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Dec 13, 2011

Don't get your hopes up yet, Higgs

Today at CERN a public meeting is taking place for the ATLAS and CMS experiments to convey their latest/greatest results on the search for the Higgs boson.

I'll sum up for the audience: Nothing we have available is conclusive as to the existence or non-existence of the Higgs boson.

You can read some nice explanations from Lisa Randall at the NY Times today. If the CERN experiments do indeed find the Higgs boson, then Peter Higgs (whom the particle and mechanism are named after) and five others (Brout, Englert, Guralnik, Hagen, and Kibble) would have a pretty good shot at a Nobel Prize. However, neither CMS nor ATLAS observe anything that is "not consistent" with the prediction.

You may be a little confused, because we do have some inconsistency in our data with the background-only (i.e. no-Higgs) prediction, at the percent level (for the sake of argument, let's say it's 1%). You may be wondering why we're not considering this a discovery (for instance, if you predicted that the stock market was only consistent with predictions at the 1% level, we'd call that one of the biggest economic disasters in history of humanity). For physics, though, we have stronger requirements than that. Let me explain why.

The searches in question are all statistical in nature. I don't recall exactly who said this phrase, but particle physics is not like trying to find a needle in a haystack. It's worse than that. It's like trying to find a needle in a stack of identical needles. (Pop-culture reference in Saving Private Ryan). That is, you have to predict how many needles you would find of the type you're interested, and then count all the needles you observe. If the number you observe is larger than what you predicted, then you call it a discovery, even though all the needles look exactly alike and you can't tell which exact needles are the "new kind" and which are the "old kind". And at the LHC, there are a lot of needles to sort through, and different types of needles too!

You can see why this is hard ;).

So what does it mean that we don't have enough to say anything conclusive? It means that the predictions we have are consistent with the data we observe, but only barely. For particle physicists, probabilities like 1% or 0.5% are not really unlikely. The reason for this is the sheer number of "needles" we have to look at. This is familiar to all of you who play the lottery... your chances may be small for each day, but if you play many many days then your chances are increased by that factor. Eventually you've got to hit one, right?

It turns out that 1% probability of being consistent with the background is far more probable than winning the lottery (and someone wins the lottery pretty often!) so you can see why we look for something much more improbable, like a part in a million or even less.

So what does that mean for our Higgs hunters? Well, we're going to have to wait until next year to collect more data. The good news is, we expect that the amount of data the LHC will deliver will be more than sufficient to answer the question conclusively. But alas, patience is a virtue we must exercise at present.

6 comments:

Shripathi Kamath said...

We can conclude safely though that if they find it, Nobel Prize for Higgs.

And if they don't, do you think that the search of an alternative explanation for mass will intensify?

rappoccio said...

There's a huge number of models that already exist to explain the masses without Higgs (technicolor, extra dimensions, etc). In fact the only reason why Higgs is still so popular is because most SUSY models have a Higgs-like thing floating around. In any case we'll find out next year!

Bretta Applebaum said...

If you play the lottery each day your chances don't increase if you play each day: the chance of winning is not cumulative. It's not like the chance of getting laid the more you date. The probability of winning does not change just by playing the lottery more often. The chance of finding the object in a stack of identical objects is dependent on the ability to identify the factor that makes it what you're looking for, so it is observer-dependent, not dependent on the objects themselves.

rappoccio said...

Hi, Bretta,

The cumulative probability is increased, actually. If you play twice, you're twice as likely that at least one will win. Each individual trial has the same probability, but the total increases.

If p is the probability of winning, then the probability that you win >=1 in 2 trials you have

prob of getting 0 successes = p0 = (1-p)*(1-p)
prob of getting >=1 success = 1 - p0 = 1-(1-p)^2

So for the case of p=0.5, you have

p (>=1 success) = 0.75

Bretta Applebaum said...

Then I should probably play the lottery instead of trying to get sex, because that is not working.

rappoccio said...

Hehehehehe