Thursday, July 5, 2012

The hunt ended. Let's eat the prey.

The discovery of a "resonance" with a mass of ~125 GeV that may well be the Higgs boson, the missing piece in the Standard Model (SM) puzzle, has finally been announced by the ATLAS and CMS collaborations at CERN.
The (experimental) hunt started in 1989 at CERN with the Large Electron-Positron (LEP) collider and ended in the same place, but with the Large Hadron Collider (LHC), 23 years later.
For those of you interested in details, slides from the presentations given by representatives of the collaborations can be found at

What follows may not be technically entirely correct but it is meant for people not working in particle physics to have an idea of how results are produced. Still a basic understanding of statistics is required.
For consistency, only results from ATLAS will be shown, however the reader must be aware that very similar plots have been released by CMS.

The SM is a very successful theory, tested up to an extraordinary level of precision in a variety of physics processes, which describes the interaction of fundamental particles (gravity excluded). The SM formulation is based on particular symmetries of the space-time. Unfortunately, in order to satisfy these symmetries, all the particles in the theory are required to be massless! This obviously clashes with what we see around, atoms, made of protons, neutrons and electrons clearly have a mass. Therefore, various mechanisms have been hypothesize over the years in order to allow for non-zero masses, or, in other words, for the initial symmetry to be broken.
A particularly elegant mechanism, the Higgs boson mechanism, was introduced by Peter Higgs in 1964. In its simplest form the mechanism can explain the masses of the known elementary particles with a small price to pay in terms of complexity of the theory: the introduction of only one extra, massive, spin 0 particle, the Higgs Boson.
In science, the simplest solution of a problem is often the correct one, hence the Higgs mechanism has been "adopted" by almost all the particle physics community as one of the "mainstream" physics theories to test. This pushed researchers from all over the world to join their efforts and make more and more powerful particle accelerators, to prove the existence of the Higgs boson.

Within the standard model framework, the probability of the Higgs undergoing a decay into certain particles (branching ratios) can be precisely calculated as a function of its mass, as summarised in the following plot
Branching ratios for a SM Higgs decays as a function of its mass. The grey rectangle roughly corresponds to the mass region of the newly discovered resonance.
It is noted that, for a 125 GeV Higgs, there is a rich collection of decay channels that maybe searched for experimentally. Of course, the larger is the branching ratio of a channel the better, however,  the sensitivity of an experiment depends on several factors such as the detector layout and the backgrounds from other physics processes, in particular from QCD. It turns out that, for both ATLAS and CMS, the "golden" channels (with the highest sensitivity) are the Higgs boson decaying into two photons, H → γ γ, or into two ZZ and then 4 leptons in the final state leptons , H → (Z → l+ l-)(Z → l+ l-).
As an example, the invariant mass distribution for the H → (Z → l+ l-)(Z → l+ l-) search at ATLAS is shown below
Invariant mass distribution of  selected H → (Z → l+ l-)(Z → l+ l-) candidates for the ATLAS experiment with the contributions from various processes in different colors.
The light blue peak at ~125 GeV is interpreted as due to Higgs boson decays.

Finally, the Higgs searches in several decay channels are combined into the (in)famous exclusion plot, here shown for the ATLAS searches
The exclusion plots for Higgs searches at ATLAS.
Explaining this plot would require a dedicated post,  I'll try to give a brief and naive, non-exhaustive explanation below.
The dotted line is the estimated 95% CL limit that can be put by on the cross section of the SM Higgs and the green and yellow bands correspond to the 1 and 2 σ uncertainty on this estimation respectively. In short, if that line is below 1, it means that the experiment could, in principle, exclude a SM-like Higgs with that mass. The solid lines is the same as the dotted one but it comes from data and it is strictly related to the number of events seen in a given mass range. The discrepancy at ~125 GeV between the dotted and solid lines means simply that, looking at the data, a SM Higgs cannot be excluded, even if our experiment had the capability to do it if it was not there.
If you find this oversimplified description of the plot non-satisfactory, a more detailed explanation can be found at

Let's finally explain what a 5 σ discovery means. When a physicist looks at the mass distribution and see a signal-like peak usually asks himself the question: "What is the probability for the background to have a statistical fluctuation as large as the peak I see?". In other words, what is the the probability that I'm just looking to an unfortunate fluctuation of the background instead of a signal?
Neglecting the details of how this probability is calculated, its value and evolution with time is shown in the plot below (y -axis on the left side of the plot) as a function of the Higgs boson mass
P-value, and corresponding sigmas, for a background fluctuation as large as the one seen at different times as a function of the Higgs mass.
The steep drop at ~125 GeV means that the probability for the peak in the mass distribution we see at 125 GeV to be just background is one in a million! If the number of background events follows a Gaussian distribution, this probability would roughly correspond to a 5 σ deviation from the mean number of background event expected. The fact that we had to wait for 5 σ before announcing the discovery is due to a convention between scientists. Below 5 σ one can only claim an "evidence".

What's next?
Well, again this would require a separate post...
From the practical point of view, the next step after drinking all the bottles of 20 years old champagne and recovering from the hangover, is to measure the properties of the "supposed to be Higgs" particle, such as spin and branching ratios. This kind of study will tell us whether what we see is really a Higgs boson, whether it is really compatible with the SM, or whether we have a strong hint of new physics (by far the most exciting scenario for physicists)...

My colleagues will forgive me for anything wrong I may have written and help me to correct it, right?

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