**More data confirms that they have discovered a new particle.**

The combined result yields a 5.9 sigma significance level for the hypothesis that there is a Standard Model Higgs boson relative to the Standard Model without a Higgs boson null hypothesis (reduced to as little as 5.1 sigma with look elsewhere effects, which still unambiguously meets a scientific discovery threshold in physics). This is roughly a one sigma improvement over the five sigma significance standard for particle discovery it reported on July 4 and is really unsurprising and no big deal by itself.

**The new particle is consistent with a Standard Model Higgs boson**

Now that everyone knows that there is a Higgs boson (and really, most of us have been convinced since the "inconclusive" LHC results announced in November 2011 on that point), the big question remaining is whether what we have seen is really the Higgs boson predicted by the Standard Model or if its properties show beyond the Standard Model behavior. Refinements in its estimated mass are also interesting.

On that score, the important numbers are the deviations from the Standard Model with the right mass Higgs boson expectation. These numbers should average about 1 sigma in any given channel, and shouldn't be far in excess of two sigma, if the Standard Model is correct (results that are consistently too perfect across the board suggest data falsification to favor the theory advanced).

In the ZZ to 4 lepton channel, the fit to the SM with SM Higgs prediction is 1.4 +/- 0.6 sigma. In the diphoton channel the fit is 1.8 +/- 0.5 sigma and the mix of subtypes of collisions in which diphoton events are observed to the predicted value is also within 1.5 sigma of the Standard Model with Standard Model Higgs boson expection. In the WW to lvlv channel the fit is 1.4 +/- 0.3 sigma. Overall, the combined channels at a 1.4 +/- 0.3 sigma fit to the Standard Model (although the combined result is somewhat less meaningful in this kind of hypothesis testing than the individual channel results). Thus, overall, the experimental results in all three channels are very consistent with a Standard Model Higgs with no beyond the Standard Model physics and there are good statistical reasons to expect a bit of an excess over the expected number of non-Standard Model events right at the moment of discovery in highly diagnostic of a Higgs boson decay channels.

The best fit ATLAS has for the Higgs boson mass is 126.0 GeV +/- 0.4 GeV statistical, +/- 0.4 GeV systemic, which is based mostly on the four lepton and diphoton channels that have the highest mass resolutions. The qualitative results of the excess events arae also consistent with a neutral electrical charge, spin zero or spin two boson (the Standard Model Higgs boson has a neutral electrical charge and spin zero and no one seriously expects a spin two boson, of which the graviton is the only really strongly proposed example).

In conclusion, the new paper states:

The decays to pairs of vector bosons whose net electric charge is zero identify the new particle as a neutral boson. The observation in the diphoton channel disfavours the spin-1 hypothesis. Although these results are compatible with the hypothesis that the new particle is the Standard Model Higgs boson, more data are needed to assess its nature in detail.

These conclusions were not a sure thing on July 4. The initial excess in the diphoton channel was so great that it suggested that there might be beyond the Standard Model physics enhancing the signal in that channel, while the tau-tau channel was much weaker than the Standard Model with Standard Model Higgs boson expectation. The fact that additional data has not unduly exaggerated the diphoton or WW channel deviations from the Standard Model (and that the reanalyzed Tevatron data on the bb channel are also perfectly consistent with a 126 GeV Standard Model Higgs boson).

The new report does not address the deficit in the tau-tau channel which exactly matched the Standard Model with Standard Model Higgs expectation through December 2011, but was far below the expected level in the first half of 2012. But, the margin of error in that channel is quite high. Overall, the update from ATLAS is good news for the likelihood that the newly discovered particle is precisely a Standard Model Higgs boson with a mass of 126 GeV +/- 0.8 GeV, and bad news for proponents of beyond the Standard Model theories. Measured channels making up about 83% of the possible Higgs boson decays are within two sigma of the expected values, a channel representing about 1.2% of expected decays is perhaps lower by barely more than two sigma, and the remaining decay channels haven't been measured. This doesn't leave much room for the predicted branching ratios of a Standard Model Higgs boson to be wrong.

**UPDATE (8/2/12):**

The CMS paper (the other LHC experiment) reports a Higgs mass of 125.3 Gev +/- 0.4 GeV statistical, +/- 0.5 GeV systematic and reports results for searches performed in five decay modes: diphoton, ZZ, WW, tau-tau, and bb. CMS reports an overall consistency of the results with the SM with a SM Higgs boson of 0.87 sigma +/- 0.23 sigma and a 5.0 sigma finding relative to the null hypothesis of the Standard Model without a Higgs boson considering look elsewhere effects.

Its results in the ZZ, WW, and bb channels are very close to the SM with a SM Higgs boson expectation. The tau-tau result is about 1 sigma below the SM expectation. The diphoton result is not quite two sigma above the Standard Model expectation. Overall, this too is perfectly consistent with a Standard Model with Standard Model Higgs boson with no beyond the Standard Model physics. The average of the ATLAS and CMS predictions for the Higgs boson mass is 125.65 GeV and a mass range of 125.2-126.2 GeV is within one sigma of the predictions of both experiments (that is not the proper way to determine the standard deviation from the mean of the two results, but in this case hte actual combined margin of error assuming equal weighting of the results is pretty close to +/- 0.6 GeV, so it heavily overlaps with the combined one sigma bands, but is a bit wider).

There really is very little room for this to be anything but a plain vanilla Standard Model Higgs boson, the result which is far better theoretically motivated than any other possibility.

**The Expected Decay Width and Mean Lifetime of A Standard Model Higgs**

The expected decay width of a Standard Model Higgs boson (the reduced Planck's constant divided by decay width equal to mean particle lifetime, which is proportional to a particle's half-life) at the mass indicated by the LHC results is definitely less than 10 MeV and really closer to 1 MeV (compared to 1.4-2.7 GeV for a top quark which corresponds to a half-life of 5*10^-25 seconds see also 2011 estimates for top quark widths found here. ), and for the weak force bosons 2.495 GeV for the Z and 2.141 GeV for the W, implying lifetimes on the order of 3*10*-25 seconds. Thus, the lifetime of a Higgs boson should be on the order of at least 7*10^-23 seconds and probably closer to 7*10^-22 seconds. The mean life for a tau lepton is about 2.9*10^-13 seconds. The lifetime of most, but not all, composite two quark particles (mesons) and three quark particles (baryons) for which a mean lifetime duration is known is longer or about the same than the expected mean lifetime of a Standard Model Higgs boson. But, measurements so far at LHC may be hard pressed to bound the total decay width of the Higgs boson to being much less than something on the order of 100 MeV due to the limited precision of the LHC experiment in making this measurement, although the thousands of clever people involved might be able to find some way to do a bit better than that.

**Conjectures And The Higgs Vacuum Expectation Value**

The Higgs mass suggested by the equation 2H=2W+Z implies a mass of 125.988 +/- 0.015 GeV at current Particle Data Group estimates for the W and Z masses is a value that is within about 0.5 sigma of the averaged mass measurement of ATLAS and CMS, and the LHC is probably incapable of ever ruling out this value. Even a proposed International Linear Collider (which would probably be the next big thing in particle physics if any major new colliders of any kind are built) would be hard pressed to rule it out.

The Higgs vacuum expectation value is often quoted as approximately 246 GeV, but is apparently known with greater precision although I can't find the value anywhere. This is a value suggestively close to 2H minus the sum of the masses of all quarks lighter than the top quark. The Higgs vev (which does not count as mass-energy for general relativity purposes) is not to be confused with cosmic microwave background radiation at 2.725 Kelvin which also fills the vacuum, or with "dark energy" aka the cosmological constant of general relativity.

## 1 comment:

Excellent summary, thanks for all the nitty gritty details!

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