy reading, spin, etc.) at every point in space. However, for most of these points in space, the fields are at their lowest possible energy state, in which case we measure nothing happening in those fields at those points; in order to measure something happening, those fields must possess, at those points, a higher energy than the lowest energy level in order to have an energy differential in order to perform "work" on (i.e. cause changes to) our measuring devices (which would mean changing the quantum state of our measuring device, either by accelerating our device and displacing it to a different point in space, via mechanical force, or it could mean changing the charge, color, etc. of some element of our device).

In this sense, it is not possible to measure the "absolute energy level" of a field at any particular point, just as it is not possible to define an "absolute voltage" in electronic circuits. The only thing we can do is compare differences in energy levels to find the amount of actual "free energy" available to do work, and for all practical purposes we can call the lowest possible energy state of a field the state of "zero energy," even though in reality it could be revealed at a later date in the universe to be merely a local minimum or "false vacuum," with even lower energy states being possible, and thus even more free energy available in the universe to perform work.

So far, so good?

If so, then already I don't understand how the lowest energy state of the Higgs field (which is the same thing as its "vacuum expectation energy," or VEV, right?) is able to perform work on, or influence, or make changes to, matter (by giving matter mass). Also, what is this VEV measured with respect to? I read that the VEV is 246 GeV, so does this mean that the Higgs field in every point in space has AT LEAST an energy value of 246 GeV (except where there is a perturbation and an even higher value, which is read as the presence of a Higgs particle?)? But what does this mean? If this is the lowest possible energy state, then it shouldn't be able to perform any work on the universe, and it should be unmeasurable, right? Then why don't we just re-label this baseline as 0 eV?

 

[PeterDonis]

At higher temperatures, certain physical processes have multiple possible outcomes.

This is not correct, and it's not a good starting point for understanding what you are trying to understand.

I'm looking for a physical metaphor, not a wall of math and symbols please.

Physics is not metaphor. The gauge symmetries and other stuff that you are trying to avoid are the concepts you need in order to understand what you are trying to understand. It is as if you said you wanted to understand arithmetic, but without using the concept of addition. It can't be done.

 

[PeterDonis]

My understanding of quantum field theories is that they hypothesize that there are fields in every point in space for the electromagnetic force, strong force, weak force, and Higgs mechanism, and that each of these fields has a quantum state (energy reading, spin, etc.) at every point in space.

You have listed the fields corresponding to what are usually called "forces" or "interactions", but they are not the only quantum fields. There are also quantum fields for what is usually called "matter": electrons, quarks, and neutrinos. Each of these fields also has a quantum state at each point in spacetime (not space--quantum field theory is relativistic, so you have to think in terms of spacetime). A "vacuum" state of, say, the electron field corresponds to zero probability of measuring an electron to be present at that point in spacetime (but see below for a complication). What you would normally think of as an "electron" is basically a set of events in spacetime at which the electron field is in a particular state that corresponds to measuring one electron present, with a certain energy-momentum and spin.

in order to measure something happening, those fields must possess, at those points, a higher energy than the lowest energy level in order to have an energy differential in order to perform "work" on (i.e. cause changes to) our measuring devices

It's not that simple. Measuring devices can register results even if quantum fields are in their vacuum states. More precisely, the notion of a quantum field being in a "vacuum" state is not invariant: different observers in different states of motion (more precisely, different states of acceleration) will not agree on which quantum field states are vacuum and which are not. An example of this is the Unruh effect, which you can Google, or search for previous threads here on PF discussing it. So measuring devices in different states of acceleration can also register different results even if the quantum field itself is in the same state.

it is not possible to measure the "absolute energy level" of a field at any particular point

This is true, at least as long as we leave out gravity. But quantum gravity is a whole other can of worms that I don't think we want to open in this thread (not least because we do not have a good quantum theory of gravity).

I don't understand how the lowest energy state of the Higgs field (which is the same thing as its "vacuum expectation energy," or VEV, right?) is able to perform work on, or influence, or make changes to, matter (by giving matter mass)

The short answer is that "giving matter mass" does not require doing work on it; the phrase "giving matter mass" is misleading because it makes it seem like the Higgs field has to transfer energy somehow, when in fact it does not.

The more complicated answer starts with the fact that the Higgs field, in the simplest version of the Higgs mechanism, does not give mass to "matter"; it gives mass to the W and Z bosons, which are force carriers for the weak interaction--actually electroweak, but we are talking about temperatures low enough that the electroweak phase transition has taken place and the two interactions have separated. The "matter" fields--electrons and quarks (and now apparently neutrinos, but that wasn't known at first) get masses via a different mechanism, which I'll talk about in a separate post. The phase transition itself is really what we need to focus on here. Let me try to give a heuristic picture, first of how things look before the phase transition, and then how things look after, so they can be compared.

Before the phase transition, heuristically, we have the following quantum fields for the three non-gravitational interactions:

8 gluons (strong interaction)
W1, W2, W3, B (electroweak interaction)
H+, H-, H0, H0* (Higgs)

The key point is that all of the above fields are massless.

After the phase transition, heuristically, we now have the following fields:

8 gluons (strong interaction)
W+, W-, Z (weak interaction)
p (photon--electromagnetic interaction)
H (Higgs boson)

Here the gluons and the photons are massless, while the W+, W-, Z, and H all have mass. What has happened? Notice that three fields have apparently disappeared: there were four Higgs fields before, now there is only one. What happened to the other three? They were "eaten" by the W+, W-, and Z. But something else also happened: before we had W1, W2, W3, and B, and now we have W+, W-, Z, and p. Heuristically, what happened was this:

W+ = W1 + i W2, "eats" H+ and gains mass
W- = W2 - i W2, "eats" H- and gains mass
Z = cos θ W3 - sin θ B, "eats" a combination of H0 and H0* and gains mass
p = cos θ B + sin θ W3
H = what's left of the combination of H0 and H0* after the Z has "eaten" part of it

Here θ is an angle called the "Weinberg angle"; it also appears in the formulas for the masses of the W and Z particles, and the model predicts a certain ratio between those masses. Measurements in the late 1970s and early 1980s of those masses confirmed the predicted ratio and gave us an experimental value for θ.

In other words, what we call the W+, W-, Z, p, and H quantum fields are really particular mixtures of other quantum fields, mixtures that are useful to use in our theory because they correspond directly with things we can physically measure at low temperatures. But at high temperatures, those mixtures are not useful; instead it's more useful to use a different set of fields, the ones called W1, W2, W3, B, H+, H-, H0, and H0*. The number of fields decreases by three because adding mass to a quantum field adds a degree of freedom, which has to come from somewhere; the list above tells where they come from.

Physically, what happened during this transition? One way to think of it is to consider a ball at the top of a perfectly symmetrical hill (the crown of the "Mexican hat"); this corresponds to the four Higgs fields at high temperature. Because the temperature is high, the ball is constantly being kicked, so even if it starts to roll down the hill, it will quickly be kicked back up again. However, as the temperature drops, the kicks get less powerful, and finally a point is reached where the ball starts to roll down the hill and doesn't get kicked back up to the top; so it keeps rolling and eventually reaches the bottom (the trough of the "Mexican hat"). Once it's in the trough, it's stuck, because there is another upward incline on the other side, and the temperature is too low now to kick it uphill any significant distance.

When the ball reaches the trough, it has to reach it at some particular point. When it's at that point, its state is no longer symmetrical about the origin (the origin corresponds to the point at the top of the hill). In other words, even though the overall shape of the hill is symmetrical, the final state of the ball at the bottom is not--it has to end up at a particular point, in a particular direction from the origin. That is why the term "symmetry breaking" is used: because the underlying symmetry of the hill itself does not appear in the final state of the ball.

Also, the process of the ball rolling down the hill released energy, because the height of the hill corresponds to the average energy of the ball. Where did that energy go? Into the masses of the W+, W-, and Z bosons. In other words, the ball rolling down the hill in this heuristic picture corresponds to the following things taking place: the four Higgs fields give up their starting energy (what they had at the top of the hill) by having three of their four degrees of freedom be "eaten" by the W+, W-, and Z, leaving the fourth behind as the Higgs boson we observe. The Weinberg angle θ tells us, heuristically, the direction from the origin of the point where the ball ended up in the trough; this angle determines how, exactly, the H0 and H0* degrees of freedom get "mixed" into the Z and photon.

I should emphasize that this heuristic picture has limitations; as I said before, physics is not metaphor. For example, I said above that the Weinberg angle determines the ratio of the masses of the W and Z bosons; but in the simple "Mexican hat" model I just described, the trough is the same depth everywhere, and the difference in height between the top and bottom of the hill is the energy released into the boson masses, so it doesn't seem like anything about the actual values of the masses should depend on the Weinberg angle; but it does. That is why you need to go beyond these metaphors and heuristic pictures to fully understand what is going on.

 

[PeterDonis]

The "matter" fields--electrons and quarks (and now apparently neutrinos, but that wasn't known at first) get masses via a different mechanism, which I'll talk about in a separate post.

Here is the follow-up on how the matter fields get mass in the Standard Model. Go back to the "Mexican hat" picture, where the ball has rolled down the hill into the trough. It is now sitting at a particular point away from the origin, whose direction is described by the Weinberg angle θ.

In this model, the point where the ball is sitting corresponds to the vacuum expectation value of the Higgs field. The origin would be a zero value; any other point is a nonzero value. So the ball sitting in the trough has a nonzero vacuum expectation value, which we'll call $\phi_0$.

Each of the fermion (i.e., "matter") fields in the Standard Model has a basic interaction with the Higgs field, which, at high temperature (i.e., before symmetry breaking), can be written, schematically, as $\bar{\psi} \phi \psi$ (where $\psi$ and $\bar{\psi}$ are the quantum field of the fermion and its conjugate, respectively). At high temperature, the value of $\psi$ is jumping around (because the ball is constantly being kicked). But once the ball falls down into the trough and gets stuck at a particular point $\phi_0$, heuristically, the interaction with the fermion field becomes $\bar{\psi} \phi_0 \psi$, and since $\phi_0$ is just a constant, we can pull it out in front and call it the "mass" $m$ of the fermion field, so we have $m \bar{\psi} \psi$, which is exactly what a "mass term" for a fermion field with mass $m$ looks like. So fermion masses come from the interaction of the fermions with the Higgs field once it has acquired a vacuum expectation value.

Again, this heuristic picture has limitations. For example, in the Standard Model, at high temperatures, before the electroweak phase transition, the fermions are massless; but they are still interacting with the Higgs field, so why don't they behave as massive fields whose masses are fluctuating as the Higgs field fluctuates? I don't know of a way to fully understand that without going beyond the metaphors and heuristic pictures and actually understanding the math.

 

[nikkkom]

Again, this heuristic picture has limitations. For example, in the Standard Model, at high temperatures, before the electroweak phase transition, the fermions are massless; but they are still interacting with the Higgs field, so why don't they behave as massive fields whose masses are fluctuating as the Higgs field fluctuates?

Interaction of fermions with another _fluctuating_ field is usually described as "interaction between particles". E.g electron is said to emit or absorb photons when it interacts with photon field.

Interaction with variable but periodic in space fields can cause particles to acquire "mass" as well. One well-known example is photons traveling through matter (say, a transparent crystalline material) - they travel slower than speed of light. Just like with electroweak symmetry breaking, you can look at such photon either as a massless particle constantly interacting with electron field, or as a massive freely-propagating particle.

 

[Comradez]

That was very helpful, PeterDonis! And I understand that, to truly understand this stuff, I would need to understand the math. But you did a pretty good job of creating the sort of metaphors I was looking for!

I just have one final question: from what I have seen of the "Mexican hat" graph of the Higgs field, it appears that the trough of the hat has a circular shape centered on the origin. My question is, does this imply that the spontaneous symmetry breaking could have happened differently? In other words, could the ball have rolled away from the peak along a different angle? In other words, could the "Weinberg angle" have been different? And if so, would this different way of breaking the symmetry have permanently changed the nature of the W and Z bosons and the photon throughout the universe? What exactly is at stake here? In other words, how is this "spontaneous symmetry breaking" different from just any ordinary phase change? Because, as I understand ordinary phase changes, like water going from solid to liquid, or back again, there's no ambiguity about how the substance will end up on the other side of the phase change. Each time it's the same transition. Is this how the spontaneous symmetry breaking happened? Or was there a range of possibilities for how it could have played out, and did we just get "lucky" (for the eventual formation of intelligent life) that it happened the way that it did?

And if the Higgs field is ever locally reheated (or "kicked" to the top of the Mexican hat again), as I assume is the case during supercollider experiments, does that mean that the symmetry temporarily becomes "unbroken" again, and if so, does it then have a new chance to break in a different way as it cools again? And if so, would this different symmetry breaking apply only locally, or what? Thanks!

 

[nikkkom]

And if the Higgs field is ever locally reheated (or "kicked" to the top of the Mexican hat again), as I assume is the case during supercollider experiments, does that mean that the symmetry temporarily becomes "unbroken" again

In our "cold" vacuum way below electroweak breaking temperature, "kicking" Higgs field means exciting oscillations in "h" part of H0+h decomposition of Higgs field. Since Higgs field is a 4-component scalar field, it has four possible "directions" for h to oscillate in. Three of them are observed as W+, W- or Z particle. The fourth kind is the Higgs boson.

 

[nikkkom]

To get basic understanding of the math involved, read this:

https://profmattstrassler.com/artic...-basics/fields-and-their-particles-with-math/
https://profmattstrassler.com/artic...s-basics/how-the-higgs-field-works-with-math/

 

[PeterDonis]

could the ball have rolled away from the peak along a different angle?

The basic theory would say yes. However, it's possible that there were other constraints involved that made one particular value of the angle preferred. We don't really know for sure.

would this different way of breaking the symmetry have permanently changed the nature of the W and Z bosons and the photon throughout the universe?

It would change the masses of the W and Z bosons, which would change the relative strength of the weak interaction as compared with the others. It would also change the masses of the fermions.

It would not change the photon or the electromagnetic interaction, because there is always a massless boson "left over" after the symmetry breaking (the Weinberg angle just determines what particular mixture of the W3 and B fields before symmetry breaking ends up as this massless boson), and that massless boson will always have the same properties, the ones we are familiar with as the electromagnetic interaction.

 

[PeterDonis]

Since Higgs field is a 4-component scalar field, it has four possible "directions" for h to oscillate in. Three of them are observed as W+, W- or Z particle.

Note: the W+, W-, and Z are not oscillations of the Higgs field alone; they are oscillations of particular combinations of components of the Higgs field with the W1, W2, or W3/B fields. The only oscillation, in our current low temperature universe, which is a "pure" oscillation of the Higgs field is the Higgs boson.

 

[PeterDonis]

if the Higgs field is ever locally reheated (or "kicked" to the top of the Mexican hat again), as I assume is the case during supercollider experiments

Our current supercolliders are many orders of magnitude short of the energy it would take to achieve temperatures at which electroweak symmetry would be unbroken again. (That's why we have no prospect of directly testing whether the symmetry could be broken a different way.) As @nikkkom said, all that is happening in our current experiments is that the various degrees of freedom of the low energy fields (the "after symmetry breaking" ones I listed before) are being "kicked" slightly above their vacuum states (where "slightly" means "by comparison with the energy it would take to unbreak the symmetry").