Tuesday, December 13, 2011
Posted by Nic Eggert at 5:36 PM
Hi folks. It's been an embarrassingly long time since I last posted, but today's news on the Higgs boson has brought me out of hiding. I want to share my thoughts on today's announcement from the CMS and ATLAS collaborations on their searches for the Higgs boson. I'm a member of the CMS collaboration, but these are my views and don't represent those of the collaboration.
The upshot is that ATLAS sees a 2.3 sigma signal for a Higgs boson at 126 GeV. CMS sees a 1.9 sigma excess around 124 GeV. CERN is being wishy-washy about whether or not this is actually a discovery. After all the media hype leading up to the announcement, this is somewhat disappointing, but maybe not too surprising.
First of all, what does a 2 sigma signal mean? The significance corresponds to the probability of seeing a signal as large or larger than the observed one given only background events. That is, what's the chance of seeing what we saw if there is no Higgs boson? You can think of the significance in terms of a Normal distribution. The probability of the observation corresponds to the integral of the tails of the Normal distribution from the significance to infinity. For those of you in the know, this is just 1 minus the CDF evaluated at the significance. For a 2 sigma observation, this corresponds to about 5%.
For both experiments, there was a 5% chance of observing the signal they observed or bigger if the Higgs boson doesn't exist. In medicine, this would be considered an unqualified success. So why is CERN being so cagey? In particle physics we require at least 3 sigma before we even consider something interesting, and 5 sigma to consider it an unambiguous discovery.
The reasons why the burden of proof is so much higher in particle physics than in other fields aren't entirely clear to me. I suspect is has to do with the relative ease of running the collider a little longer compared to recruiting more human test subjects, to use medicine as an example.
Given what I've just told you that we need a 3 sigma significance in particle physics, why is everyone so excited about a couple of 2 sigma results? Well, the first reason is that both results show bumps at approximately the same Higgs mass. Although it's not rigorous, you can get a rough idea of what the significance of the combined results are by adding the significances in quadrature. This gives us about 2.8 sigma. Higher, but still not up to the magic number of 3.
The explanation for the excitement that is most compelling brings us to Bayesian statistics. The paradigm of Bayesian statistics says that our belief in something given new information is the product of our prior beliefs and a term which updates them based on the new information. Physicists have long expected to find a Higgs boson with a mass around 120 GeV. So our prior degree of belief is pretty high. Thus, it doesn't take as much to convince us (or me anyway) that we have observed the Higgs boson. In contrast, consider the OPERA collaboration's measurement of neutrinos going faster than the speed of light. This claims to be a 6 sigma result, but no one expected to find superluminal neutrinos, so our (or at least my) prior for this is much lower. (Aside: If the OPERA result is wrong, it is likely due to a systematic effect rather than a statistical one. Nevertheless, I stand by my point.)
The final thing that excites me about this observation is that what we've seen is completely consistent with what we would expect to see from the Standard Model. Forgetting about significances for the moment, when the CMS experiment fits for the Higgs boson mass, they find a cross section that agrees very well with that predicted by the Standard Model. In the plot below, you're interested in the masses where the black line is near 1. The ATLAS experiment actually sees more signal than one would expect. This is likely just a statistical fluctuation, and explains why the ATLAS result has a higher significance.
In conclusion, while CERN is being non-committal, in my opinion, we have seen the first hints of the Higgs boson. This is mostly due to my high personal prior that there the Higgs boson exists around the observed mass. Unfortunately, Bayesian priors are for the most part a qualitative thing. Thus, ATLAS and CMS are sticking to the hard numbers, which say that what we have looks promising, but is not yet anything to get excited about.
I'll close by reminding you all to take this all with a grain of salt. There is every possibility that this is just a fluctuation. I'll remind you that at the end of last summer, CMS and ATLAS both showed a 3 sigma excess around 140 GeV, which went away just a month later at the next conference. So let's cross our fingers that next year's data will give us a definitive answer on this question.
By the way, if anyone wants to know more, fire away in the comments. I'll do my best.