**Updated Higgs boson decay cross sections and type indicators**

None of the Higgs boson decay cross sections reported is meaningfully more than two sigma from the Standard Model prediction. Both the combined diphoton and the combined ZZ numbers are on the high side rather than the low side, but that should happen at least 25% of the time by random chance, and more often when the bias in the data due to discovery threshold triggers that statistically favor excesses over deficits at the moment a new particle is declared to be discovered in its diagnostic channels are considered. The results below include some mentioned by Woit.

__ZZ Cross-Sections Relative To SM Higgs Predictions__ATLAS ZZ cross-section relative to standard model is 1.7 +- 0.5 (i.e. 1.4 sigma from SM).

CMS ZZ cross section relative to standard model is 0.91 +- 0.27 (i.e. 0.33 sigma from SM).

The combined ZZ result is closer than either of them to the SM prediction because the deviate from the SM value in opposite directions. The combined mean is about 1.35 which is about one sigma from the SM which is the expected value of the deviation.

__Diphoton Cross-Sections Relative To SM Higgs Predictions__ATLAS diphoton cross-section relative to standard model is 1.65 +- 0.24(stat) +- 0.21(syst) (i.e 2.04 sigma from SM adding errors in quadrature).

CMS diphoton cross-section relative to standard model (rumored) is 1.0 +/- 0.2 (i.e. zero sigma from SM).

**CORRECTION: The rumor is that the diphoton cross section relative to the Standard Model expectation is 2.0 not 1.0 which is rumored to be the excess over the Standard Model expectation. This also throws off some of the global fit ratios discussed below.**

The combined diphoton result (if the rumors are true) is aboutr 1.325 which is just a bit more than one sigma from the SM which is very close to the expected value of the deviation.

__WW Cross-Sections Relative To SM Higgs Predictions__ATLAS WW cross-section relative to standard model is 1.5 +/- 0.6

CMS WW cross-section relative to standard model is 0.76 +/- 0.21

The combined result is 1.13 which is less than one standard deviation from the standard model expectation.

__Bottom Quark and Tau Channels Relative To SM Higgs Predictions__CMS Bottom quark cross-section relative to standard model is 1.3 +/- 0.6

CMS Tau cross-section relative to standard model is 1.1 +/- 0.4

Both results are less than half a sigma from the Standard Model expectation.

ATLAS doesn't have enough of a signal in either channel to make a comparison to the standard model prediction (presumably due to differing systemics between the experiments in these less clean Higgs signal channels).

__Non-Cross Section Indicators of Higgs Boson properties__As previously noted, the evidence is strongly consistent with the particle having zero electromagnetic charge, spin-0 and even parity just as in the Standard Model.

**No Sign Other Other Higgs Bosons**

SUSY theories predict that there are at least three electromagnetically neutral Higgs bosons and at least five Higgs bosons in all.

All of the preliminary CMS data in the WW and ZZ channels from 110 GeV to 1 TeV (aka 1000 GeV) is within the two sigma brazil bands of the single Standard Model Higgs boson at 125 GeV mass expectation. LEP did not see any sign of a non-Standard Model Higgs boson at lower masses, although SUSY advocates note that in some SUSY models LEP would be insufficiently sensitive to see them in those mass ranges.

Absence of evidence may not be evidence of absence, but it isn't evidence of presence either.

**Updated Higgs boson mass estimates**

The Higgs boson mass estimates (in GeV/c^2), while not pinned down as precisely as one might like yet, aren't statistically incompatible with each other at this point.

CMS Higgs mass from ZZ decays is 125.8 +- 0.5(stat) +- 0.2(syst) (previously 126.2).

ATLAS Higgs mass from ZZ decays is 124.3 +- 0.6(stat) +- 0.4(syst) (previously 123.5)

ATLAS Higgs mass from diphoton decays is 126.8 +- 0.2(stat) +- 0.7(syst) (previously 126.6).

We are waiting for the latest update to the CMS Higgs mass from diphoton decays. The last report from CMS on Higgs mass in this channel was about 125 GeV.

These four numbers would imply an avergage of the four results of 125.475 which is within two sigma of all of the current values (and both of the plausible theoretical proposals below).

__Theoretical Candidates For Higgs Boson Mass Compared__These data can be compared to two leading theoretical candidates for the Higgs boson mass in my mind (using quite precise Particle Data Group numbers for inputs into the formulas):

(1) The sum of the four electroweak boson masses (W+, W-, Z and the photon) divided by the square root of the number of electroweak bosons is 125.99 GeV.

(2) The mean of the top quark mass and the W boson mass is 126.65 GeV.

Both of these data points are closer to the mean value than either of the ATLAS Higgs boson mass data points. Both are within 0.2 GeV of at least one LHC Higgs boson mass data point, which is considerably less than one standard deviation from the respective particular measurements.

**Pre-Discovery Theoretical Predictions Compared**

The range of experimental central values in the channels measured is now less than half of the error bar range of the 126.3 GeV +/- 2.2 GeV prediction made pre-discovery based on asymptotic safety. Just five other published predictions (out of 96) made pre-discovery has central values consistent with the experimental value (two at 124 GeV, one at 124.2 GeV, and two at 125 GeV with error bars of +/- 4 GeV to +/- 23 GeV). Two of those were based on supersymmetry (out of twenty-six supersymmetry based predictions in all) and three had other theoretical sources. One of five predictions based upon the Coleman-Weinberg potential was close. One of ten compactified additional dimension based predictiosn was close. A prediction based upoon dynamical symmetry breaking and the Higgs as a deeply bound state of two top quarks was close.

Another six lower predictions and another fifteen higher predictions were consistent with the current experimental result due to the large uncertainties in the predictions themselves. One lower bound prediction and one upper bound prediction were wrong. While one lower bound prediction (> 120 GeV) and thirty-six upper bound predictions were correct but often far in excess of the actualy value (just four consistent with the current date were upper bounds of under 130 GeV).

Some theoretical grounds for predictions uniformly produced incorrection or grossly off central values for their predictions, including those motivated by "dynamical symmetry breaking via a neutrino condensate", "four predictions from Connes’s noncommutative geometry", two from Lattice gauge theories, and eight "based on the (approximate) vanishing of particular terms related to quantum corrections." Four predictions based upon embedding the electro-weak Lie Algebra SU(2)*U(1) in the Superalgebra SU(2|1) all failed. Several of the twenty-six supersymmetric based predictions were reasonably close including two with central value predictions within the current error bars. None of the three superstring inspired predictions was particularly close.

**The Global Fits Are Consistent With A Standard Model Higgs Boson**

These cross-sections make up a very large share of the total cross-sections of a decaying Standard Model Higgs boson at the observed mass. Specifically, the expected decays of a a 125 GeV Standard Model Higgs with 100% constituting all of the Standard Model Higgs boson decays are as follows (with channels where we have data from LHC consistent with the Standard Model expectation from at least one experiment shown in bold):

**60% of such particles would decay to bottom (b) quark/antiquark pairs****21% would decay to W particles**- 9% would decay to two gluons (g)
**5% would decay to tau (τ) lepton/antilepton pairs**- 2.5% would decay to charm (c) quark/antiquark pairs
**2.5% would decay to Z particles****0.2% would decay to two photons (γ)**- 0.15% would decay to a photon and a Z particle.

A slightly higher Higgs boson mass tweaks these percentages a bit: decreasing the rates of fermion decays, increasing the rates of massive boson decays, and having only modest impacts on photon and gluon decays which are near relatively flat peaks on the curve of decay rate relative to mass at 125 GeV plus or minus.

The most useful global fits at this point would be to look at the ratios of the various cross-sections relative to the Standard Model expectations in the combined data available at this point.

The ZZ to diphoton ratio so far in the combined data is almost exactly equal to the Standard Model expectation. The bottom quark to ZZ cross-section ratio and bottom quark to diphoton cross-section ratios are also almost exactly equal to the Standard Model expectation. The ratio of the tau cross-sections to the WW cross-section is almost exactly the Standard Model expectation. The WW to diphoton and WW to ZZ ratios are very close to the Standard Model expectation, as are the other tau cross-section ratios.

In general, the fits of the cross-section ratios from the combined data are a quite a bit better than the fits of the absolute cross-sections themselves, which is notable because the ratios are more robust relative to discovery threshold biases and uncertainties in the Higgs boson mass because they control for uncertainties in Higgs boson production rates, but are also more vulnerable to true random statistical error in branching fractions relative to the theoretical expectations.

The global fits suggest that Higgs boson production in the LHC data to date is elevated relative to the Standard Model expectation which is a natural thing to expect given the statistical discovery threshold bias in the current experiment. Put another way, we can say that Higgs boson decays are precisely consistent with the Standard Model expectation much more confidently than we can say that Higgs boson production is precisely consistent with the Standard Model expectation, given the LHC data that we have so far.

The data aren't complete enough to make a single comprehensive global fit yet and rule out any alternative set of percentages, but it is a pretty impressive confirmation that doesn't leave all that much wiggle room for non-SM cross-sections.

**Implications For SUSY**

This non-detection of additional Higgs bosons is particularly problematic for more constrained SUSY models that could have at least one Higgs boson that looks like the Standard Model Higgs boson, but come with expectations about the masses of the other Higgs bosons relative to either the light or heavy neutral, even parity SUSY Higgs boson that could mimic the Standard Model Higgs boson.

In the MSSM, a 125 GeV Higgs boson has to be the "H" boson, and the similar but undetected missing "h" boson has to be less than 90 GeV and must have an undetectably small cross-section missed at LEP. Further LHC experimental work won't be able to see these lower mass ranges. This scenario would motivate a post-LHC collider with lower energy levels but more precision.

In contrast, in SUSY models where the 125 GeV Higgs boson detected so far is the "h" boson, all of the other SUSY Higgs bosons must have masses that are similar to each other and in excess of 1 TeV. This scenario would motivate a bigger than LHC but similar in concept post-LHC collider.

Either outcome implies a tight bound on the permissable boundaries of SUSY parameter called tan beta which relates to the ratio of the Higgs boson masses.

**Conclusion**

The fact that cross-sections in five different Higgs boson decay channels (three of which with data from two experiments) are all consistent within two sigma with a single Standard Model Higgs boson at 125.5 GeV mass +/- about 0.7 GeV.

There are also three different non-cross-section based lines of evidence that the particle has Standard Model Higgs boson properties. And there is an absence of any affirmative evidence of an additional non-Standard Model higgs boson up to 1 TeV, after a complete first run of LHC data, makes quite an impressive case for the argument that this is the SM Higgs boson and that there are no BSM physics at this energy scale.

It is not easy to come up with a well motivated Standard Model deviation that is consistent with these results and with the non-detection of additional Higgs bosons from 110 GeV to 1000 GeV.

## 3 comments:

Strassler's recap of the new data concurs that the evidence for this being a simple SM Higgs boson is strengthening considerably. Some highlights from his post that I don't capture quite as specifically:

* There is "a 15% theoretical uncertainty in the prediction in the overall rate for Higgs particle production in the Standard Model,"

* "there are no strong indications that the new particle isn’t a Higgs particle of the simplest possible type (a “Standard Model Higgs particle”.)"

* "it interacts with W and Z particles with strengths that are proportional to the W and Z particle masses, and with a form of interaction that would be expected for a particle that gives the W and Z particles their masses"

* "measurements of processes that should be too rare to observe, if the Higgs is of Standard Model type, but that might be observable if the Higgs is of a more complex type, have found nothing: these include decays to a Z particle and a photon, to a muon/anti-muon pair [which should be rare since the muon has a small mass], to particles which would go undetected at ATLAS and CMS [such as neutrinos, dark matter particles, or something else unknown], to certain types of previously unknown long-lived particles that decay to known particles while crossing the detector, and to clusters of electron/positron [i.e. anti-electron] pairs."

He also discusses at several points the importance of the CMS diphoton results that have been delayed a bit but are rumored to be closer to a Standard Model prediction value than they were last time. These are expected possibly as soon as next week and surely within the next few months.

Problems with non-SM Higgs spin and parity models are discussed and ruled out here. Jester also disparages spin-2 particle options given the data in hand.

Jester notes "the CMS update in the h→ττ decay channel. Almost 3 sigma evidence for a signal brings up to 4 the number of channels where we clearly observe the Higgs signals (I'm not counting the bb channel, as the Tevatron no longer claims an evidence there). It's also the first direct evidence that the Higgs couples to fermions, although indirectly we knew that before (the rate of Higgs production via gluon-gluon fusion is roughly consistent with the process being mediated by a top quark loop). It's also an evidence that Higgs couples to down-type fermions, which excludes a chunk of the parameters [a] 2-Higgs doublet model."

Strassler slams down spin-2 Higgs boson theories too.

"spin 2 (with positive parity) is now strongly disfavored, as a result of new results from the ATLAS and CMS experiments at the Large Hadron Collider. CMS has disfavored it at the 98.5-99.9% confidence level (the number depending on assumptions about whether the particle is produced in collisions of gluons or in collisions of a quark and anti-quark) using their data from the particle’s decays to two lepton/anti-lepton pairs. ATLAS has disfavored it at the 95%-99% confidence level (similarly depending on assumptions) using their data from decays of the new particle to a lepton, anti-lepton, neutrino and anti-neutrino. Meanwhile, there is no reason for a spin-2 particle (especially with negative parity) to have the relative decay probabilities that are observed in the data, so the fact that all these probabilities are similar to those of a simple Higgs particle disfavors spin 2 and favors spin 0. And there’s simply no theory of a spin-2 particle (with either parity) that doesn’t have other observable particles rather nearby in mass. No one of these arguments is definitive, but in combination they are pretty convincing.

Meanwhile all the data is consistent with a spin 0 particle with decay probabilities roughly similar to that of a Standard Model Higgs (the simplest type of Higgs particle.)"

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