Why Would Anybody in Their Right Mind Build the LHC?

In the comments following the silly accelerator poll, onymous wrote:

[T]he point of the LHC isn't to discover the Higgs. No one in their right minds would build a 14 TeV pp collider if their only goal was to discover the Higgs.

While it's true that the ultimate goal of the LHC is to discover more exotic particles that may or may not exist (blah, blah, supersymmetry, blah) most of the hype has focussed on the Higgs, which is the one thing they're pretty sure they'll find (comments later in that thread notwithstanding). This is one of the potential problems with the way the machine has been marketed, but that's a whole different topic.

I did want to pick up on one thing, though, that relates to this question in a slightly different way, and that's the big difference between the masses of the particles being sought and the machines that are used to look for them. Looking at the rumors that kicked this off, after all, they're talking about a Higgs boson with a mass of around 150 GeV. The Tevatron, where they're doing these experiments, already has an energy of around 2000 GeV (or 2 TeV), a full factor of ten bigger than the mass of the particle they're trying to create. The LHC, when it eventually reaches its full energy, will be another factor of almost ten bigger than that.

So, why do you need such a big accelerator to look for such a small particle? If the goal is just to have enough energy to create the Higgs by converting the energy of the colliding particles into mass (E = mc2, baby), why do you need more than a few hundred GeV?

There are lots of ways to answer this, but they mostly come down to one thing: while the colliding particles may have a huge amount of energy, you almost never get to use all of it.

Here's a classical analogy that, while not perfect, will get you the basic idea. If you've ever played pool, you know that it's possible to send the cue ball into a stationary ball (the eight ball, say, because I'm sure you're an excellent pool player, and are winning the hypothetical game) in such a way that the cue ball stops, and the eight ball moves off in exactly the direction that the cue ball was headed, at just about the speed that the cue ball had immediately before the collision.

Of course, if you've ever played pool, you also know that this is a little tricky to do. It's not impossible by any means-- even a mediocre player like me can manage it-- but it takes some care, especially if the eight ball is at the far end of the table. If you don't hit it exactly right, the eight ball will go off at a bit of an angle from the cue ball's original path, and the cue ball will keep moving along a path that's deflected in the opposite direction (the angle between the two will be very close to ninety degrees, as it happens).

When you hit the the shot perfectly, all of the kinetic energy of the cue ball (less a little bit that's carried off as sound, or converted into an infinitesimal increase in the temperature of the two balls) gets transferred to the eight ball. When you're a little bit off, the energy transferred to the eight ball is a bit less than the total, and the cue ball keeps some of its original kinetic energy. When the shot is a little bit off, the eight ball is moving a little slower than when you hit it correctly, and the cue ball is still moving a little bit.

Now, try to do the same thing with golf balls (you don't need to hit them with a cue-- feel free to just roll them with your hands). Golf balls are a lot smaller than billiard balls, and as a result, your aim has to be a whole lot better. It's very difficult to get golf balls to collide in exactly the right way to have the moving one transfer all of its kinetic energy to the stationary one-- most of the time, they'll hit at an angle, and both will be moving. The amount of the original energy transferred to the target ball will, in general, be less than that with billiard balls.

Now, imagine doing the same thing with protons. And you get some idea of what's going on.

This analogy is far from perfect-- for one thing, the collisions between billiard balls or golf balls are what physicists call "elastic" collisions, in which the kinetic energy after the collision is the same as the kinetic energy after the collision. These sorts of collisions happen with protons, too, but they're not particularly interesting. What particle physicists are after is the inelastic collisions, in which some of the initial kinetic energy gets turned into rest mass energy of new particles.

The basic idea, though, carries over. In order to convert all of the kinetic energy of the original colliding protons into rest mass energy of new particles, you would need to be incredibly lucky. The vast majority of the time, only a small fraction of the kinetic energy of the colliding particles will get turned into mass, with the rest of it remaining kinetic energy of the stuff that was already there.

That's why you need a 2000 GeV accelerator to look for a particle with a mass equal to 150 GeV. It's extremely rare to get 200 GeV worth of new stuff out of a 2000 GeV collision. I don't know a good estimate of this, but we're probably talking one-in-a-billion type odds, given the tiny bit I know about particle physics. (Anybody with actual knowledge, please let me know the real odds).

And that's also a big part of why the LHC has a much better chance of finding the Higgs than the Tevatron does-- the higher the collision energy, the better the chance of getting a given amount of new stuff. The odds of getting 10% of the kinetic energy out as new particles don't get any better, but if you increase the collision energy by a factor of ten, you only need 1% of the collision energy to create the particles you're after. That happens considerably more often, which means that a peak-performance LHC will see vastly more events with 200GeV worth of new particles than a peak-performance Tevatron (even if they both used the same number of protons in the beam, which they probably don't).

So, if you've ever wondered why they need huge accelerators to detect relatively light particles, that's (one of) the reason(s). At least, that's how I would explain it to the dog...

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They built the LHC because there's no multilateral bonding experience quite like burning an enormous amount of money on something that might make history. I wish it had anything to do with physics, but no. (Although, at the same time, it does give one a nice cosy feeling, of course, if one's inclined to like this sort of Union stuff.)

I forgot to say that, of course, you provided a wonderful description of why we'd like to burn our money in this specific way :)

Dear Chad,

you write that "most of the hype has focussed on the Higgs". That may be true but the physicists who were deciding what kind of a collider should be built and what it should be designed or able to do were not answering the question according to any "hype".

Hype may affect people who have no clue (and this set may include the people who may influence the existence and size of funding for physics in general) but the number of such people among the architects of particle colliders (who actually decide about their technical traits) is hopefully very small.

Your golf and billiard analogies have nothing to do with the reason why the protons' energies have to be an order of magnitude higher than the new particles that are gonna be found.

The reason is simply that the actual collision, as seen from the high-energy physics viewpoint, is not a collision of two protons, but a collision of two quarks or gluons or antiquarks that exist within these protons.

Because a proton contains 3 quarks - and it actually also contains some gluons and/or additional quark-antiquark pairs and their "effective number" grows with energy - a typical energy carried by one colliding quark or gluon is approximately 10 times smaller than the total energy of the proton. The latter is being divided among the partons.

That's why protons have to be much more energetic than the new particles that will be produced. This argument is only valid for composite particles such as protons: for example, LEP collided electrons and positrons (acronym!) and the center-of-mass energy was indeed 209 GeV at the top. But it was easily able to produce pairs of W bosons, among other things.

By the way, the 150 GeV Higgs produced with a bottom quark would be the "heavier CP-even neutral Higgs H" in a supersymmetric model. There's another rumor that the light Higgs "h", below 130 GeV and possibly near 115 GeV, has (also?) been spotted in the data.

Best wishes

Yeah, the billiard and golf ball analogy isn't doing it for me; is there not a better analogy that gets the real point across without being technical? Like, say you're colliding water balloons each containing a few golf balls, and the goal is to get the golf balls to recoil with most of the energy of the whole water balloon. That's a better model of hadron collisions.

I'm not an accelerator physicist, and I know there are a lot of technical obstacles to building a linear collider big enough, but I think if we really believed that the Higgs and only the Higgs needed to be discovered, the thing to do would be to build an e+e- collider that could scan in energy up to a few hundred GeV. (LEP may have even been good enough, given another year or two....)

The advantage of the LHC over the Tevatron is partly about higher energy, but a lot of it is also about luminosity. I think that again, if your only goal is to find the Higgs, 14 TeV is overshooting by a lot; a lower-energy collider that can reach higher luminosity than the Tevatron would suffice. Or just running the Tevatron longer.

I'm too young to have been around for all the detailed technical debates about what machine to build, but I'm sure that if people weren't reasonably confident that they would find something beyond just the Higgs, they would never have wanted a 14 TeV pp collider.

The LHC was built in the finest tradition of hypothesis driven science.

They had the hypothesis that they would find interesting physics in this energy range, so they set out to test it. If they don't find interesting physics, then their hypothesis will have been falsified and they can seek to test a different hypothesis, probably at a higher energy.

[I]s there not a better analogy that gets the real point across without being technical? Like, say you're colliding water balloons each containing a few golf balls, and the goal is to get the golf balls to recoil with most of the energy of the whole water balloon.

I try to restrict my analogies for ordinary people to situations that ordinary people might actually have seen happen.

It's not a perfect analogy by any means (and I ought to know better), but I think it gets the key idea across, which is that when you collide objects with some structure-- whether it's the extended size of billiard or golf balls or the composite nature of hadrons-- you're much more likely to get something less than the total energy out.

I don't think people really understand that the vast majority of the time you shoot protons at one another, nothing happens. And even when something does happen, the vast majority of the time, you don't get all 2 TeV worth of energy out as new particles. That's the aspect of things I'm trying to get at, here.

Because the cross-section for Higgs production rises with increasing energy, faster than the QCD background.

Well, except that top is also way way bigger at LHC than Tevatron, and tends to be a background for many things.

The Leek theory of particle physics: "The harder you hit something, the more pieces you get."

I like the analogy! It works well to get the key concepts across. One of the things I like most is that it combines qualitative and quantitative reasoning. Nice work!

The comment @3 beat me to it, but not realizing that the protons aren't the actual "colliding particles" isn't your only error. These are colliding beams, so it is more like a cue ball and an 8 ball being hit towards each other, not hitting one at rest.

A better analogy would be pointing two shotguns loaded with buck shot at each other and looking for a di-bullet like they found on the Shiloh battlefield, IIRC. Lots of misses, and lots of crap flying off to the side that is of little interest but mucks up the detector. Few direct hits and those hits will never have more than a fraction of the total energy put out by the two shotguns. Also, since the individual particles do not all come out with identical speeds or directions, you can't guarantee a true head-on collision resulting in zero velocity afterwards.

Also, at the Tevatron, the two projectiles are anti particles so some of the quark collisions can look like ideal annihilation collisions where all of the mass energy of that pair goes into new particles (or pairs of particles). That is not the case at the LHC. None of these are as clean as e+ e- collisions, however.

As CCPhysicist was getting at in 12, we have to worry about the conservation of baryon number. We are colliding two protons, our baryon number is 2, so we must get two baryons back in addition to whatever higgs or other new particle is produced.

Also, adding to the Higgs-search reasoning, and along with the comment @5, I wanna mention too that there are predictions of Higgs masses by various papers and authors essentially allowing for a pseudo-continuum of possibilities, with a low-end prediction of ~120 GeV and a high end reaching 2 TeV (and even one outlier at 10^18 GeV)! There's a paper which exists simply to list these here: