I have been promising for a long time to talk about what the LHC experiments are looking for, if not just the Higgs boson. There’s a tremendous amount of material available on this, but I am not going to look up or link to any of it; this will give you, at least, a snapshot of what I know and how I think about it. If any theoretical particle physicists read this and feel the urge to slap their foreheads in anguish, I invite them to consider this an interesting study in how much information experimentalists actually retain from classes and seminars.

**Edit (June 29, 9:30 EDT):** As you might expect given the above, I made some oversimplifications and at least one outright error, which have been kindly pointed out by theoretical physicists in the comments. For one mistake — mixing up two different kinds of extra dimensions — I have made some corrections with strikethroughs and italics in the appropriate section of the text.

To discuss what the LHC experiments are looking for, we need to understand what problems there are in our current understanding of particle physics — in other words, what makes us believe there ought to be any new particles at all? The strongest case is for the Higgs boson or something like it; it plays a critical role in the behavior of the weak force and the masses of the associated W and Z bosons, which we already know behave *exactly* the way we would expect if there were a Higgs boson. You might ask what happens if the W and Z boson masses and interactions are just a coincidence, and they just *look* like a Higgs Boson is involved, but actually there’s no such thing — the answer is that the Standard Model of particle physics becomes mathematically inconsistent, and makes senseless predictions at energies the LHC will investigate! So there has to be something to make the theory behave. However, that doesn’t mean there’s exactly one “Standard” Higgs boson, an issue I’ll get back to.

The next best clue to new physics — or the next biggest problem with what we know now, if you’d rather think of it that way — is called the Hierarchy Problem. This is expressed most easily as the question, “why is gravity so much weaker than other forces?” However, because the strength of each force changes as the energy of interactions changes — at different rates for different forces — we particle physicists prefer to frame the problem in terms of this question: “why are the W, Z, and (apparent) Higgs boson mass energies so much smaller than the energy at which the gravitational force becomes strong?” If we take the Standard Model as the complete picture as far as we can, so that we assume there’s nothing for the LHC to find except the Higgs Boson, then the “desert” between the Higgs boson mass energy and the energy where gravity beccomes strong is a factor of about 10,000,000,000,000,000! That’s aesthetically displeasing, but it’s actually worse than it sounds at first. The reason is that the Standard Model has to include the effects of quantum fluctuations on the masses of particles — and the fluctuations have to be allowed to have any energy up to the energy where the Standard Model “breaks down.” If the Standard Model works up until a theory of Quantum Gravity (for example, String Theory) kicks in, then we have to allow energies up to where gravity is strong — that factor of 10,000,000,000,000,000 really hurts, because the quantum fluctuations force the Higgs boson to have a much higher mass than it needs to for the theory to work! Here are some solutions to this problem:

- The Higgs Boson has a “bare mass” — i.e. the mass it starts with before quantum fluctuations — that is very large and
*negative*, and cancels out the quantum fluctuations almost perfectly. This is allowed, but seems rather implausible.
- The quantum fluctuations get cancelled out because of new particles whose effects balance out the old ones. This suggests Supersymmetry, in which every existing particle has a supersymmetric partner, and the pair’s effects on the Higgs Boson mass do indeed cancel.
- There isn’t really a Higgs boson. Instead, there is a new force with a new set of particles that “pair up” to
*act like *the Higgs boson at low energies. These are called Technicolor theories, because the new force looks a lot like the “color charge” found in theories of the strong force.
- Gravity isn’t really as week as it seems. Instead, it appears weak because it spreads out in several extra spatial dimensions that are curled up on themselves. These dimensions would be something like a millimeter in size at most, but are called “Large Extra Dimensions” because they’re pretty big compared to the size of most things in particle physics. So gravity would spread out in these dimensions, making us think that it’s so weak that it only becomes as strong as the other forces at very high energy — but actually it would surprise us by being strong at much lower energies, maybe even LHC energies. This would mean that the range of energies allowed for quantum fluctuations affecting the Higgs Boson mass would be greatly reduced — if we want them to be “small enough,” that strongly suggests that gravity becomes strong at energies the LHC can investigate, and we can expect all kinds of new particles and phenomena.

I know that reasoning is rather complicated, but hopefully you’ll retain at least this basic idea: starting just by asking why gravity is so weak, and following the reasoning of our current theories of particle physics, we get that something very strange is going on with the Higgs boson — and the only way to fix it is to appeal to an amazing numerical cancelletion, or to make a change to our understanding of particle physics. And most changes we can make turn out to add a bunch of new particles, at energies right around the mass of the W and Z bosons, or just above them — in other words, exactly the energies the Large Hadron Collider will explore!

Let’s look at these new ideas in more detail.

- In Supersymmetry, we have a new particle for each existing fundamental particle. We know they’re all as heavy or heavier than the particles we’ve seen before, because otherwise they would have shown up in previous experiments, but they also can’t be too heavy or they won’t cancel those quantum fluctuations properly. So we’ll see some new particles decaying into particles we know — and maybe into a non-interacting Lightest Supersymmetric Particle, which might turn out to be dark matter (a nice bonus)!
- If there are Large Extra Dimensions, then we would effectively see new particles also. This is because an ordinary particle that was moving in a circle around such an extra dimension would appear, in our three dimensions, to have its energy of motion “acting like” mass energy. Motion in the extra dimension would only be allowed at certain speeds — for essentially the same reason that Hydrogen atoms only have certain energy levels, if you remember that from chemistry — so we would see familiar particles, but with a certain amount of apparent extra mass, and then another “copy” with the same amount of extra mass added again, and so on. This would actually be pretty hard to distinguish from Supersymmetry, except that where in Supersymmetry the new partners always have different spin from the original particle, in this case they’d have the same spin.
*All of that is right for a different kind of extra dimensions, but rather than get into that, let me just put down what we’d actually see for Large Extra Dimensions. It’s fun too — basically, because gravity will be strong at the LHC, we’ll be able to directly explore whatever theory unifies gravity with the other forces. This could result in some very dramatic objects, including microscopic black holes. (To be reminded why we know that such black holes cannot be dangerous, whatever their properties might turn out to be, click here.) Black holes would decay into all kinds of things, making spectacular events in our detectors, and could actually be one of the easiest things to find if they’re light enough!*
- If there’s technicolor instead of a Standard Model Higgs Boson, the LHC experiments might have a pretty big challenge. The new particles might be too heavy to produce, and only through careful and detailed study of certain interactions would we get indirect clues about what was going on.

This is hardly a comprehensive look at all the the issues woth thinking about that might require new theories and new particles, but it perhaps gives you a bit of an idea of the possibilities that are out there. Personally, I wouldn’t bet on any particular theory — but there are common features to new theories that make some kind of new “zoo” of particles at LHC energies a very real possibility. Of course, finding all those new particles would raise all kinds of new questions; first we’d ask what theory described the new particles, and then there are all sorts of questions to ask about the new theory. (For example, in Supersymmetry, we’d have to ask why the new particles are so much heavier than the ordinary particles they’re paired with.) But answering old questions, and finding new ones to ask, is a particle physicist’s idea of heaven — it helps us understand a little more of the universe, and gives us lots more work to do!