The Higgs field: so important it merited an entire experimental facility, the Large Hadron Collider, dedicated to understanding it. This mysterious field is on average non-zero, suffusing the universe almost like an invisible fluid, affecting the masses of the known elementary particles. What if it were zero on average instead? What would the world be like then?
Well, it would be lethal for us — atoms wouldn’t exist —- but in a certain sense, it would look much simpler, and much better organized. Let’s see how.
Take Fig. 2 from this earlier article about the known particles [which I recommend you read first, if you haven’t already.] This figure shows the known elementary particles of nature (plus the conjectured Higgs of the Standard Model) and the lines indicate which particles directly affect one another. You see three of the four known forces of nature (gravity is left off to avoid clutter): the strong nuclear force (with gluons as force carriers), electromagnetism (whose force carrier is the photon) and the weak nuclear force (with W’s and Z as force carriers). And you see that the neutrinos, charged leptons and quarks do not interact directly with one another; they are directly affected only by the force carriers. And finally, the Higgs field, which is non-zero in our universe [you might want to look at these video clips for more info], and is indicated by the green swath, affects all of the known massive elementary particles, and in fact is responsible for making them massive.
Now compare this with Fig. 3, which shows what the world of particles would be like if the Higgs field were zero. Look closely. You’ll see many differences! [In a little while we’ll see where some of them come from.]
- Instead of the electromagnetic and weak nuclear force present in our world, with its non-zero-Higgs-field, a zero-Higgs-field world has these forces scrambled and rearranged. The rearranged forces are called hypercharge and isospin (for historical reasons; the names are just that, names, without other significance.)
- As part of this scrambling, the force carrier particles are changed; there are 3 W particles and an X particle, and the Z0 and photon are missing. And the W and X particles are all massless now.
- The force carriers are now simpler in another sense. The photon affects the W+ and W– particles directly; you can see that in Fig. 2, where they are connected by a purple line. But the X particle does not directly affect any of the three W particles. The gluons affect themselves as before (the red curved line); the W’s affect themselves too; but the X particle affects no force carriers at all.
- For every matter particle (except neutrinos) there are now two particles with the same name. But they’re different, as different as Arnold Palmer and Arnold Schwarzenegger. Physicists (for complicated reasons) have several naming schemes for them, but a top quark by any name would smell as sweet — so for current purposes I’ve indicated them as different by rotating one to the left and one to the right. We can call them top-left and top-right. [This happens in fact to be one of the naming schemes physicists use and it does have a bit of an underlying meaning, but it’s best to just view these as names.]
- Notice that the left-particles all come in pairs, one pair for each generation (a term defined here), and are affected by the isospin force. The electron comes with the neutrino-e (or “electron-neutrino”), the up quark comes with the down-quark, etc.
- But the right-particles come singly, one for each generation, and are not affected by the isospin force.
- There are only neutrino-lefts; there are no neutrino-rights.
- In Figure 1, I used the labeling neutrino-1, neutrino-2 and neutrino-3 for the neutrinos, but in Figure 2 I use labels that correspond to the names “electron-neutrino”, “muon-neutrino”, and “tau-neutrino”. This is a subtlety you can ignore unless you are really interested in it, in which case you should read this article.
- All of the particles shown are massless — except for the Higgs particles, of which there are four! (That’s a minimum; the Standard Model, in which one assumes the simplest possible Higgs fields, has four, but the full story could be more complicated.)
How did the non-zero Higgs field alter this simpler and better-organized (but uninhabitable) world and turn into the complicated one that we live in (Fig. 2)? It all has to do with how the Higgs field interacts with the isospin and hypercharge force carriers and with the matter particles. How this works for the top quark, as an example, is sketched in Figs. 4 and 5. The top-left quark and the top-right quark interact strongly with each other and the Higgs particle… and not with other matter particles. In particular, if a top-left quark encounters a Higgs particle, it can turn, with high probability, into a top-right quark. Once the Higgs field is non-zero, this type of interaction causes the two versions of the massless top quark to become a single massive top quark, with a large mass.
This linking of the top-left and the top-right is not to be confused with the binding of two particles into a composite object, as a proton and an electron are bound together by the electromagnetic force to form a hydrogen atom. It is a different kind of combining, in which two elementary particles are mixed together into a single elementary particle.
How does this work? Fig. 5 shows a sketch. When the Higgs field is not zero, a top-left particle would travel at the speed of light, alone. The same would be true of a top-right. But when the Higgs field is not zero, its presence, and the fact that it has a direct interaction with the top-left and the top-right, forces the top-left to convert over to a top-right, and back again. How often does this happen? About a 100 trillion trillion (100,000,000,000,000,000,000,000,000) times a second. This conversion process makes it impossible for us to think of the top-left and the top-right as separate particles, because they are inextricably linked together; if you have one, you will very soon have the other. (You never have both at the same time, which is why the top quark remains elementary, not composite.) We call this mixture of these two particles the top quark, collectively. And the non-zero Higgs field, whose presence causes the flipping back and forth between top-left and top-right, endows this mixture with an additional intrinsic energy, even when it is sitting still. That intrinsic energy is indistinguishable from mass-energy (E=m c-squared energy); it behaves the same way in experiments. In other words, what we call the mass-energy of the top quark is really, if you prefer, the energy it picks up when sitting in a non-zero Higgs field. Take the Higgs field away — make it zero — and the top quark goes back to being two separate massless particles, the top-right and top-left.
The same phenomenon makes the electron massive too, but the interaction of the Higgs field with the electron-left and the electron-right is very weak, and so the electron, in the presence of a non-zero Higgs field, is massive but still relatively lightweight. The flip-flopping between electron-left and electron-right happens only .000003 times as frequently as for the top-left and top-right, and it follows (from a little bit of mathematics) that the electron mass is .000003 the mass of the top quark.
All the other quarks and charged leptons get their masses in a similar way. The stronger the interaction of the left- and right- object with the Higgs, the larger the mass that results for the mixed object when the Higgs field is non-zero.
What about the force carriers? The Higgs does not affect the gluons, but it rearranges the isospin and hypercharge forces, making the photon out of a mixture of the W3 and X, the Z0 out of a different mixture of the W3 and X and the Higgs particle called the A0, and the W+ and W– out of mixtures of the W1, W2, the H+ and H–. [Warning: very small white lie here, a technicality important mainly for experts; will fill this in in a supplementary post.] This process, called the Higgs Mechanism, makes the W+, W–, and Z0 massive, leaving the photon massless.
Aha!! So that’s how a non-zero-Higgs-field world ends up with 1 Higgs particle (the h) whereas a zero-Higgs-field world has 4, the H+ and H–, A0 and H0. Similarly to the mixing of top-left and top-right to make a massive top quark, the three extra Higgs particles end up mixed with the three mixtures of the massless W’s and X particles to make the massive Z0, W+ and W–!
A force whose force carrier is massive turns out to be ineffective at long distances, and this is why the weak nuclear forces seem so weak to us. If the Higgs field were zero, the isospin and hypercharge forces would all be comparably strong. Instead, our world has a rather strong electromagnetic force with a massless photon as carrier, and a weak nuclear force that is so weak that our daily lives are little affected by it — although admittedly it is essential in the internal furnace of stars, including the sun!
The reason that the world looks so complicated, with all those particles with wildly different masses, is partly that the Higgs field and Higgs particle interact with the different matter particles with such different strengths. The problem of diverse particle masses thus is actually a problem of their diverse interaction-strengths with the Higgs field/particle. Why are these interaction strengths so very different? There is no consensus as to the answer to this question (which particle physicists call the “flavor problem” — referring to electrons, muons and taus as different charged-lepton flavors, and similarly for quark flavors). We hope the Large Hadron Collider might give us some insights here, but there is no guarantee that it will.
A loose end — how did the neutrinos get their masses?! The answer is that we’re not entirely sure. One possibility is that there are in fact neutrino-right particles in nature — these would be very difficult to produce in experiments because they are not affected by any of the three forces shown in Figs. 2 and 3 — and the mechanism for giving neutrinos mass is the same as for the other particles. A second possibility is that neutrino-left particles get their masses from an indirect effect involving the Higgs particle — an effect which is not an option for the other particles. This second option is favored by many of my colleagues because it naturally would explain why the neutrinos are all so much lighter than the quarks and charged leptons. But this is a long story…
I’ll end with an important point, one which I hope you’ll find interesting. Many people (including aspiring physicists) assume, when they first encounter the story of the Higgs field, that it must be connected with gravity, which also engages heavier particles more strongly than lighter ones. Gravity pulls on top quarks harder than it pulls on electrons, and so do Higgs forces. But experienced physicists reject this notion. Why?
The point is that for gravity there are no exceptions — gravity always pulls on particles proportional to their masses. (Actually that’s itself a misconception; gravity pulls on things proportional to their energies. In daily life, any object’s energy is dominated by its mass-energy, E = m c-squared, so for rocks, people and stars, energy and mass are in almost exact proportion to one another. But gravity also bends starlight! If gravity only pulled on mass, then it wouldn’t pull on light, which consists of massless photons.)
By contrast, only those particles that get their masses from the Higgs field have a relationship between their masses and the strength of their interactions with the Higgs. In particular, as you can see in Figs. 3 and 7, the Higgs particle itself does not get all of its mass from the non-zero Higgs field — and the strength of its interaction with itself is not directly related to its mass. [There is a correlation, but not proportionality.] This is not unusual. In other articles on this site, you will see many other examples of conjectured particles, such as those that arise in the speculative theories known as supersymmetry and as warped extra-dimensions, that get their masses in other ways.
So the link between gravity and energy (and thereby mass, in daily life) is absolute, while the link between the Higgs and mass is likely to be true only for the known elementary particles, and may not be true for other elementary particles yet to be discovered — and is not even true for the Higgs particle itself.
In other words, any resemblance between the Higgs field and gravity is purely coincidental!