Science: Higgs decay and statistics

Atoms smashing in an atom smasher

The ATLAS Experiment reports about a possible decay route that is predicted for the Higgs boson in the Standard Model of the universe. It had not yet observed in huge atom smashers. Observation of the Higgs subatomic particle was first publicly announced on July 4, 2012. Higgs is the particle that gives almost all other particles their mass. Its discovery and verification cements the theoretical foundation of matter that forms us and everything we see around us in the universe. ATLAS writes:

Evidence for the Higgs boson decay to a 𝒁 boson 

and a photon at the LHC

The first evidence is presented for the Higgs boson decay to a 𝑍 boson and a photon, with a statistical significance of 3.4 standard deviations. The result is derived from a combined analysis of the searches performed by the ATLAS and CMS Collaborations with proton-proton collision data sets collected at the CERN Large Hadron Collider (LHC) from 2015 to 2018. 

Wikipedia comments on the statistics needed to satisfy physicists that something they observe is real and not a statistical fluke:  

To conclude that a new particle has been found, particle physicists require that the statistical analysis of two independent particle detectors each indicate that there is lesser than a one-in-a-million chance that the observed decay signatures are due to just background random Standard Model events – i.e., that the observed number of events is more than five standard deviations (sigma) different from that expected if there was no new particle. More collision data allows better confirmation of the physical properties of any new particle observed, and allows physicists to decide whether it is indeed a Higgs boson as described by the Standard Model or some other hypothetical new particle.  

To find the Higgs boson, a powerful particle accelerator was needed, because Higgs bosons might not be seen in lower-energy experiments. The collider needed to have a high luminosity in order to ensure enough collisions were seen for conclusions to be drawn. Finally, advanced computing facilities were needed to process the vast amount of data (25 petabytes per year as of 2012) produced by the collisions. For the announcement of 4 July 2012, a new collider known as the Large Hadron Collider was constructed at CERN with a planned eventual collision energy of 14 TeV – over seven times any previous collider – and over 300 trillion (3 × 10⁺¹⁴) LHC proton–proton collisions were analyzed by the LHC Computing Grid, the world's largest computing grid (as of 2012), comprising over 170 computing facilities in a worldwide network across 36 countries.

Woof! I thought the calculations could be done with fingers, toes and an abacus. Guess not. 

Anyway, as we all want to know, what does 1, 2, 3, 4 and 5-sigma level of statistical significance mean when translated into standard American? 

5-Sigma significance corresponds to a p-value, or probability, of 3 x 10^-7, or about 1 in 3.5 million.** Here, there is only 3.4-sigma significance for the observed Higgs decay into a Z boson and a photon. That means the researchers will need to collect a lot more data from this kind of decay in atom smashers to hit the 5-sigma goal.

** SciAm writes about the statistics of Higgs: This is not the probability that the Higgs boson does or doesn't exist; rather, it is the probability that if the particle does not exist, the data that CERN scientists collected in Geneva, Switzerland, would be at least as extreme as what they observed. "The reason that it's so annoying is that people want to hear declarative statements, like 'The probability that there's a Higgs is 99.9 percent,' but the real statement has an 'if' in there.

For context, the FDA approves new drugs based on a p-value of 0.05 or less, which is at least about 2-sigma significance. A p = 0.05 means there is a 5% chance that the efficacy found for a new drug is bogus or not real. Thus for every 20 new drugs at p = 0.05 the FDA approves, one of them is likely going to be ineffective. It would be better for the FDA to go to a more stringent standard, say about a 3-sigma standard, so that about only 1 in 100 new drugs are likely to be bogus. For more context, from 2013 through 2022, the FDA averaged about 43 new drug approvals per year.

This is what the raw data sort of looks like

Computers have to sort through it

By Germaine: The non-statistician