What's the Matter with the Higgs Boson?S

The search is on for the Higgs boson, and it seems likely that soon we'll find this mysterious particle that creates matter in the universe. But what if we don't? In this week's "Ask a Physicist," we'll find out.

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The Higgs boson has the unique distinction of being the only particle in our standard model of particle physics that we haven't yet discovered. We may be on the verge of detecting it in the next few years, and yet, for some reason, almost nobody has asked anything about it, even though I've been chomping at the bit to write about it.

Luckily, a former student of mine, Bailey McCreery, decided that he just needed to know:

If the Higgs boson is found to exist, how would it change the way we understand mass? If it's not found, where will that leave us?

This is a big, fairly complicated question. To answer it, I'm going to have to explain what the Higgs actually does, and why we expect to find it. If you want, you can content yourself with saying, "The Higgs particle gives other particles mass," and skip to the last section, and I won't think any the worse of you. Others might, but I won't.

I also warn you that I'm going to say almost nothing about history. All I want to mention is that a bunch of people independently came up with similar ideas for what we now call the Higgs Boson in the 1960's, including Peter Higgs. We're not going to correct the historical injustice of scientific naming here, but if you want to read all about it, the good folks at Wikipedia have got your back. I'm also not going to get into the details of how the big accelerators work or how we actually figure out if we've detected a particle, though I'd be happy to answer that sort of question in a future column.

Most importantly, though, I need to say a thing or two about...

Particles, Fields, and Waves

If you know one thing about quantum mechanics, it's that particles have both wave and particle properties. But today we'll talk about high energy interactions, and that means talking about "fields." You might suppose that fields and waves are the same; they are not. You see, with a quantum-mechanical wave, the assumption is that there is just a single particle, and we're describing the probability of finding it in one place or another. With fields, particles pop into and out of existence constantly.

What's the Matter with the Higgs Boson?S

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The best known field is the electromagnetic field. A little chunk of that field is the particle called the photon, although you may know it as "light." Every particle has a corresponding field, and the standard model tells us a lot about how they work.

Besides the photon, I need to introduce three other force-carrying particles: the W+, W-, and Z0 bosons, and their corresponding "weak fields." The weak force controls, among much else, nuclear fusion in the sun and neutron decay.

The Higgs is also going to be both a field and a particle. The Higgs field is everywhere, giving mass to other particles, but since the Higgs boson (the particle itself) is so massive, it can only be created in high energy accelerators, and even then it only lasts a very short time before decaying into heavy particle-antiparticle pairs.

What's the Matter with the Higgs Boson?S

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Where the fields come from

The bewildering thing about the standard model is that it seems to be an incredible hodge-podge of lists and rules that seem to have no real connection to one another. The amazing thing, though, is that there's a very deep set of symmetries that (if you are a good guesser and know a crapload of math) would allow you to derive most of the rules of the standard model basically from scratch.

I know you know what symmetry means, but humor me. A symmetry is something that you can do to a system that somehow leaves it in the same condition in which it started. A simple symmetry might be moving every atom in the universe 10 feet to the right. Supposing you did it to absolutely every atom, no one could ever know the difference. That sounds like no big whoop, but to a physicist, it means that we have conservation of momentum.

In my article on the fine structure constant, I casually explained how we can derive all of electromagnetism. Suppose that the dynamics of all the particles in the universe stay exactly the same if you magically were to change the phases of all of the quantum mechanical waves. This transformation is called local U(1) gauge invariance. I would recommend trying to work that into conversation. The problem is that if you go around changing all of the phases, somebody's going to notice. There are extra terms in the dynamics equations. The simplest way to get rid of those extra terms is to add in a new field to cancel it — the photon field.

The cool thing is that this new field has all of the properties that we want in a real-world photon: it's massless, chargeless, and can be polarized, just like what we actually observe.

We can try this same trick with more complicated transformations. For instance, in the weak force, electrons and neutrinos behave exactly the same way. What if we imagine switching all electrons for neutrinos and vice-versa? If you want the fancy term for this, it's called local SU(2) invariance.

In order to make the extra terms cancel, we end up with three new fields, one with a negative charge, one with a positive charge, and one neutral, exactly as we see. On the other hand, this simple model also predicts that the W and Z bosons will be completely massless, which is most certainly not the case. The W bosons are both about 86 times the mass of a proton, and the Z boson is about 97 times as massive as the proton.

What's the Matter with the Higgs Boson?S

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The Higgs, finally

So here's the idea: at very high energies (like in the first 10-12 seconds after the big bang) electromagnetism and the weak force were exactly the same. They were unified into a single force, called "electroweak," consisting of 4 particles/fields (the W's, Z, and the photon). Meanwhile, there was another field hanging around: the Higgs.

In those early days, the temperatures were so high that the Higgs field hung around in what's known as a "false vacuum energy" state. I'll explain why this is important in a moment, but you should think of this as standing on top of an icy hill. If you balance just right, you can stay up there for a while, but eventually, you'll go sliding down to the bottom.

At the bottom of that hill — at the "true" vacuum energy — two things happen. First, the Higgs gains mass, and a lot of it. The reason is that Einstein's familiar equation can be re-written in a very telling way:

m=E/c2

In other words, just as mass can be turned into energy, the energy of interactions can turn into mass.

Secondly, the Higgs couples to the electroweak field. What "coupling" means in this case is that there is an interaction energy between the Higgs field and the electroweak field. And with energy comes, you guessed it, mass.

This coupling may be a bit confusing, but I think it's better than the "molasses" analogy that is sometimes used. According to this, the Higgs field is like a giant pool of molasses and as particles move through it, they acquire a resistance to their motion — just like mass! But you try swimming through molasses. You'll continually slow down until you come to a stop, and you know that's not how particles really move. If you remember one thing from your high school physics class, it's probably Newton's old (and still true) "Objects in motion stay in motion..."

The Higgs gave three of the four electroweak particles mass, and not just any old mass. Working through the details, it turns out that this theory predicts a very specific ratio, that the Z should be about 113.5% the mass of the W's. And when they were discovered in the early 1980's, that's exactly the ratio that we found.

Another hint that we have that we're on the right track, is that this mechanism tells us approximately how massive the Higgs should be. At the moment, between the theoretical constraints and those ruled out by the Fermilab Tevatron, the Higgs is presumably somewhere between 122-168 or 187-197 times the mass of the proton.

If it exists.

What's the Matter with the Higgs Boson?S

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And if we don't find it?

Personally, I'd be willing to put down cash money that the Higgs is real. The standard model has done a spectacular job in predicting the form of the forces, and especially the ratio of the W and Z particles. It's hard to imagine a scenario in which we are just that far off base (but somehow managed to make such ridiculously good predictions). But suppose we are?

For one thing, the standard model as we know it would have to be thrown out the window. I don't doubt the resilience of theoretical particle physicists. Certainly, there are theories abounding which have more than one Higgs. There are non-standard theories that can account for much more massive models than we can currently probe even in the LHC. But I personally think it would be a disaster for the standard model.

There are also lots of things that discovering the Higgs won't answer. It doesn't explain dark matter, for example. While it explains where the masses of the W's and Z's come from quite nicely, it doesn't really explain why the other particles have the masses that they do, although the assumption is that they, too, have to couple to the Higgs field.

And while the Higgs may explain where mass comes from, it doesn't explain where gravity comes from. At the moment, our best theory for gravity is general relativity, but we're a long way off from figuring out a Theory of Everything that unifies gravity with the other forces.

Finding the Higgs also wouldn't explain why the universe has the symmetries it does. I mentioned a few buzzwords, U(1) and SU(2), above, but to be perfectly honest, we have no idea why the universe has these symmetries and not others. This list is far from complete. In the "User's Guide" we make a long list of the things that we still really have no idea about. I won't spoil the surprise here.

I bring up all of these limitations to point out something important. You'll occasionally read a comment by a physicist saying that in many ways it would be more interesting if we didn't find the Higgs. The implication is that if we do find it, then we'll have solved all of the big mysteries. I respectfully disagree. We've still got a lot of work to do to figure out how the whole puzzle fits together, and it would be really nice to finish up this particular piece.

Dave Goldberg is the author, with Jeff Blomquist, of "A User's Guide to the Universe: Surviving the Perils of Black Holes, Time Paradoxes, and Quantum Uncertainty." (follow us on twitter, facebook or our blog.) He is an Associate Professor of Physics at Drexel University. Feel free to send email to askaphysicist@io9.com with any questions about the universe.