According to the best estimates of CMS the "Mass of Higgs is 125.3 += 0.6 GeV", while according to the best estimates of the ATLAS experiment the mass of the Higgs is 126.5 GeV and should have a similar margin of error. These estimates suggest that a Higgs boson weighs about as much as an atom with a combined 133 protons and neutrons, close to the mass of an iodine atom (but has a very short half-life). The Tevatron result estimates the Higgs boson mass to only about +/- 10GeV to 15 GeV, but is not inconsistent with the LHC estimates of the Higgs boson mass.

**The statistical significance of combined Higgs boson data**

The combined data from all the experiments indicates that a Higgs boson exists at a considerably higher level of significance.

The data is reported by statistical significance in each decay channel. For the combined data the significance level, computed using some shortcuts from a truly accurate combination that have proved to be immaterial when the final analysis is done is as follows (the term "sigma" used in the quoted material is the term used in high energy physics for standard deviations of statistical significance):

The combined diphoton plot gives a 6 sigma signal. It is 2.4 sigma stronger than the standard model. . . . for ZZ to four leptons. Significance is an impressive 4.6 sigma . . . in this channel it matches perfectly the standard model Higgs. . . . the two low resolution channels across ATLAS+CMS [diphoton+ZZ] . . . gives [a] 7.4 sigma [signal]. . . we have now eliminated any possibility of a second boson nearby, unless they are too close to separate.

Put all of the data together and you get a combined statistical significance of 7.45 standard deviations for the existence of a Higgs boson of a mass of approximately 125.5 GeV (note that the date in the image below reflects the European convention and would read 7/4/2012 in the American numerical date order convention).

**Is it the Standard Model Higgs boson?**

As the pre-eminent Higgs blogger in the world (whose blog is the source of all of the links in this post) explains, the data, taken together, probably support the a priori favored result that the particle that has been discovered is a Standard Model Higgs boson with all of its properties, although an unexpectedly high number of diphoton channel decays leaves open the possibility that we may also be seeing some beyond the Standard Model physics as well.

Is it the Higgs? . . .

The facts are that the boson discovered with a mass of about 125 GeV or 126 GeV interacts with a wide range of particles in exactly the way the Higgs boson should.Its decay modes to Z, W, b and tau have just the right ratios and its production has also been tested in different ways confirming indirectly that its coupling to the top quark is also about right. Its spin could be 0 or 2 but 0 is much more likely. All these features point to the standard model Higgs boson.

The only fly in the ointment is its decay rate to two photons. This is nearly twice as large as expected. The significance of the discrepancy with the standard model is about 2.5 sigma.We have learnt to show some healthy skepticism when it comes to observations of physics beyond the standard model.

It could be a fluke.However it is also consistent with an enhancement due to the presence of another charged boson. If that boson exists it must have a mass at least a bit larger than the W otherwise the Higgs would decay to this particle in pairs and we would see the effect on the other decay rates. It can’t be too massive otherwise it would not enhance the diphoton rate enough.But it is likely to be possible to find a range of masses and properties that is consistent with all the observations.

So it is not necessary to invoke any properties for the observed boson that are any different from the standard model. Separate new physics will suffice. So the observed boson passes several tests required by the Higgs and I think that it is reasonable to assume that is indeed the Higgs boson until some observation suggests otherwise.

It is worth noting that the diphoton channel was the primary means by which scientists at the LHC determined that there was a Higgs boson at all (because it is such a "clean" channel that is relatively free of "background" events from other processes), so a Higgs boson discovery at an arbitrary five sigma level is more likely to take place during a run where random statistical variation produces an above average, rather than a below average or average number of diphoton events.

Also, the raw number of diphoton events isn't particularly great. The diphoton channel is a quite uncommon form of Higgs boson decay, even though it a very clean Higgs boson detection channel since almost nothing else but Higgs boson decays produce diphoton channel decays, while almost all higher frequency Higgs boson decay results can also be produced by other decaying particles whose background frequency must be statistically separated from the Higgs boson sourced events. The most common Higgs boson decay channel is actually the bottom quark-anti-bottom quark channel, but the LHC actually has a harder time identifying Higgs boson source events than Tevatron, because the LHC's higher event energies produce such much background noise in that decay channel.

Flukes in rare events happen. Notwithstanding the fact that Gaussian estimates of statistical sampling variation should capture this tendency and reflect it in the sigma levels of low frequency events, the lessons of experience have taught physicists the conventional wisdom that even three sigma events turn out to be statistical flukes about half of the time. Put another way, the sigmas that physicists calculate are roughly twice as large as their real life experiences would suggest that they are, because somehow or other, there are systemic flaws in the way that they estimate error as a consequence of hard to accurately quantify factors like look elsewhere effects and systemic experimental errors.

So, a 2.5 sigma excess in the number of diphoton events observed when the Higgs boson is first detected is really much less exceptional that it would seem, especially given the considerations, both statistical and theoretical, that favor the a priori expectation that this is a Standard Model Higgs boson rather than a Beyond the Standard Model experimental result.

If we have seen a beyond the standard model diphoton result, rather than just a statistical fluke, the excess should fade in the next couple of years of LHC data. If this is an additional signal, however, the diphoton excess will be the dominant focus of beyond the standard model theoretical expectations at the LHC, since no other really notable beyond the standard model results, and certainly none with real statistical significance, have cropped up so far at the LHC.

Diphoton events are characteristically the product of even integer spin particle decays (i.e. spin zero or spin two), so it couldn't be experimental evidence of a new kind of quark or charged lepton. But, while the Standard Model predicts that there is just one Higgs boson, supersymmetry theories (SUSY) generically predict that there are multiple Higgs bosons, although different versions of those theories predict different numbers of them, with the most heavily discussed models featuring five rather than one Higgs boson, two of which typically have electrical charges. As Wikipedia explains:

The minimal Standard Model . . . contains only one complex isospin Higgs doublet, however, it also is possible to have an extended Higgs sector with additional doublets or triplets. The non-minimal Higgs sector favored by [beyond the standard model] theory are the two-Higgs-doublet models (2HDM), which predict the existence of a quintet of scalar particles: two CP-even neutral Higgs bosons h0 and H0, a CP-odd neutral Higgs boson A0, and two charged Higgs particles H±. The key method to distinguish different variations of the 2HDM models and the minimal SM involves their coupling and the branching ratios of the Higgs decays.

The so called Type-I model has one Higgs doublet coupling to up and down quarks, while the second doublet does not couple to quarks. This model has two interesting limits, in which the lightest Higgs doesn't couple to either fermions (fermiophobic) or gauge bosons (gauge-phobic). In the 2HDM of Type-II, one Higgs doublet only couples to up-type quarks, while the other only couples to down-type quarks.

Many extensions to the Standard Model, including supersymmetry (SUSY), often contain an extended Higgs sector. Many supersymmetric models predict that the lightest Higgs boson will have a mass only slightly above the current experimental limits, at around 120 GeV/c2 or less. The heavily researched Minimal Supersymmetric Standard Model (MSSM) belongs to the class of models with a Type-II two-Higgs-doublet sector and could be ruled out by the observation of a Higgs belonging to a Type-I 2HDM.

Thus, a sustained excess diphoton event signal would be the first really meaningful experimental evidence yet suggesting beyond the Standard Model particles seemingly similar to those predicted to exist in SUSY models. The quoted material on the diphoton excess above is obliquely alluding mostly to the possibility that we may be seeing the signal of charged Higgs particles H± within a pretty narrow mass range (more than 80 GeV but not all that much more than the Higgs boson that has just been discovered).

So, a disappearing diphoton event signal could essentially kill SUSY, while a sustained diphoton event signal could breath new life into SUSY and string theory. Still, the absence of other replicated experimental evidence that is confirmed at LHC (e.g., the lack of excess top-antitop asymmetry, the non-detection of a lightest supersymmetric particle, the non-detection of neutrinoless double beta decay, the absence of vacuum instability given some fairly plausible assumptions about asymptotic safety in quatum gravity), leaves open the strong possibility that even if we are seeing the sign of a beyond the standard model particle in the excess diphoton decays, that we may not be seeing evidence of SUSY itself.

Of course, a sustained excess diphoton event signal could also point to something far less notable, like a subtle flaw in how the theoretically expected diphoton decay rate for Higgs bosons has been calculated, rather than anything as exciting as a newly discovered particle or force. Something as simple as a single sign error in the calculation that caused one Feynman diagram in a calculation to be doubled rather than cancelling out another diagram in the calculation could produce this discrepancy. A Higgs boson mass at the high end of the expected range could also reduce the magnitude of the discrepancy.

The clear discovery of a Higgs boson, however, clearly damages truly Higgsless models including technicolor, even if they leave some room for models with multiple Higgs bosons or composite Higgs bosons.

**Coincidences associated with the current Higgs boson mass estimate**

Crudely averaging the CMS and ATLAS mass results (arguably they should be weighted for their slightly different sample sizes) gives a result of 125.8 GeV +/- a one sigma amount of a bit less than 0.6 GeV.

This is not inconsistent with a previously observed possible empirical relationship between the Higgs boson mass and the mass of the W boson and Z boson that has no theoretical basis in the Standard Model itself: that the Higgs boson mass is approximately one half of the sum of twice the W boson mass plus the Z boson mass.

The currently estimated Higgs boson mass calculated with this formula used the best available W and Z boson mass estimates about 125.15 GeV, about 0.65 GeV off from the measured result, just a bit more than one sigma from the measured Higgs boson mass. In addition to uncertainty about the exact Higgs boson mass, there is some margin of error in the "theoretical prediction" of the formula due to the uncertainty in the masses of the W and Z boson mass used to estimate a 125.15 GeV mass from the formula. And, since there is a theoretically predicted relationship between the W and Z boson masses in the Standard Model via a "mixing angle constant" from the Standard Model, an error in one estimate of a weak force boson mass is not independent of an error in an estimate of the mass of the other weak force boson. There is a one sigma margin of error of something on the order of 0.2 GeV for this estimate from the uncertainty in the W and Z boson mass estimates. The combined uncertainties in the W boson, Z boson and Higgs boson mass estimates puts the experimental results within one sigma of each other.

The experimentally measured Higgs boson mass is probably inconsistent with a Higgs boson mass that is simply equal to one half of the vacuum expectation value of the Higgs field which would be 123 GeV.

All of these empirical formulas are complicated, however, by the fact that boson mass in the Standard Model "runs" with the energy level of the interaction according to a formula that is a function of the "beta functions" of the weak force and electromagnetic force coupling constants in the Standard Model. Particle masses are ordinarily stated at the coupling constant strength associated with the mass of the particular particle whose mass is reported, and when one is mixing the masses of multiple particles in a single equation it is arguably necessary to make some adjustments to the ordinary values of those masses to a common interaction energy level to be comparing apples to apples. These adjustment ought to be modest, since the Higgs boson is only a little more than 50% heavier than the W boson, the lightest of the particles in the formula. But, it isn't possible that after theoretically well motivated adjustments for the running of force coupling constants and particle masses with interaction energy levels that both the 2H=2W+Z and the 2H=Higgs vev formulas could be exactly correct. I'll leave the math and physics considerations regarding how these beta function adjustments could or should be applied to the physicists (at least for now).

**Is the Higgs boson a quantum superposition of weak force bosons?**

Notably, and this is merely my own speculation and I am sure, not an original one, a Higgs boson might be a quantum superposition of a the weak force bosons (the W+, W- and Z), rather than a fundamental particle. This is a theoretical approach that could produce such a simple mass formula for a Higgs boson along the lines of 2H=2W+Z in some manner, and has some Standard Model precedents.

We see something similar to this in the way that the eight rather than nine gluons that arise from different combinations of three color charges are described in the Standard Model, all of which have the same mass.

We also employ a similar mode of analysis to our understanding of a number of experimentally observed mesons (two quark composite particles) of the pseudoscalar (spin 0) and vector (spin-1) varieties. This include the neutral pi meson, the eta meson, the eta prime meson, the K-long meson and K-short meson (both of which are types of neutral kaons), the neutral rho meson, and the omega meson. All of these mesons are understood as linear combinations/quantum superpositions of different combinations of two or more pairs of charged quarks that have similar properties in some respect.

This kind of analysis could in principle suggest a way in which one could have anomalously high diphoton events consistent with a charged particle of the same mass making up some percentage component of the linear combination, in a manner similar to the way that the anomalous magnetic moment of a neutral composite particles like the neutron is generated which is much higher than it would be if it were a fundamental neutral particle rather than a composite one with charged quark components, without resorting to new fundamental particles not found outside the Standard Model. For example, this 2010 paper suggests that a composite Higgs boson model (perhaps based on a non-linear sigma model) could prduce an excess in a diphoton channel of production at LHC (see also here and here mentioning the similarity of non-linear sigma and "Little Higgs" models (e.g. reviewed here)).

This kind of linear combination/non-linear combination/quantum superposition analysis could kill both the Higgs boson mass coincidence and the diphoton event excess relative to the Standard Model in one stroke.

I'm probably wrong for reasons that I would understand if someone more knowledgable explained them to me, but the ansatz does present itself given what I do know.

The bottom line, at any rate, is that now that all of the constants of the Standard Model except the CP violation parameter for the lepton mixing matrix have at least somewhat meaningful experimental values, that it is now possible to engage in more serious consideration of potential deeper connections between the constants of the Standard Model than we have today, which could help point us towards some way to unify the three Standard Model forces and table of particles with a more fundamental theory. While a numerical coincidence does not prove a functional relationship between Standard Model constants, the more precisely know those constants are, the more plausible it is to think that empirical relationships between them have a deeper theoretical basis.

**One more footnote**

This result also continues the empirically perfect record the the humorous meta-theory of high energy physics that holds that fermions are always discovered in America, while bosons are always discovered in Europe.

UPDATE July 5, 2012: Slightly corrected to reflect comment.

## 4 comments:

I wouldn't call the date in the chart erroneous; it's just presented according to the little-endian day-month-year convention. Maybe if the US had funded the SSC, the date in the chart would be something like 07-04-2002.

Indeed. Off topic - I had to watch you're fireworks on TV rather than my own hometown show, because ours was cancelled due to fire risk and thunderstorm risk.

The eta meson is particularly suggestive in a linear combination. Most meson combinations are described as one meson plus or minus another meson divided by the square root of the number of mesons (two), or as one meson plus or minus another meson plus or minus another meson divided by the square root of the number of mesons (three). But, the eta meson, which is uu'+dd'-2ss' divided by the square root of six is an exception. It has four component mesons but is divided by the square root of six not the square root of four. One way to discern a theory here is that you really have uu'+dd'-strange meson term divided by square root of three multiplied by the square root of two since there are two mesons in the strange meson term instead of two.

If you see the Z+2W term that way, you get a division by the square root of two since there are both Z and W terms, and an additional division by the square root of two due to there being two W terms. Square root of two times square root of two is the square root of four, which is two. Hence, (Z+2W)/2 gives the mass in a matter analogous to eta meson combinations, which is a pseudo scalar (spin zero) meson with zero net electromagnetic charge, just like a Higgs boson, an eta prime, a neutral pion and a neutral kaon. (The linearly combined vector neutral rho and omega mesons are also electromagnetically neutral). Both eta mesons and neutral pions (also a linear combination) produce diphoton decays, and in the absence of gluon source mass which makes hadron masses non-linear relative to their quark components, since the weak force bosons don't interact via the strong force, the should be nothing but the constitutient particles to give rise to the composite Higgs boson mass.

All of the pseudoscalar and vector mesons for which masses are known are heavier than the Higgs boson, presumably in part due to a lack of a gluonic mass contribution.

The Higgs may be analogous to the instanton solution of the chiral anomaly in QCD that gives rise to the eta and eta prime mass discrepency involving a triangular Feynman diagram that may also describe the interactions of the three weak force bosons.

A potential experimental source for diphoton excess is found here (tetraphoton events that look like diphoton events to the detectors).

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