Tomorrow, CERN will be webcasting a talk on the latest results in its search for the Higgs boson, a particle that is theorized to provide other particles with mass. The director of CERN has gone on record as saying there won't be any announcement that we've definitively discovered the Higgs, nor will there be any statement indicating that we've completely ruled out its existence. Still, expectations are high that we'll find some signal indicating the Higgs is probably at a specific mass—rumors have it near either 120 or 140GeV.
Even as the webcast proceeds, science writers everywhere will be scrambling to explain the results. We thought we'd get a jump on things and give you an explanation of what exactly the scientists at the LHC's two general-purpose detectors, ATLAS and CMS, are looking for, and why it's so hard to be certain about what they've seen.
To create the Higgs (and all the other particles it produces), the LHC smashes high-energy protons together, which converts some of that energy to mass. This will produce a spray of particles, many of which are unstable and also decay. By the time anything reaches the actual detector hardware, it's often several decays removed from the particles produced in the actual collisions. Researchers try to use the particles that reach the detectors to work their way back and infer the particles that decayed to produce them.
Theoretical models of the Higgs indicate it has several ways of decaying; one example is by producing two high-energy photons. The problem is that many other processes can also produce two high-energy photons. How do you tell when you're looking at the product of the Higgs? The short answer is that you figure out all the other things that can produce a Higgs-like signal, and the typical frequency at which they will occur. If you see more of these signals than those frequencies suggest, then you know you have something that looks like the Higgs.
But we can't just accept any excess of signal as being a sign of a particle; many events are probabilistic, so there's always a chance of an excess of events occurring at random. How do we know when we've got enough signal to confidently say we've seen the Higgs?
Rolling the dice... over and over again
The easiest way to explain this is by analogy. Imagine you're rolling a set of 60 dice. Most of them are normal, but you suspect one or two are unusual—they have the same number on all of their faces. For example, you think that they have five on each of their faces, so you get that every time you roll them. But there's a problem: you can't look at the dice (just as the detectors can't look at the Higgs directly, just at its decay products). It's still possible to know whether your suspicions are correct, though—the trick is to roll your set of 60 enough times, and track the results.
If you rolled the entire set once, you'd expect most of the numbers to show up in the results about 10 times. But you wouldn't expect exactly 10. Since it's a random process, you might see a dozen ones, nine twos, and so on. Even if your all-five die was present, there's still a chance you'd see less than 10 fives rolled. You can measure the amount of variation around your expected result of 10 with a statistical value called the standard deviation. And, in this example, even if your unusual dice were present, the signal from them—the number of fives you rolled—would probably be within a standard deviation of what you'd expect from a purely random set.
So you roll the whole set again. And again. With each roll, the standard deviation should shrink relative to the total number of rolls, as the random fluctuations from chance start to cancel each other out. And, if your special dice are present, you should start to see an excess of fives that stands out from the random noise—it may end up two or more standard deviations away from what you'd expect. Statistically, we know that there's a 95 percent chance that any random result will be within two standard deviations of your expected one. But that still leaves a five percent probability that a two standard deviation signal is the result of chance. Not good enough for what may be the LHC's most important find. So you keep rolling.
As you get more and more rolls, one of two things can happen. In some cases, you may find that the results are so close to the expected value that finding a signal there would be very unlikely—you may end up needing to roll 500 twos in a row in order to get a signal more than two standard deviations away from the expected value. This lets you rule things out. In this example, we can safely say that, if there is a funny die in our set, it doesn't have twos on every face. The other thing is that real signals should end up being easier to distinguish from random background—they should be a greater number of standard deviations away from the expected value.
Photon, boson, or what?
So, back to particle physics. For a given energy, it's possible to estimate the number of events of a given type—two photons, a W boson and a jet, etc.—that you would get from processes we already know about. And you can measure the number of events of that type you actually see. By comparing the two, you can tell whether the events you see are a standard deviation or more away from the expected result. Or you can see whether the value is so close to what you expect that you can safely say the Higgs isn't at that energy.
Last year, ATLAS and CMS recorded a number of events at various energies where we think the Higgs might be hiding. For the most part, these have been around the number of events we'd predicted. At this point, it's extremely unlikely that we'll see a sudden excess there—we're not going to do the equivalent of rolling 100 twos in a row—so physicists have concluded that we can exclude these energies as location of the Higgs. But there are some areas, mostly in the 120-140GeV range, where things are ambiguous. There are hints of a signal, but the signal is within two standard deviations from the expected background.
Now, we've got significantly more data—thanks to an impressive run this year, we've got an amount of data that it took the Tevatron decades to produce. The teams behind the two detectors are expected to have processed a lot of it to look for a signal. Expectations are that one has risen to about three standard deviations (this is commonly called a "three sigma" signal) from the background of standard model events. Three sigma is considered to be "evidence" for the existence of the Higgs. It takes up to five sigma before anyone is willing to declare discovery, and nobody expects that we will have that level of certainty for a while yet.
We'll know whether any of those rumors are accurate by this time tomorrow. Stay tuned for our coverage.
Listing image by Photograph by Anders Adermark
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