What do these numbers mean? Are the CMS analysts correct in combining the results from two years? A couple of things appear to be clear. If the July 4 announcement had been based on just the new 2012 8-TeV data and a luminosity of 19 inverse femtobarns, then the 2- or 3-sigma strength for the diphoton decay channel would not have justified CERN announcing the discovery of a new boson! However, combining the 7- and 8-TeV data from the two years yields a result that strengthens the case for the standard-model Higgs boson.
Fabrice Hubaut from Aix-Marseille University presented the ATLAS results for the two-photon channel at the Electroweak Session. He announced the Higgs boson mass as 126.8 GeV, and the best-fit signal strength as 1.65 +0.34 or −0.30. This was a small decrease in the signal strength compared with the ATLAS data obtained at 7 TeV energy and 5 inverse femtobarns in 2011. The probability value for this result was a significant 7.4 sigma, which means that the ATLAS results still show a significant excess of events over and above the signal strength predicted by the Higgs boson model for the two-photon decay channel. The ATLAS results differ significantly from the CMS results, and the experimentalists will have to determine which result is correct.
Theoretical particle physicists have been discussing heatedly this excess of events in the two-photon decay, both in the earlier 2011 CMS data and even more so in the ATLAS data. One wonders how this large discrepancy between the new CMS and ATLAS data could have convinced unbiased physicists that the Higgs boson has been discovered “beyond any reasonable doubt.”
Personally, I find it disturbing that the data for the two-photon decay are jumping about, and have not settled down to a statistically significant and definite value for both the CMS and ATLAS collaboration results. As for the reasons for the discrepancy, many papers have been published recently suggesting, for example, that the excess of events in the two-photon decay channel can be explained by including new charged vector boson particles in the calculation of the boson decay into two photons. If the excess of events in the two-photon decay is real, such charged particles would have to be detected at the LHC as new particles. Another explanation for the difference in the CMS and ATLAS results is that perhaps one detector could be more accurate in its ability to detect particles than the other. Some claim that the CMS muon–lepton detector is more accurate than the ATLAS detector. On the other hand, the noisy background problems and the differences in the methods of analyzing the data are complex and can certainly produce significant differences in the results. Perhaps it would be prudent to wait until these difficulties have been resolved before declaring the definite discovery of the Higgs boson.
OTHER DECAY CHANNELS
The other golden channel reported at the Moriond meeting by both the CMS and ATLAS collaborations, the X or H boson decaying into two Z bosons, which in turn decay into four leptons, showed an increase in signal strength since November 2012. The number of events observed above background had increased to a level that proved convincingly that a new boson had been discovered at an energy of about 125 GeV.
The CMS and ATLAS groups also reported new results for the important decay of the X boson into a pair of W bosons, which then decay into two neutrinos and two leptons. The results for the two detectors were different, with one claiming a stronger signal than the other. The problem with this decay channel is that, of the final four leptons, the two neutrino leptons are electrically neutral, and their presence can only be inferred through an amount of missing energy when one reconstructs the decay events and demands the conservation of energy and momentum. The need to determine accurately the missing neutrino energy causes significant background problems, because many particles are decaying into neutrinos as the collisions of the two streams of protons spew out debris. The distribution of the new boson decay events in this channel is flat, rather than appearing as a resonance peak. The calculation of the WW and neutrino background is very complex, and must be done carefully so as not to obscure the true boson signal.
A critical result reported at Moriond was the decay of the X boson into fermion–antifermion pairs, such as the leptonic tau+–tau− decay channel and the quark bottom and antibottom decay channel. It is important to establish beyond a doubt that these decay channels are observed, because an important part of the standard electroweak model is that the Higgs boson couples to (decays into) fermions through the Yukawa interaction. The Yukawa Lagrangian in the standard model couples the Higgs boson to pairs of fermions. When one adjusts the coupling constants that measure the strengths of the interactions of the Higgs field, and substitutes the constant vacuum expectation value for the Higgs field, the masses of the fermions are produced. Without establishing firmly the coupling of the X boson to fermions such as quarks and leptons, it cannot be claimed that the newly discovered boson is the standard-model Higgs boson.
Victoria Martin from the University of Edinburgh reported the results of the ATLAS collaboration for the fermion–antifermion decay channels. She reported the signal strength for the tau+–tau− decay as 0.7 +0.7 or −0.7, which can be considered a null result, consistent with the standard model, but also consistent with zero—that is, indicating no interaction of the Higgs boson with the tau leptons. She also reported null results for the bottom–antibottom decay channel, which is disappointing, because this is the dominant decay channel for a standard-model Higgs boson.
As Martin stated in her talk, the big problem in the tau–tau channel is the background caused by the huge number of decays of the Z bosons into pairs of tau leptons. This large background must be subtracted from the total detected signal to reveal the tiny signal of events resulting from the Higgs boson decaying into pairs of tau leptons. In practice, when reconstructing the tau lepton decay channel, one does not actually observe the tau leptons, because they have a short lifetime of 10−13 seconds. What one observes is the final decay products of the tau leptons: neutrinos, electrons, positrons, and muons. Again, because neutrinos are neutral, and because of the conservation of energy and momentum in the scattering process, the presence of the neutrinos is inferred from a missing energy in the scattering. The neutrinos contribute to a large, problematic background that has to be removed.
For the dominant bottom–antibottom decay channel, the background problem is a serious obstacle to determining the signal strength for this decay. The number of hadrons produced during the proton–proton collisions is enormous; indeed, the quark background is more than a million times bigger than the predicted signal of the standard Higgs boson decaying into bottom and antibottom quarks. Martin summed up the whole problem as “looking for a needle in a haystack.”
Valentina Dutta of MIT reported on the CMS results for the same decay of the new boson into fermion–antifermion pairs. As with the ATLAS collaboration, the big problem at the CMS detector is cutting through the background to see the decay of the new boson into a pair of taus and bottom and antibottom quarks. But the CMS group handled the background produced by the reconstructed neutrino and lepton data differently than the ATLAS group for the tau pair decay channel. The reported signal strength for a pair of tau decays was 1.11 +0.4 or −0.4, or a little more than a 3-sigma signal strength, which is quite different from the null result reported by the ATLAS collaboration.
The difference in the CMS and ATLAS results for this fermion–antifermion decay of the new boson could be the result of systematic errors caused by instrument problems in one or both of the two detectors, but in my opinion this is unlikely. The difference is more likely a result of the calculation of the background. An error in the analysis of a few percent when subtracting the background to reveal the signal for the tau pair decay can cause a significant difference in the reported signal strength between the two collaborations. The same applies to the more problematic bottom and antibottom decay channel.
Which result should we believe for the critical decay of the new boson into a pair of fermions and antifermions? Unfortunately, unless both collaborations find new results by reanalyzing the 2012 data for these
decay channels, we will have to wait for the startup of the LHC in 2015 at an energy of 13 TeV and a much higher luminosity of, say, 100 to 200 inverse femtobarns.
With no conclusive, current information about the two dominant decay channels (the bottom-antibottom and tau–tau), how can so many physicists, as well as the CERN press office, be so confident that the beast that may have been cornered is indeed the standard-model Higgs boson? Yet, as we can see in Figures 11.2 and 11.3, the combined 2011/2012 data for the important decay channels of the Higgs boson are consistent, within the current accuracy of the data, with the predictions of the standard model. These data represent, in 2011, an energy of 7 TeV and in, 2012, an energy of 8 TeV. We must conclude from Figures 11.2 and 11.3 that the overall accumulated evidence at this stage for the new boson being the standard-model Higgs boson has reached a statistically convincing level based on the decay channel data.
With the startup of the LHC in 2015 at an energy of 13 TeV and a luminosity of possibly 100 inverse femtobarns or more, the comparison of the new data with the standard model will most likely confirm the new boson is the Higgs boson.
Figure 11.2 The best fit for the major Higgs boson decay channel data for the combined 7 TeV and 8 TeV data from the CMS detector. For 7 TeV, the luminosity is 5.1 inverse femtobarns; for 8 TeV, the luminosity is 19.6 inverse femtobarns. The best fit for the ratio of the observed cross-section to the standard-model predicted cross-section should be equal to one or unity. The horizontal bars represent the sizes of the errors deviating from the horizontal axis value of unity. The corresponding signal strength, or mu (μ), of these results is 0.80 ± 0.14. The signal strength of unity (one) would be a perfect fit to the standard model. © CERN for the benefit of the CMS Collaboration
DETERMINING THE SPIN AND PARITY
As we know, two important quantum numbers needed to identify a new particle are its spin and parity. The spin and parity of elementary particles are like items on ID bracelets, crucial to the identification of particles. As mentioned, spin is the intrinsic angular momentum degree of freedom of an elementary particle; parity is the operation on the particle of space inversion. That is, the x, y, and z coordinates associated with the particle are transformed to −x, −y, and −z. If, under the space inversion, the particle does not change sign, then it has positive parity and is a scalar particle; if it does change sign, it has negative parity and is a pseudoscalar particle. In practice, spin and parity are often considered together.
New results were presented at the Moriond sessions on the critical issue of the spin and parity of the new boson. As we recall, according to the theorem by Landau and Yang, the observation that the new boson decays into two photons means that, because of conservation of angular momentum and spin, the boson can only have spin 0 or spin 2, and not spin 1, like the photons it decays into. So which is it? Spin 0 or 2?
Figure 11.3 The ATLAS summary of the combined 2011/2012 data. Similar to the CMS data, the 2011 energy is 7 TeV with a luminosity of 4.6 to 4.8 inverse femtobarns, whereas the 2012 energy is 8 TeV with a luminosity of 13 to 20.7 inverse femtobarns. The horizontal axis represents the signal strength, mu (μ), and for the combined fit for the 7-TeV and 8-TeV data, μ equals 1.30 ± 0.20. A signal strength of unity (one) would be a perfect fit to the standard-model prediction. © CERN for the benefit of the ATLAS Collaboration
Here we can turn to the other decay channels for information. The complicated analysis of the decay of the X boson into two Zs, which subsequently decay into four leptons (pairs of e+, e− and mu+, mu−), should be performed ideally by measuring certain angles to the horizontal axis on which the decaying particle sits at rest. Only five of the angles shown in Figure 11.4 are relevant for the determination of the spin and parity of the particle. The spin and parity are determined by a computer code that calculates the correlations of the measurements of the relevant angles.
A recent publication by the CMS collaboration1 claims that the spin-0 scalar Higgs boson is favored by the data—and the scalar nature of the boson means that it has positive parity. The speakers from the ATLAS and CMS collaborations at the Moriond conference echoed this claim for the spin and parity of the X boson.
Figure 11.4 The Cabibbo–Maksymowicz angles in the H to ZZ decays. © “Higgs look-alikes at the LHC,” by Alavaro De Rujula, Joseph Lykken, Maurizio Pierini, Christopher Rogan, and Maria Spiropulu. ArXiv:1001.5300v3 (hep-ph) 5 Mar 2010
JULY 2013: FURTHER SPIN-PARITY ANALYSIS OF THE DATA
After the March 2013 Moriond workshop, the LHC collaborations continued their efforts to analyze the data that were collected in 2011 and 2012. An important new result is the determination of the spin and parity of the observed Higgs-like particle by the ATLAS group.2 The group analyzed the decays of the X particle into two photons, into two Z-bosons further decaying into four charged leptons, and into two W-bosons further decaying into two charged lepton-neutrino pairs. (Recall that the first two of these are considered “golden” channels because they do not possess neutrino and hadronic background problems.)
The new analysis focusing on spin and parity uses a larger data set3 collected by the ATLAS collaboration. The interactions of hypothetical spin-0, spin-1, and spin-2 resonances with standard-model particles are described in a way that depends on the theoretical model. The study focuses on specific production and decay processes that are the most relevant for spin and parity determination.
The statistical analysis aimed at determining the spin and parity of the X particle must be able to distinguish between signal and noise events. The specific statistical method, called likelihood ratio analysis, compares the likelihood of competing models being correct by comparing them to actual observations. One of the models tested is the standard-model Higgs boson, whose properties are known from the predictions of the standard model. Alternative models, such as the pseudoscalar Higgs model or the composite resonance model, are less specific in their predictions. However, their unknown properties can be described by what experimental analysts call “nuisance parameters.” This way, comparing the standard-model Higgs boson with competing models can be independent of the assumptions of any specific competing model.
The likelihood ratio analysis requires knowledge of the statistical distributions of expected signal and noise events in both the standard-model Higgs case and competing models. The complex mathematics that describes the models makes it impossible to calculate these distributions using simple formulas. Instead, physicists use the so-called Monte Carlo method, which simulates a large number of events to obtain the required probability distribution for each competing model.4 For each of the models, comparing actual observations to these simulated statistical distributions yields the likelihood value. These likelihoods can be compared, and their ratios calculated. Such ratios then determine how two competing models fare in the light of observations.
To determine the spin and parity of the observed Higgs-like particle, a favored process to investigate is the decay into two Z bosons and then into four leptons. Experimental physicists can measure a set of five distinct decay angles (Figure 11.4). The presence of neutrinos in the decay process that involves two W bosons complicates the analysis, as direct calculation of the decay angles becomes impossible. Unfortunately, no simple, conventional statistical method of analysis can discriminate between the Monte Carlo simulated distributions of competing models using presently available data. The ATLAS experiment, for example, produced 43 candidate signal events, 18 of which represent a signal for a 125.5-GeV Higgs boson.
There is a sophisticated statistical method that can help overcome these difficulties and improve the results of the likelihood analysis. This method is called the boosted decision tree algorithm (BDT).5 This is a learning algorithm that can be “trained” using simulated signal events to achieve maximum sensitivity so that it will be able to determine the probability distributions for the competing models. Using the likelihood analysis based on the BDT results, LHC analysts have shown that the data favor the st
andard-model prediction of a scalar, positive-parity Higgs boson over the alternatives. (See citations in footnotes 1 and 2.)
The ATLAS data for the decay of the X resonance into four leptons via two Z-bosons exclude the negative parity (pseudoscalar) hypothesis with a probability of 97.8 percent. The data for the decay into two charged lepton-neutrino pairs via a pair of W-bosons also agree with the standard model. These data can be used to exclude the spin-2 hypothesis for the new boson, too, but with less statistical significance.
The CMS collaboration’s published paper, which obtained spin-parity results using statistical methods similar to those of ATLAS, also claims that the scalar Higgs spin-0 boson hypothesis is preferred over the pseudoscalar alternative.
The ATLAS collaboration excluded the alternative models that they studied without making assumptions about the strength of the couplings between the hypothetical Higgs-like particle and the other particles of the standard model. The accumulation of more data at energies 13–14 TeV with a much bigger luminosity will strengthen the statistical determination of the spin and parity assignments of the new resonance. If, during future spin-parity studies by both the CMS and the ATLAS collaborations, the statistical likelihood of the scalar spin-0 Higgs boson model continues to increase in comparison with the likelihood of alternative models, then we must conclude that the new boson with a mass 125–126 GeV is indeed the Higgs-like boson. Determining whether it is in fact the minimal, standard-model, elementary Higgs boson, or a more complicated particle, remains an open question.
LOOKING AHEAD
The standard-model Higgs boson, which is an electrically neutral scalar boson with spin 0 and positive parity, has the quantum numbers of the vacuum. Such an elementary particle has never been observed before. In the interactions of the elementary particles of the standard model, such as the quarks, the W and Z bosons, and the gluons and photons, the scalar Higgs boson has a somewhat specter-like quality. The confirmation beyond a doubt that the new boson is indeed the standard-model Higgs boson, would be an extraordinary discovery in the history of science, for the particle has unique features that have never been observed experimentally until now.
Cracking the Particle Code of the Universe Page 26
