Ask Ethan: Can you explain the Higgs boson in depth?

One of the great quests in all of science is to discover, at a fundamental level, what the Universe is actually made of. If you took every amount of matter and energy that existed — or even could exist — and cut it up into its smallest possible chunks, until only something that was uncuttable was left, you’d be left with the fundamental, elementary particles that composed our Universe. In physics, this took us first down to the level of the atom, then to atomic nuclei and electrons, then to protons, neutrons, and electrons, and finally to our modern Standard Model of elementary particles: complete with quarks, charged leptons, neutrinos, their antimatter counterparts, the gluons, the photon, the W-and-Z bosons, and one additional unique particle, the Higgs boson.

Of all of those particles, the Higgs boson is the most recently discovered particle: found only at particle accelerators, like the Large Hadron Collider at CERN, in 2012. But what’s the story of the Higgs boson? What makes it so unique, where does it come from, and how does it fit in with everything else that we know? That’s what Vu H Nguyen wants to know, asking:

“Can you explain the Higgs boson in depth? [It is] difficult for me to understand, but I think this is very important in particle physics. Maybe you can explain it in an easier way?”

When we think about matter, we normally think about “fundamental” in the way we outlined above: by cutting it up into its smallest indivisible component parts. But there’s more to the story, and the Higgs boson requires us to go deeper than any other known particle in order to understand it. Here’s the story.

Here in our Universe, we’re mostly familiar with the particles that are common and stable today: atoms and the subatomic particles they’re composed of. Atoms are made of electrons that orbit the atomic nucleus, which in turn is made of protons and neutrons, which themselves are made of quarks and gluons.

If you want to see what types of quarks are in there, however, you have to collide particles together. You have to collide them hard enough to break inside the atom, to crack open the atomic nucleus, to split apart the individual protons and neutrons, and to smash them directly into individual elementary particles.

When you do that, you discover something amazing. You don’t just reveal what these composite structures inside the atom are made of; you also gain the ability to create brand new particles, including heavy, unstable, short-lived particles. Through the power of colliders, we don’t just make electrons and the up-and-down quarks that compose protons and neutrons, but also:

• muons and taus, the heavier cousins of electrons,
• positrons, antimuons, and antitaus, the antimatter counterparts of those charged leptons,
• strange, charm, bottom, and top quarks,
• the antimatter counterparts of all six flavors of quarks (the antiquarks),
• photons, gluons, and W-and-Z bosons, which are the gauge bosons,
• and the Higgs boson as well.

These, along with the neutrinos and antineutrinos (which can’t be directly observed in colliders, but can be observed through other means), make up all of the known elementary particles, and the entirety of the Standard Model of elementary particles.

We can measure all sorts of properties about these particles from our collider-detector experiments. In particular, we can, by creating enough of them and building detectors around the collision points where those particles come into existence — created from energy via Einstein’s E = mc as long as all of the necessary quantum properties like energy, momentum, angular momentum, electric charge, and so on are conserved — measure all sorts of properties associated with them. We can determine:

• their rest masses,
• their electric charges,
• their intrinsic angular momenta (i.e., their spin),
• their mean lifetimes,
• their weak hypercharge and weak isospin,
• their possible decay products (all of the different pathways through which the unstable ones can decay),
• and their branching ratios (the rate at which they decay through their various pathways),

chief among them. The Standard Model isn’t just about the particles that exist, but about their key relationships and properties. The quarks and leptons make up what we conventionally know of as “matter” (while the antiquarks and antileptons make up “antimatter”), but the gauge bosons determine how they interact with one another. We normally talk about this as the four fundamental forces, as particles and antiparticles interact through gravity (which we don’t know whether it’s quantum in nature; it’s outside of the Standard Model), electromagnetism (mediated by the photon), the weak nuclear force (mediated by the W-and-Z bosons), and the strong nuclear force (mediated by the gluons).

Sure, there are still mysteries that we have that the Standard Model can’t explain: gravity, the values for the rest masses of the particles, the abundance of matter over antimatter in the Universe, and the existence of dark matter and dark energy among them. But for what the Standard Model does give us, it’s an incredibly powerful description of reality.

So where does the Higgs boson come from?

In order to answer that, we can’t start here in our Universe today, nor can we even start with the “little bangs” we create in our particle colliders here on Earth. Instead, we have to go all the way back to the hot Big Bang, where higher energies and hotter temperatures were achieved than in anything we can create here on Earth.

Back then, we still had the quarks and leptons (and antiquarks and antileptons) that we have today, as well as the gluons. They all still needed energy in order to exist, but they didn’t possess the rest masses that they have today. (You might have heard the phrase “the Higgs gives mass to the Universe,” but that refers to the Higgs field being “switched on” as opposed to “switched off,” not the Higgs boson!) Still, the particles existed just as they do today; that much was the same.

However, the other bosons looked very, very different. We didn’t have the photon, the W-and-Z bosons and the Higgs boson at all back in the early stages of the hot Big Bang. Instead, we had four massless bosons: the W1, W2, W3, and the B. The Higgs field was also there, but in a very different state to how it exists today. Whereas today, the Higgs field is in what’s known as a state of “broken symmetry,” like a ball that’s rolled down into a valley along the brim of a hat, early on, the Higgs field was in a “restored symmetry” state: like being at the top of the peak of the hat, where all directions appear equivalent.

What this means, at the high energies associated with the early stages of the hot Big Bang, is that there are the same spectrum of Standard Model fermions (quarks and leptons, and antiquarks and antileptons) that we have today, albeit without rest masses, but a different spectrum of forces that they interact through.

They interact through:

• gravity (which isn’t included in the Standard Model),
• the strong nuclear force (which is still mediated by the gluons back then, as it is today),
• by the electroweak force (which is mediated by those W1, W2, W3, and B bosons, instead of today’s W-and-Z bosons and photon which mediate the weak nuclear and electromagnetic forces),
• and through the Higgs field, which has four degrees of freedom in the same fashion that the electroweak force has four bosons associated with it).

According to the Standard Model, the Higgs field isn’t a vector field or a spinor field (like the other bosons and fermions), but rather is a scalar field. (In technical language, we call the structure of this field a complex SU(2) doublet.) At this point, there is still a Higgs field and a Higgs interaction, but no Higgs boson. In addition, the Standard Model particles haven’t yet acquired a rest mass.

And then, a critical transition happens: the Universe cools through an energy-equivalent of about 250 GeV, which happens about a picosecond (0.000000000001 seconds) after the start of the hot Big Bang. This is known as the electroweak phase transition: where the Higgs mechanism spontaneously breaks the unified electroweak force down into the separate electromagnetic and weak nuclear forces.

You’ll sometimes hear the terms “electroweak symmetry breaking” and “Higgs symmetry breaking” as though they are separate things; they are not. They are one and the same: the Higgs mechanism is the cause of electroweak symmetry breaking, and it occurs when the energy of the Universe drops significantly that it’s no longer energetically favorable to be on the “peak” of the hat-like potential. When you fall off of the peak and down towards the brim, that’s where it all occurs, and that’s ultimately the origin of the Higgs boson.

But before we get there, you have to understand there’s a theorem in physics known as Goldstone’s theorem that states that every time you have a continuous symmetry that’s spontaneously broken, you get a new massless scalar particle out of it: a particle known as a Nambu-Goldstone boson.

Because the Higgs field has a specific structure — that of a complex SU(2) doublet — that means it has four degrees of freedom with it, and hence, in its unbroken state, four continuous symmetries to it. When symmetry breaking occurs, we get, by Goldstone’s theorem, four massless scalar particles out of it.

But hang on! Doesn’t the Higgs boson have mass?

This is why it’s so important that we understand how the Higgs mechanism works. When those four continuous degrees of freedom all have their symmetry broken, four theoretically massless scalar, Higgs-related particles emerge:

• a positively charged one, H+,
• a negatively charged one, H–,
• and two electrically neutral ones, normally called H0 and h.

But these are not isolated massless particles; they exist amidst the rest of the Universe. And here in this Universe, we also had those electroweak bosons: the W1, W2, W3, and B bosons.

Now, there’s one more piece of information we have that we need to put together. In our quantum Universe, if two distinct quantum particles have the same quantum numbers, they inevitably wind up having their wavefunctions overlap, and they mix together. With the new arrival of the H+, H–, H0 and h particles, the W1, W2, W3, and B bosons now have something to mix with.

The W1 and W2 particles already have the same quantum numbers, so they already mix together. (The W3 and B bosons also mix together, and that will be important in a bit.) One combination of the W1 and W2 then combines with the positively charged Higgs boson, H+, and creates the positively charged W-boson, W+. The other combination of W1 and W2 combines with the negatively charged Higgs boson, H–, to make the negatively charged W-boson, W–. These combinations, as gauge symmetries, now become massive.

There are also going to be two combinations of the W3 and B bosons, in similar fashion. One of those combinations combines with one of the neutral Higgs-related particles: H0. That combination becomes the neutral weak boson: Z0. The other combination of the W3 and B, however, doesn’t combine with, absorb, or eat anything; it remains massless, and that’s what becomes the photon. (If you’re asking, “hey, does that mean that prior to electroweak symmetry breaking, the Universe didn’t have photons in it?” The answer is yes!!)

That just leaves one degree of freedom left, h, with nothing to combine or mix with. That’s what becomes the massive Higgs boson.

But why does it become massive? Take a look, above, at the hat-like potential associated with the Higgs field. Three of those degrees of freedom of the field represent what’s called the azimuthal direction of the field: the components of the field that go around, either clockwise or counterclockwise, of the “brim” of that hat within the valley. (More technically, they correspond to the positive, negative, and neutral currents in that azimuthal direction.) That’s what combines with the three of the initial electroweak gauge bosons to make the W-and-Z bosons, with the last uncombined electroweak gauge boson making the massless photon.

However, that last degree of freedom — the one associated with h — moves in the radial direction instead: the one that fights to go up-and-down towards or away from the hat’s center. Unlike the “around” going (azimuthal) direction, which is flat and uncurved, the radial direction is heavily curved. If you think of that component of the field as a ball, it’s going to roll up-and-down the sides of that hat, and therefore will oscillate. Those oscillations is how that component of the field acquires a mass, and is why the Higgs boson, the particle associated with h, turns out to be massive.

It’s the coupling to the Higgs field that gives the massive Standard Model particles their non-zero rest masses, but it’s a self-coupling, or the interaction of the Higgs boson with the Higgs field, that gives the Higgs boson its mass. Now that the Higgs boson has been discovered, and we’re certain that the Higgs mechanism is the correct and valid explanation for how the Standard Model acquired its current structure, it’s no longer comprehensive and complete to say that there are “four fundamental forces” as we’ve so often said.

Instead, there’s a Higgs force as well. It isn’t so simple to measure this force as a push or pull between two particles, but it certainly exists and plays a role: weaker than the strong nuclear and electromagnetic forces, stronger than gravity, and perhaps somewhere more comparable to the magnitude of the weak nuclear force.

But that force is separate from the Higgs boson itself. The keys to remember when it comes to the Higgs boson is that:

• it begins from an unbroken, four-component scalar,
• when symmetry breaking occurs, those four components, or four degrees of freedom, lead to four scalar bosons,
• three of them combine with the electroweak sector, giving the massive W-and-Z bosons, where the remaining electroweak combination yields the photon,
• and then the last of those four degrees of freedom oscillates radially, creating the massive scalar particle known as the Higgs boson.

That’s as simple as I know how to make it without oversimplifying it in an incorrect way. I hope it helps you wrap your head around the Higgs boson just a little bit better! (And for more information and an additional perspective, I can recommend Matt Strassler’s excellent 2024 book, Waves in an Impossible Sea: How everyday life emerges from the cosmic ocean.)

Send in your Ask Ethan questions to startswithabang at gmail dot com!

This article is featured on Big Think.