The CMS (Compact Muon Solenoid) experiment at the LHC (Large Hadron Collider) in CERN, Geneva, presented its Higgs data at the Moriond QCD conference on March 14, 2013. The talk was by Christoph Ochando. The analysis covered their complete data from 2011 (5.1 /fb at 7 TeV) and from 2012 (19.6 /fb at 8 TeV).

In short, CMS convincingly confirmed the new particle, showed that the process of Higgs to two photons is consistent with the standard model and not hinting of a discrepancy as with the ATLAS detector, and established that the new particle has the spin of zero and positive parity expected of the Higgs. Hence the press announcements that the Higgs has been confirmed.

This blog post is written for my Osher Lifelong Learning Class at UC Irvine, so I am including some extra explanation for a general audience learning the subject.

For the new reader, 7 TeV is 7 trillion electron volts total collision energy, resulting from two proton beams of 3.5 TeV each colliding from opposite directions. 8 TeV is from the proton on proton beams of 4 TeV colliding. The total energy is often called √s in figures. The symbol /fb, (or fb^(-1) in the figures) is read “inverse femtobarns”, and is the measure of luminosity or number of beam on beam collisions. When multiplied by a probability for a process in the form of an effective area or cross section (σ) in femtobarns (10^(-39) cm²), it gives the expected number of events for that process. For the old reader, /fb is just the coin of the microscopic realm for how many Higgs can be produced.

In the process Higgs to two photons (H → γ γ, where high energy photons are called gammas) the measured rate compared to the standard model predicted one are consistent to within 68% probability. There are two analysis methods, using other particles involved (MVA) and using cuts on variables (Cuts). For MVA, the ratio of observed production to that predicted by the standard model is called mu (μ) and is

μ = 0.78 + 0.28 – 0.26,

where the + error is in the positive direction, and the – error is in the negative direction. These are the bounds of the 68% probability regions. For the cuts-based analysis:

μ = 1.11 + 0.32 – 0.30.

We compare the H to two photons in CMS with ATLAS, which is high by 2-σ at μ = 1.43 ± 0.21. You can’t really make a joint results by yourself, since some of the systematic errors may be common errors, and you would enlarge the error by not knowing this. ATLAS does have the smaller error, but a 2-σ discrepancy is expected to occur 5% of the time statistically. I leave it for individual physicists to judge if there is some discrepancy to pursue here.

In the process of Higgs to two Z bosons to four leptons, one of the Z’s is real, and one is virtual. Each Z can decay to lepton pairs of electrons or muons. The shorthand for this process in the figures is H → ZZ → 4l. Here is the actual Higgs bump in that process, found on the CMS public TWiki page:

The green and blue processes are those that occur without the Higgs, and are called “background”. The red line is the number expected including the Higgs being the white space below the red line. The black circles are the number of events observed for each energy bin. The black vertical lines are the statistical and systematic errors, within which the number of events is expected to fall 68% of the time, or so called 1-σ of a bell shaped probability curve. The bin at 125 GeV (giga or billion electron Volts of mass for the Higgs) contains 13 events, of which three are expected for background, so 10 are signal events of the Higgs. The adjoining bins contain 2, 5, and 3 extra signal events. So there appear to be 20 Higgs events. The fitted Higgs mass is

m_H = 125.8 GeV ± 0.5 GeV (statistical) ± 0.2 GeV (systematic)

where the ± show the 1-σ errors or 68% probability limits.

The ratio of production to that expected by the standard model for the H → ZZ → 4l process is called mu (μ)

μ = 0.91 + 0.30 – 0.24

μ = 1.00 would be exact agreement with the standard model, and the difference of 1.00 – 0.91 = 0.09 is well below the smaller 1-σ error of 0.24.

This would be a good time to insert a bell shaped curve or normal or Gaussian distribution, and the association of the number of σ’s with included and outstanding probability ranges:

The existence of the new particle is confirmed to the 6.7 σ level, far beyond the 5 σ used as the standard for certainty in particle physics. Just for fun, 3-σ on one side is a 1/370 chance of exceeding, 4-σ is 1/15,787, and 5-σ is 1/1,744,278 chance of exceeding. The 5-σ result is often called one out of 2 million in the press. However, the true value could be outside the range on either side, making a 5-σ discrepancy twice that above, or about 1 in 3.5 million, also often quoted by the press. Since errors are often not understood well and are therefore underestimated, there have been several 3-σ discrepancies that have not held up.

The three processes of the Higgs to two vector bosons (photons, W bosons and Z bosons) are shown below, compared to the standard model predictions

All three agree with the standard model expected result of 1 within their 1-σ errors. In the talk, they did not give a combined value for all three processes. The Higgs to two photon result plotted here looks like the MVA lower result.

The Higgs must be a spin 0 or scalar particle, and also have positive parity under reflection of each spatial coordinate. Other possibilities for bosons are spin 1 or 2, with either positive or negative parity, and spin 0 with negative parity. By studying the angular distributions of decays, CMS has set the following limits: on spin 2 positive parity and spin 1 either parity, the probability is less than 0.1 %; on spin 0 negative parity, the probability is less than 0.16%. I didn’t see a spin 2 negative parity result.