There are new data analyses from ATLAS and CMS at CERN in the properties of the Higgs Boson and in the search for new particles. The analyses cover the complete 2011 data set at total center of mass energy of the proton on proton beams at the Large Hadron Collider (LHC) of 7 TeV (tera or billion electron volts), and the 2012 data set at 8 TeV total energy. The SLAC summer institute numbers from July 9, 2013 combine errors and are slightly different from the earlier Lepton-Photon 2013 conference numbers, so I will give those.

We start with the ATLAS results presented by Jason Nielson of UC Santa Cruz. The agreement or disagreement of the numbers of Higgs production and decays of a certain type to that predicted by the standard model of Higgs couplings proportional to the mass of the heavy particle involved is called the ratio mu (μ). For the combined processes, the weighted average is μ = 1.33 + 0.21 – 0.18, where the plus and minus show the range of possible variability in the determination of the average of 1.33. If the range is simply taken as ±0.20 for simplicity, than the deviation from the standard model prediction of μ = 1.00 is 0.33 higher, with expected deviation of less than 0.20 for 67% of the time. This ratio of 0.33/0.20 = 1.65 is called 1.65 sigma, and is a little rare, but still not conclusive of a real effect.

The results of the other complete high energy detector at the LHC, called CMS, was presented by Kevin Patrick Lannon of the U. of Notre Dame. Here, the combined ratio to the standard model is μ = 0.80 ± 0.14. Here, the one sigma fluctuation range is 0.14, and the deviation from the standard model prediction of 1.00 is low by 0.20. The ratio to the sigma is -0.20/0.14 = -1.43 sigma.

So ATLAS is high and CMS is low. The obvious thing to do is to statistically combine these. This can never be done correctly by an outsider, since part of the error range on both detectors are common systematic errors that would be double counted in the naive combination of the experiments. Also, the ATLAS experiment is reporting a skewed error, which we approximate as a symmetrical one of value 0.20. Such a naive outsider would end up with the result of combining the two mus from both experiments to get a weighted average of mu-avg = 0.98 ± 0.12. But since the experiments deviate by more than this error of 0.12, the error range would have to be expanded. To do that correctly, we find the chi-squared value of the goodness of both experiments’ mus with the average mu-avg, and get chi-squared = 4.71. The error on the average should then be increased by the square root of 4.71 which is 2.17. The expanded error is then 2.17 x 0.12 = 0.26, giving mu-avg = 0.98 ± 0.26. However, when two measurements are combined to form an average, there is one degree of freedom left. Generally, chi-squared should be around one for one degree of freedom, not as large as 4.71. This means that the two measurements of mu have only about a 3% likelihood of having a larger deviation. The experiments have at least two years to improve the data analyses and systematic and theoretical errors before new data will be available in 2015. At some point the two experiments will provide a correct merging of their values. Since errors and backgrounds are different for each process, they will have to first merge results process by process.

The Higgs to two photon (or γ γ) decay is often used as a rare but cleaner process to determine, so we cite its comparisons to the standard model here. One should note that the other processes such as the W+virtual W and Z + virtual Z processes have similar errors. For ATLAS, H → γ γ has a ratio to the standard model prediction of μ = 1.55 + 0.33 – 0.28, which is higher than the standard model. This is higher than its combined discrepancy, but with larger errors. For CMS, H → γ γ is μ = 0.77 ± 0.27, still below the standard model prediction, but overlapping it at one sigma.