Amir D. Aczel has been closely associated with CERN and particle physics for a number of years and often consults on statistical issues relating to physics. He is also the author of 18 popular books on mathematics and science.
By now you’ve heard the news-non-news about the Higgs: there are hints of a Higgs—even “strong hints”—but no cigar (and no Nobel Prizes) yet. So what is the story about the missing particle that everyone is so anxiously waiting for?
Back in the summer, there was a particle physics conference in Mumbai, India, in which results of the search for the Higgs in the high-energy part of the spectrum, from 145 GeV (giga electron volts) to 466 GeV, were reported and nothing was found. At the low end of the energy spectrum, at around 120 GeV (a region of energy that attracted less attention because it had been well within the reach of Fermilab’s now-defunct Tevatron accelerator) there was a slight “bump” in the data, barely breaching the two-sigma (two standard deviations) bounds—which is something that happens by chance alone about once in twenty times (two-sigma bounds go with 95% probability, hence a one-in-twenty event is allowable as a fluke in the data). But since the summer, data has doubled: twice as many collision events had been recorded as had been by the time the Mumbai conference had taken place. And, lo and behold: the bump still remained!
This gave the CERN physicists the idea that perhaps that original bump was not a one-in-twenty fluke that happens by chance after all, but perhaps something far more significant. Two additional factors came into play as well: the new anomaly in the data at roughly 120 GeV was found by both competing groups at CERN: the CMS detector, and the ATLAS detector; and—equally important—when the range of energy is pre-specified, the statistical significance of the finding suddenly jumps from two-sigma to three-and-a-half-sigma!
This means that if you pre-specify that the Higgs must be “light” (in the low end of the energy spectrum, as, in fact, the Standard Model indicates), the chance that the data bump is a fluke quickly goes down to 1 in 5,000, and the probability that the Higgs boson actually exists jumps from a little over 95% to more than 99.98%–an excellent probability. By convention, however, physicists demand a five-sigma level of proof for all particle discoveries, which means a probability of 99.99997%. Such strict standards of proof would require a lot more data. So, at present, we have only “hints of a Higgs” and we are still waiting for the final, five-sigma word on the Higgs’ existence. But as Rolf Heuer, CERN’s director general, put: “We’ll be open all next year…” So stay tuned.