WHEN IS A BUMP A REAL BUMP?
During the past 20 years, bumps have come and gone in the search for the Higgs boson. Supposed signals of the Higgs would create a lot of excitement and then die down when additional data showed the signals to be merely statistical fluctuations in the data. A standard statistical measure of the significance of observed bumps is the number of standard deviations, or sigmas that can be attached to the resonance bump as it rises above or sinks below the background data. The proton–proton collision observations are represented as curves on a graph, compared with the computer-simulated background. The curve representing the observational data is never smooth because fluctuations in the data occur normally and randomly. These fluctuations are caused by the statistical analysis itself, which never produces a purely nonrandom signal. A 2-sigma result corresponds to about one chance in 20 that the bump in the data is not a statistical fluctuation, but represents something real. A 3-sigma bump is a chance of about one in 20,000 that it is not a fluctuation, whereas a 5-sigma bump signifies that there is only one chance in about 1.7 million that the signal is a statistical fluctuation rather than a real particle resonance. Experimentalists demand that any announcement of a discovery of a new particle must reach the 5-sigma level, removing the possibility that it is caused purely by a statistical fluctuation. Most 3-sigma “discoveries” eventually disappear with the collection of more accurate data. As recently as July 2011, Kyle Kranmer, an experimentalist from ATLAS, reported an excess of events in their Higgs search that reached 2.8 sigma. This was a bump in the data curve at about 140 to 143 GeV. But, then, with the subsequent data presented at the December 13, 2011 press conference this bump was shown to be a statistical fluctuation and had disappeared.
When data are analyzed, it is necessary to put observed events into statistical “bins,” which are like storage compartments for data. Bins are a way of organizing the data so that many trillions of events can be analyzed with reduced memory storage on computers. The bins, containing the many data events, are displayed as histogram graphs, with vertical rectangular blocks displayed over a certain range of energy. Experimentalists choose the energy width of each bin to be, for example, 1 GeV, so that any event that falls within this bin is counted. Typically, at a boson energy level of 126 GeV, background events from non-Higgs decay processes will contribute about 400 events per bin. Every statistical background fluctuation of 1 sigma or more could be misidentified as a real Higgs boson signal of 20 events. A 2-sigma fluctuation might be miscounted as 40 extra events. A real Higgs signal could possibly account for 40 events in total, which when boosted by an upward statistical fluctuation, could look like 50 or 60 events. Therefore, a favorable Higgs signal on top of a background fluctuation could be read as a 2-sigma or 3-sigma excess of events. What I have just described accounts for only one bin, whereas several are needed to confirm the existence of a new particle.
The background consists of debris from collisions of other particles. The debris is called hadronic because most of it consists of hadrons. Two of the Higgs boson’s decay channels are called golden channels because they have less hadronic background noise to confuse the picture than the other decay channels. The first is the decay of the standard-model Higgs boson into two photons. The second golden channel is its decay into two pairs of leptons, mediated by the decay of two Z bosons (H0, a neutral Higgs boson, into a Z boson and a Z*, which is a virtual Z boson off the “mass shell”1; the Z and Z*, in turn, decay into four leptons).
When considering the two golden channels, we have to be cautious about claiming that a 3-sigma excess of events is a discovery, because there are many bins in the data analysis. The significant question arises: Does a 3-sigma uptick in one of the bins signal a Higgs boson? Or is it just a statistical fluctuation by chance? The possibility that any one bin would fluctuate upward by as much as 3 sigma is less than one percent, but we don’t just consider one bin. The probability that one among 25 bins would fluctuate by this amount, or that three bins would fluctuate up by something less than three standard deviations each, is far more than one percent. In particular, the probability that you would get a two-standard deviation upward fluctuation just by chance when accounting for 25 bins now reaches a 50 percent probability.
This phenomenon of statistical fluctuation in data analysis is called the look-elsewhere effect (LEE). It means that you cannot draw conclusions from just one or two bins of events; you must “look elsewhere” in the range of the probable mass of the Higgs boson to determine whether other bins at other energy levels are ticking up; if they are, this lessens the chance that your original bump is significant. The problem is that the standard model does not predict the mass of the Higgs boson, so its mass–energy can exist in a large range of possible values.
There are two kinds of probabilities. One is called the local probability (local p value) and the other is called the global probability (global p value). The local probability only takes into account the bins of events at a particular energy value, whereas the global probability takes into account all the possible energy values of where the Higgs boson could be located in the data, and this second probability is where the LEE applies. This kind of statistical analysis plays an important role in many scientific studies. For example, it was used to understand whether the earthquake and hurricane that occurred more or less simultaneously in summer 2011 in the northeastern United States was a statistical coincidence or was caused by a natural convergence.
There are some classical examples that illustrate the LEE. The probability that you will win the lottery is very different from the probability that someone will win the lottery. Similarly, if you are in a room with 100 people, the probability that you will have the same birthday as someone else in the room is small, but the probability that a pair of people will have the same birthday is large. For a given accelerator experiment, the probability that any particular bin in the data will have a 3-sigma excess by chance is very small, but the probability that one of the 25 bins will have a 3-sigma excess is much larger.
If enough data are accumulated by the CMS and ATLAS collaboration that can exclude a Higgs boson outside only a small window of energy, then the significance of the LEE is diminished, and we may be looking at a real discovery.
MEANWHILE, BACK AT THE LAGO MAR AUDITORIUM…
In the slide presenting the contents of my talk, I paraphrased a quote from T.S. Eliot’s poem “The Love Song of J. Alfred Prufrock”: “In the room, 3-sigma bumps come and go/talking of Michelangelo.” I was suggesting that during the past 20 years of experiments searching for new particles, bumps (or resonances) at the 2- and 3-sigma levels appeared in the data, and then disappeared with increased data and accuracy of the experiments.
I began my talk by discussing the current status of the data on the Higgs boson search from a theorist’s point of view. The detectors at the accelerators cannot observe a Higgs directly because of its very short lifetime, but can discover evidence of it by searching for its decay products in various particles of the standard model, such as two W particles, two Z particles, two tau leptons, two muons, two bottom (b) quarks or two photons. All these decay channels are predicted for the Higgs by the standard model, if the Higgs particle mass is known; but, to complicate the issue, other known particles can also decay into these same pairs. As we have just discussed, the decays into two Z particles (and then four leptons) or into two photons are dubbed the golden channels because the background of hadronic particles is almost absent, which allows for a clearer signal for the detection of a Higgs particle. On the other hand, the backgrounds that we have to worry about for these golden channels are the photon and lepton backgrounds. However, for the case of the diphoton decay, the CMS and ATLAS electromagnetic calorimeter detectors are cleverly designed to select Higgs decays from decays of other particles into photons and leptons, like electrons and neutrinos. However, a dominant decay channel of the Higgs boson is its decay into bottom and antibottom quarks. In contrast to the golden chan
nels, this main decay into two b quarks has to be detected against a background of hadronic decays—such as the Z boson decaying into bottom and antibottom quarks—which is millions of times bigger than the Higgs signal to be detected. However, although the decay of the Higgs into two photons does not suffer from this large hadronic background, a great many particles can decay into two photons, so this also represents a difficult background that can obscure the decay of a real Higgs boson.
An important aspect of the decay of the Higgs boson is the “branching ratio”—that is, the relative percentage significance of each decay channel. The branching ratio is the decay rate of the channel one is focusing on divided by the sum of all decay rates of all the possible decay channels. The decay rate is the inverse of the width of the resonance bump in appropriate units. The branching ratio for the decay of the Higgs into two photons is only about 0.26 percent compared with the branching ratio of the decay into two b quarks, which is closer to 60 percent. The signal strength of the decay of the Higgs into two photons is obtained by multiplying this branching ratio by the number of Higgs bosons produced, as measured by the production cross-section at a given energy. Because of the tiny branching ratio of the diphoton decay, this signal is very small and is hidden by the photon background. However, even though the percentage significance for the two-photon decay is far less than for the bb decay (decay of the Higgs into a bottom and antibottom quark), the lack of hadronic background in the two-photon decay still makes it a much easier decay channel to explore.
I pointed out in my talk that the bumps seen in the possible decay of the Higgs into two photons at about 126 GeV were actually significantly greater in the CMS data than the expected tiny bump calculated by the theorists. In other words, the excess of events representing the decay of the Higgs into two photons was greater than what was expected from theory, which actually suggests that the bump may be a statistical fluctuation. I concluded this part of my talk by saying that we needed more data and significantly greater luminosity to make any decisive statements about whether the bumps were indeed signals of a real Higgs boson.
Figure 6.1 ATLAS result for two-photon decay of the new boson, December 2011. The vertical axis shows the ratio of the observed cross-section divided by the cross-section prediction from the standard model; the horizontal axis is the new boson mass in billions of electron volts (GeV). The first, darker band above the line represents 1 sigma, whereas the lighter, top band represents 2 sigma. The plot shows one bump well above 2 sigma, at 126 GeV. © CERN for the benefit of the ATLAS Collaboration
Another issue I raised is that, in the CMS results, two bumps had been detected, one at 124 GeV and one at about 137 GeV. I had acquired this information from papers from ATLAS and CMS posted on the electronic archive for the December 13 announcement (compare Figures 6.1 and 6.2). The bump at 137 GeV was almost as big as the one at 124 GeV. So I asked: Which is the real Higgs boson and which is a fluctuation in the data? Will the real Mr. Higgs please stand up?
Figure 6.2 CMS diphoton results December 2011. Here there are two data bumps above 1 sigma. The axes represent the same quantities as in Figure 6.1 for the ATLAS results. © CERN for the benefit of the CMS Collaboration
I ended this part of my talk by stating that the CERN results were inconclusive; no one should claim, on the basis of these data, that the Higgs boson had been detected. However, there were strong hints that a new boson had been discovered and further data obtained at the LHC would confirm whether or not it was the Higgs boson.
At this statement, David Cline, a well-known experimentalist who had been part of the Rubbia team in 1983 that had found the W and the Z bosons, made a loud comment from the back of the hall, saying that I should take into account that the positions of the bumps were the same in the CMS and ATLAS data. I responded that they were not, in fact, in the same position. They could be as much as 2 to 3 GeV apart. Because the width of the bump, or “resonance,” that was claimed to be a signal of the decay of the Higgs into two photons, was less than about 1 GeV, one had to be careful about claiming that the bumps were at the same position in energy. The experimentalists were able to resolve the energy position of a resonance to within a few percent. The fact that these two bumps at the different detectors were as close as they were could just be a coincidence. Indeed, the positions of the bumps in the two experiments had better be at the same energy and within the experimental error—which they were not—for the experimentalists to claim they had seen the signal of a real particle.
In the next part of my talk, I listed possible alternatives to the Weinberg–Salam model2 that did not contain an elementary Higgs particle. These included the possibility that the spin-0 particle was a bound state of Technicolor particles—that is, the supposed Higgs could be a composite of other particles. Another possibility is that new spin-1 particles like the W and the Z existed above 1 to 2 TeV, which could help to remove the violation of unitarity without the Higgs boson. We recall that the violation of unitarity or probability was resolved in the standard model by using the Higgs boson. Without the Higgs, the standard model would have to address the violation of unitarity in a different way.
There were also possible alternative models based on extra dimensions, such as those that occur in string theory. Yet another possibility is a model based on the existence of a fourth generation of quarks, heavier than the observed quarks. This proposal has been promoted for some years by my colleague at the University of Toronto, Bob Holdom. In this model, too, it is possible to avoid postulating a Higgs boson.
Last, I outlined my models of electroweak theory without a Higgs boson, all of which involved a serious overhaul of quantum field theory. Indeed, my electroweak theory based on nonlocal interactions, which I had published earlier in 2011, was a possible candidate.3 My other model was based on local quantum field theory. It addressed directly the question: Can electroweak theory be renormalizable without a Higgs boson? To restore the necessary gauge invariance of the model required to guarantee renormalizability, I had invoked the Stueckelberg formalism. This was the model I had developed recently, containing only the observed 12 quarks and leptons, the W and Z bosons, and the massless photon and gluon (this model is discussed in Chapter 8).
During the discussion period after my talk, there were several interesting questions. Françoise Englert asked about the size of the troublesome background of the decay of the Higgs boson into two W bosons. I agreed that the background was significant, and caused one to question whether the LHC had yet observed a real Higgs boson event for this channel. I thought that Englert was referring correctly to the fact that the strength of the decay of the Higgs boson into two other lower mass bosons was proportional to the mass of these bosons. Therefore, for the Higgs model, the strength of decay would be stronger for heavy bosons such as the W and the Z, and would constitute a significant confirmation of the standard-model Higgs. Perhaps in the future, more events would be observed in this decay channel.
Next, an American veteran of experimental particle physics, Alan Krisch, put up his hand and questioned my skepticism about the LHC having discovered the Higgs. When did I anticipate, he wanted to know, that we would know, truly, that it had been discovered? My answer was: “We have waited 40 years to get to this point of being close to discovering or excluding a fundamental Higgs boson. Surely we can wait a few more months, or even a year, to be certain that the Higgs boson exists or not.” He nodded his head in agreement.
COFFEE BREAKS
One of the important reasons that one attends international physics conferences is to meet colleagues who are actively engaged in the research topics with which you are involved. During the coffee break after my talk, I spoke with David Cline. I have always valued David’s opinions on experimental results, for I feel that he has always shown integrity in his scientific judgments. David has been involved in large group searches for dark-matter particles for some years. He is currently part of the underground experiment, Xenon100, at the Gran Sasso Pass in I
taly, searching for WIMPs. During the coffee break, David expanded his views on the new LHC results, claiming that they were real; it seemed that they had discovered the Higgs boson. I went over my reasons for why I did not yet believe this, and emphasized that we should wait for more data to confirm the result.
I then joined my colleague Philip Mannheim at a table in a courtyard just outside the hotel. The morning was sunny and I enjoyed the warm Florida air after the freezing cold of Canada. We discussed my talk briefly, and Philip concurred that one should show skepticism toward the claim that the LHC had finally discovered the Higgs boson within the narrow remaining window of 12 GeV.
A woman sitting opposite us with her laptop appeared interested in our conversation. I introduced Philip and myself to her. Her name was Monika Wielers. She said that she was one of the analysts on the ATLAS experiment and that there were about 500 of them analyzing the data. I was intrigued by this news and began asking her questions. She said that, as one of the analysts investigating the data, she had not been happy about presenting these results at CERN the previous Tuesday, because the results were very preliminary. She felt that they had been forced into the announcement for political reasons. The director-general of CERN had met with the CERN Council to discuss how they should handle the issue of the Higgs boson politically. In particular, if it turned out eventually that the Higgs did not exist, how would they break this news to the public? The negative news of not discovering the Higgs boson could seriously damage the future of the LHC experiments, for much of the motivation for spending $9 billion to build the machine was to discover the Higgs. If there was a final null result, the media could question the wisdom of spending so much money and time searching for a particle that did not exist. There was a great deal of anticipation in the media, as well as in the physics community, that the LHC would discover the Higgs boson.
Cracking the Particle Code of the Universe Page 14
