The CMS experiment at the Large Hadron Collider has confirmed, in yet another set of measurements released at year end, that the particle discovered is consistent in all respects measured with the properties of a 125.6 GeV mass Standard Model Higgs boson.
The properties of a Higgs boson candidate are measured in the H to ZZ to 4l decay channel, with l=e,mu, using data from pp collisions corresponding to an integrated luminosity of 5.1 inverse femtobarns at center-of-mass energy of sqrt(s)=7 TeV and 19.7 inverse femtobarns at sqrt(s)=8 TeV, recorded with the CMS detector at the LHC. The new boson is observed as a narrow resonance with a local significance of 6.8 standard deviations, a measured mass of 125.6+/-0.4 (stat.) +/-0.2 (syst.) GeV, and a total width less than 3.4 GeV at a 95% confidence level. The production cross section of the new boson times the branching fraction to four leptons is measured to be 0.93 +0.26/-0.23 (stat.) +0.13/-0.09 (syst.) times that predicted by the standard model. Its spin-parity properties are found to be consistent with the expectations for the standard model Higgs boson. The hypotheses of a pseudoscalar and all tested spin-one boson hypotheses are excluded at a 99% confidence level or higher. All tested spin-two boson hypotheses are excluded at a 95% confidence level or higher.
"Measurement of the properties of a Higgs boson in the four-lepton final state"
, CMS Collaboration (Submitted on 18 Dec 2013).
Collapsing the multiple error estimates into a single error estimate by taking the square root of the sum of the error sources in quadrature, this means that:
* The mass of the Higgs boson is 125.6 +/- 0.45 GeV.
This is essentially unchanged from previous estimates. This is based on the aggregation of estimates from 4 electron decays (126.2 +1.5/-1.8 GeV N=4), 2 electron and 2 muon decays (126.3 +0.9/-0.7 GeV N=13), and 4 muon decays (125.1 +0.6/-0.9 GeV N=8).
Based upon the conjecture that two times the Higgs boson mass equals the sum of two times the W boson mass plus the Z boson mass, and using global fit values of the W and Z boson masses, my personal expectation is that the true Higgs boson mass is 125.97 GeV, which is at the high end of the experimentally permitted value, but is certaintly not ruled out at this point.
While an uncertainty of 0.3% is impressive for a particle discovered less than two years ago, the uncertainty in the Higgs boson mass measurement and the top quark mass measurement (which also has a less than 1% precision) are the dominant sources of uncertainty in efforts to understand global properties of the mass matrix of the Standard Model fundamental particles and couplings such as: (1) the question of whether the Higgs boson Yukawa vector is unitary, (2) the question of the extent of not quite fermion-boson mass inequality in the Standard Model, (3) the possibility of hidden relationships between the Higgs boson mass and other Standard Model constants, and (4) the detection of indirect evidence of particles that are missing from the set of the Standard Model, if any.
CMS experimenters realistically hope to bring the uncertainty in this measurement down to 0.1 GeV or so by the time that the LHC experiment is concluded, a narrowing of the 1 sigma mass range of the Higgs boson by 77%.
* The width of the Higgs boson is less than 3.4 GeV at the 95% confidence level.
This is also no surprise. The Standard Model expectation is about 4 MeV
which is about 0.13% of the directly measured two sigma limit, and the measured result is perfectly consistent with the Standard Model expectation.
This large discrepancy is entirely due to the inability of the experimental apparatus at the LHC to resolve a direct measurement of the Higgs boson width more precisely.
The indirect and model dependent way to measure the Higgs boson total width is to estimate the extent to which particular measured decays in decay paths expected in the Standard Model deviate from the Standard Model expectation, and to use some form of weighted average of the measurable decay paths to estimate the percentage by which the total decay width of the Higgs boson deviates from the Standard Model expectation. Using this approach, the experimental measurements match the theoretically predicted values to within 10%-20% or so of the theoretically predicted values
, implying a total decay width that probably deviates by less than 1 MeV from the theoretically predicted value.
By way of comparison, the width of the W boson is about 2 GeV, the width of the Z boson is about 2.5 GeV, and the width of the top quark is a few percent less than 2 GeV. The expected width of the Higgs boson implies that it has a mean lifetime that is about 666 times a long as the W boson, although this is still shorter than, for example, the tau lepton's mean lifetime which is about 108
times as long as the W boson.
Generally, heavier particles have shorter lifetimes than lighter particles, but the Higgs boson's expected mean lifetime is much longer than the lighter W and Z bosons and is also much longer than that of the only modestly heavier top quark.
* The measured four lepton Higgs boson decay branching fraction, relative to a Standard Model expectation value of 1.0, is 0.93+ 0.29/-0.24.
This is within about 1/4 of a Standard Deviation from the expected value. The sample sizes used to develop these estimates are small enough that there is a great deal of statistical uncertainty in the measurements. The analysis centered on just 25 four lepton events attributable to Higgs boson decays (based upon the inferred mass of the source particle) that were culled from just 470 four lepton observations (over a much larger inferred mass range), with both the 25 and 470 event sets further broken down into three subcategories of events.
In the long run, the hardest part of the process of confirming that the experimentally observed particle matches the Standard Model Higgs boson is the task of determining if any of its branching fractions differ significantly from the theoretically expected values. For each of the half dozen of so most important Higgs boson branching fractions measured so far, there is no statistically significant difference from the theoretically expected value.
The branching fractions of the Higgs boson are highly sensitive to the existence of beyond the Standard Model massive fundamental particles. So, the closer the Higgs boson branching fractions are to their expected Standard Model values, the less likely it is that there are undiscovered massive fundamental particles of an electroweak scale mass. Experimental uncertainty in mass measurements makes it hard to rule out very light particles on this basis, and there isn't enough mass-energy in even a very energetic Higgs boson for its decays to produce particles much much heavier than a Higgs boson (e.g. at the 10 TeV mass scale) or even for the existence of those particles to have very much impact on observed Higgs boson branching fractions.
* The confidence that the Higgs boson is a spin-0 scalar boson (which is the Standard Model expectation) rather than a pseduo-scalar boson is at least three sigma, as is the confidence that it is not a spin-1 boson. The confidence that the Higgs boson is not a spin-2 boson is at least two sigma.
Realistically, the important distinction is that it is not pseudo-scalar, which is the most subtle difference from the Standard Model expectation. This is ruled out at the 99.9% level.
One very plausible possibility, in theories with multiple Higgs bosons (including all supersymmetry theories) is that there were two Higgs bosons of identical or almost identical mass, one of which was scalar (typically called H or h), and one of which was pseudo-scalar (typically called A), that combined, the H and A bosons (or h and A bosons) act like a Standard Model Higgs boson on average. A three sigma or better conclusion that the particle observed is scalar rather than pseudo-scalar largely rules out this scenario.
The spin-1 models are actually ruled out at the 99.97% level. The exclusions aren't quite so powerful for the spin-2 models, but there is very little theoretical motivation for the Higgs boson to be spin-2 and they are still strongly disfavored relative to the spin-0 model.
Further, it is important to observe that the CMS spin and parity determinations are confirmed by the ATLAS experiment's published results:
The pseudoscalar hypothesis is excluded by CMS and ATLAS experiments at a 95% CL or higher. ATLAS has also excluded at 99% CL the hypotheses of vector, pseudovector, and graviton-like spin-two bosons, under certain assumptions on their production mechanisms.
This confirmation makes the CMS conclusions more powerful.
A non-Standard Model scalar Higgs boson model with the same spin and parity as the Standard Model Higgs boson, but that does not participate in electroweak symmetry breaking and has higher dimensional operator terms than the Standard Model Higgs boson, is the least powerfully excluded of the models at CMS (unsurprisingly since it differs so subtly from the Standard Model Higgs boson), and this model has also apparently not yet been tested at ATLAS. This is excluded at a 93% confidence level.
Keep in mind that these strong exclusions have been possible despite the fact that so far CMS is using only 25 data points to reach these conclusions. As the sample sizes increase, the extent to which non-Standard Model spin and parity models can be excluded is likely to increase a great deal until the samples are about 20-40 times as large as they are now, at which point the marginal benefits of larger sample sizes starts to taper off.
Other Results Today:
* Higgs data and SUSY Fits
Another new paper
by John Ellis evaluates the impact of new Higgs boson data (although probably not today's results) on SUSY parameter space using a broader set of experimental input data, but a less generic set of models, than the recent LHC specific analysis by Matt Strassler, et al
. that was conducted in a fairly model independent manner.
As Ellis explains, other than the discovery of a Standard Model-like Higgs boson, the two LHC experiments, ATLAS and CMS "have found no trace of any other new physics, in particular no sign of supersymmetry." Not every supersymmetry model has been excluded by these negative results. But, the failure of a theory that has been around since 1964 to have even a single clear experimental confirmation in the subsequent 49 years isn't very impressive.
Some of the notable charts in his paper show:
(1) the very small non-exclusion range for SUSY theories with a lightest supersymmetric particle lighter than a top quark and a stop (SUSY top quark partner) of less than 800 GeV,
(2) the strong exclusion of an LSP of less than 400 GeV together with a gluino of less than 1200 GeV, and
(3) best fits of two simplified SUSY models to a wide range of collider and astronomy data involve characteristic masses for supersymmetric fermions and bosons in the single digit TeV range (as the heavy mass scale best fit), or alternately with fermion masses on the order of 1 TeV and boson masses on the order of half that amount (as the light mass scale best fit).
The best fit of the parameter space of mSUGRA is very tightly confined with a characteristic fermion mass around 1,400 +/- 200 GeV, a characteristic boson mass of around 1,000 +/ 100 GeV and the tan beta = ca. 42 (implying a heavy scalar Higgs boson of about 5,250 GeV). Dark matter considerations nudge the parameters to favor a point around 1600 GeV characteristic fermion mass (e.g. applicable to gluinos) and 900 GeV characteristic boson mass (e.g. applicable to stops).
Ellis finds best fits for SUSY dark matter at the high end of the range from 10 GeV to 100 GeV with exceedingly low cross-sections of interaction with other matter on the order of 10^-45 to 10^-48 (well below that of neutrinos, for example). This is a poor fit to astronomy data which discriminate between cold dark matter and warm dark matter, however, which favor dark matter particles which are each roughly a million times lighter
than those best fit values. Neither the CSMSSM nor the NUHM1 models he examines have any meaningful capacity to accommodate dark matter candidates with masses consistent with warm dark matter models.
It is increasingly hard to stomach theories that put new, heavy SUSY particles just around the corner from discovery at the electroweak scale without giving rise to even the faintest real experimental indicator of their existence at energy scales that we can measure. SUSY was invented to tame electroweak symmetry breaking, yet seems to have virtually no phenomenological manifestations at that energy scale.
* Why 125.6 GeV?
Is it significant that the Higgs boson mass is very nearly the one that maximizes the rate at which a Higgs boson decays to photons
It is remarkable that the measured Higgs boson mass is so close to the value which maximizes the Higgs decay rate to photons as predicted by the Standard Model. In this letter we explore the consequences to assume that an ∼126 GeV Higgs boson mass is not accidental, but fixed by some fundamental principle that enforces it to maximize its decay rate into photons. We provide evidence that only a very narrow slice of the parameters space of the Standard Model, which contains their measured values, could lead to a maximal Higgs boson with that mass. If the principle actually holds, several Standard Model features get fixed, as the number of fermion families, quark colors, and the CP nature of the new boson, for example. We also ilustrate how such principle can place strong bounds on new physics scenarios as a Higgs dark portal model, for example.
"Is There a Hidden Principle in the Higgs Boson Decay to Photons?"
, Alexandre Alves, E. Ramirez Barreto, A. G. Dias (Submitted on 18 Dec 2013).
The paper notes that the combined CMS-ATLAS Higgs boson mass is 125.66+/-0.34 GeV. The photon decay maximizing value is estimated to be 126.16 +/- 0.35 GeV. It notes that consistent with that principal, any "scalar dark matter" would have to have a mass of 55-63 GeV and a coupling to the Higgs boson of less than 0.01. The paper also observes that peak gluon-gluon decays, and peak photon-Z boson decays are also quite close to the measured Higgs boson mass.
This analysis a similar flavor to the the observation that the Higgs boson masses sits squarely in the metastable region between vacuum instability in the universe and a stable vacuum, at a point where the expected lifetime of the universe's vacuum stability is on the order of the age of the universe but it is not fully stable over an infinite time scale, which was the basis of one of the most successful advanced predictions of the Higgs boson mass. It also further prompts the question - why should a Higgs boson mass that maximizes photon production also imply a metastable vacuum?
* FCNC's in Top Quarks.
The proportion of top quark decays showing a flavor changing neutral current in the Standard Model is expected to be 10^-12 to 10^-17. In some BSM models, it is expected to be as much as 10^-3. The latest experiments establish that FCNC branching fractions from top quarks are less than 10^-2
, and ultimately, if there are none will be able to rule out FCNC branching fractions at the 10^-4 to 10^-5 level, ruling out some BSM models on that basis. But, this is not a measurement likely to rule out whole classes of models any time soon. Suppressing FCNC's in top quarks by a factor of 100 from a naively expected value in a BSM theory simply isn't all that hard to do.
Thus, the current results aren't very interesting because nobody has theories that predict FCNC's in top quark decays at rates that could be detected so far at the LHC. But, we are very close to the threshold where that will start to happen.
* Testing QCD Predictions.
Almost every collision at the LHC tests some aspect of QCD (i.e. the Standard Model theory of the Strong Force which is known as quantum chromodynamics). A recent paper
reviews the results.
The four best available independent estimates of the strong force coupling constant to date, normalized to the energy scale of the Z boson mass (one from each of the LHC experiments, one from Fermilab, and one from another experiment) are consistent with the world average value of 0.1184(7). But, uncertainty in theoretical QCD modeling is the dominant source of uncertainty in each of the estimates.
Equally important, energy scales from hundreds of MeVs to 1 TeV have been studied and there has been no deviation from the expected running behavior of the strong force coupling constant with energy scale
from the Standard Model expectation for this coupling constant's beta function.
This conclusion, if continued to higher energy scales, is a clear way to discriminate between the Standard Model and SUSY alternatives
, because supersymmetry theories, generically, have a running of the strong force coupling constant that is very different from that of the Standard Model, which makes gauge coupling unification (which does not naively appear in the Standard Model) possible. In the case of the running of the strong force coupling constant, the differences are quite stark and should be discernable even at energy scales of a few TeVs which are potentially within the reach of the LHC.
In principle, there are material differences between SM and SUSY predictions for the strong force coupling constant even at energy scales of just 1-2 TeV that have already been probed, but getting sufficient precision in this subset of QCD measurements and theoretical calculations at the extreme fringe of the existing data set is challenging and has thus far not been achieved.
More generally, while the experimental results across the board in countless experiments at colliders to date and the LHC in particular match the theoretical predictions of QCD, this is less impressive a feat than it is in the precision electroweak measurements. This is because the theoretical predictions of QCD have so much uncertainty, because doing the math involved in making a QCD prediction is so hard.
For example, even though we have huge data sets measuring the properties of hadrons containing up, down, strange and charm quarks, with the properties of the composite mesons and baryons often measured with extreme precision, turning those inputs into fundamental QCD theoretical inputs is extremely challenging because the calculations that have to be used to reverse engineer first and second generation quark properties from the hadrons that they form are very difficult to pin down correctly. The proton and neutron's mass, for example, are known to many significant digits of accuracy, but the mass of the up and down quarks that combine to form protons and neutrons are known only to 25% and 10% accuracy respectively, and theoretical estimates of nucleon masses from QCD first principles have only about a 1% precision. The theoretical values match the experimental ones, but the theoretical predictions aren't very specific at all.
This was the situation when Richard Feynmann wrote his book "QED" in 1988 and while progress has been made in the intervening 25 years, it remains the basic problem facing QCD physicists today.
This is why theoretical developments in how to do QCD calculations more efficiently, like the Amplituhedron
or new Monte Carlo methods for doing QCD calculations
hold so much promise for the future of high energy physics. The former works by discovering hidden symmetries in the calculations that makes it possible to ignore redundant calculations, while the latter uses a statistical sampling of the vast number of sub-calculations that go into the final result to make a reasonable estimate of it. Should one or more of these results work, the experimental power of almost every collider experiment ever conducted will be greatly enhanced, because the amount of uncertainty in the background estimates will be greatly reduced, making the signals of the phenomena that experimenters are trying to observe much more clear.