From a physical point of view little is gained by proposing that the Higgs boson accounts for mass. It is not known, for example, why the Higgs field should couple more strongly to some particles than it does to others. Nor do investigators understand how the mass of the Higgs boson itself (which is not known) comes about, although it is generally presumed to be dominantly through a self-interaction with the Higgs field. In this sense ignorance about the origin of particle masses is replaced by ignorance about particle-Higgs couplings, and no real knowledge is gained.
Moreover, the introduction of the Higgs boson creates a significant problem with respect to the "holy" field of gravitation. The equivalence of mass and energy implies that the graviton, which couples to anything that carries mass, should couple to anything that carries energy, including the Higgs field. The coupling of the graviton to the Higgs field–ever present in all space–would generate a huge "cosmological constant": it would curve the universe into an object roughly the size of a football. If the Higgs boson is assumed to have roughly the same massas the weak vector bosons, the energy density of the Higgs field in the vacuum would be 10 trillion times greater than the density of matter in an atomic nucleus. If the earth were compressed to this density, its volume would be approximately 500 cubic centimeters, or a bit more than the size of a soft-drink can. Needless to say, this is contrary to experiment.
The theorists' way out is really something. It is assumed that the "true" vacuum (one without a Higgs field) is curved in a negative sense: it has a cosmological constant equal in magnitude but opposite in sign to the one generated by the Higgs field. The introduction of the Higgs field then flattens out space to make precisely the universe as we know it. This solution is, of course, not very satisfactory, and many ingenious attempts have been made to solve the problem of the huge cosmological constant. None of the attempts has succeeded. If anything, matters have grown wor.se because theorists keep dumping more particles and fields into the vacuum.Perhaps somehow the universe became flat from the dynamics of the big-bang explosion, which is believed to have created the universe some 15 to 20 billion years ago.
The theory as it stands, with one Higgs field, does not explicitly contradict observation, even if one must accept the incredible disappearance of the cosmological constant. Certain extensions of the theory proposed over the past decade often involve the introduction of additional Higgs fields. Although the arguments for such extensions are often compelling, the phenomena associated with these extra Higgs fields have either never been seen or contradict observed facts.
To account in an elegant way for certain symmetries observed in the strong interactions, for example, a second Higgs field was proposed by Helen R. Quinn of the Stanford Linear Accelerator Center (SLAC) and Roberto Peccei of the Deutsches Electronen-Synchrotron (DESY, the electron accelerator in Hamburg). The ensuing theory predicted a new and presumably very light particle called the axion. So far, in spite of extensive searches, the axion has not been found. In addition the theory has dramatic cosmological consequences concerning a phenomenon known as "domain walls." In general a domain wall marks where two regions of differing properties meet each other. Domain walls are, for instance, found in permanent magnets, where one region of atoms whose spins are aligned in one direction meets another region of atoms whose spins are aligned in a different direction.
It is believed that certain Higgs fields would have given rise to domain walls in the early universe. When the universe was young, the temperature was extremely hot and no Higgs field is thought to have existed. At some time the universe would have cooled sufficiently to allow a background Higgs field to come into being. Unless the cooling were completely uniform, the Higgs field would quite likely have exhibited different properties from one region in space to the next. To what extent the clash of such regions would result in visible or even violent phenomena depends on detailed properties of the Higgs fields, but one would expect some kind of clash in connection with the suggestive proposal of Quinn and Peccei.
The question is why domain walls between such regions have not been observed. It could mean that there is no Higgs field, or that nature has been careful in its use of the field. Alternatively, the walls could have disappeared early in the history of the universe. This is rather typical: one starts with an excellent argument, drags in a Higgs field and then things go wrong. It certainly inspires little faith in the mechanism altogether.
The introduction of an extra Higgs boson also creates difficulties in a model that is attracting considerable attention called the SU(5) grand unified theory. The goal of unified theories in general is to account for the four forces in terms of one fundamental force. A step toward achieving that goal was reached over the past two decades with the introduction and verification of the so-called electroweak theory. The theory holds that the electromagnetic force and the weak force are manifestations of the same underlying force: the electroweak force. The electroweak theory was dramatically confirmed in 1983 at CERN, the European laboratory for particle physics, with the detection of the W+, W- and Z0 particles.
The SU(5) grand unified theory seeks to bind the strong force and the electroweak force into one common force; the designation SU(5) refers to the mathematical group of symmetries on which the theory is based. According to SU(5) theory, the strong, weak and electromagnetic forces, which behave quite differently under ordinary circumstances, become indistinguishable when particles interact with an energy of approximately 1015 billion electron volts (GeV).
The unification of the strong force with the electroweak force requires the existence of an additional set of vector bosons, whose masses are expected to be several orders of magnitude greater than the masses of the weak vector bosons. Since the new vector bosonsare so heavy, they essentially need a Higgs field of their own. In SU(5) theory, therefore, the vacuum contains two Higgs fields that couple with different strengths to different particles.
The most important consequence of the SU(5) theory is that quarks, through the new set of vector bosons, can change into leptons. As a result the proton-that "immortal" conglomeration of three quarks-could decay into lighter particles such as a positron (a type of lepton that can be thought of as a positively charged electron) and a particle called a pion. Given the existence of two Higgs fields, the decay rate can be computed. Experiments done in recent years have not, however, found any such decay. It would seem that there is something wrong with the SU(5) theory or the Higgs field or both. I believe the main concepts of the SU(5) theory will survive over the long run.
Moreover, if the SU(5) grand unified theory is correct and the Higgs field does exist, magnetic monopoles should have been created in the first 10-35 second of the universe. An example of a magnetic monopole is anisolated pole of a bar magnet. (Classically, of course, such objects are not found, because when a bar magnet is cut in half, two smaller bar magnets are created rather than isolated "north" and "south" poles.) Proponents of the SU(5) theory differ over the internal composition of the monopole and over how many monopoles should exist; it is generally agreed that the monopole should have an enormous mass for an elementary particle, perhaps from 1016 to 1017 times the mass of the proton. Although there have been scattered reports of finding monopoles, none of the reports has been substantiated; nature seems to dislike anything involving Higgs fields. The search for monopoles continues.
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MAGNETIC MONOPOLES should exist if the Higgs boson exists. Classicall, of course, magnetic monopoles are not found because when a bar magent is cut in half, two smaller bar magnets are created—not isolated "north" and "south" poles. Magnetic monopoles could, however, be formed by sweeping magnetic field lines uner the Higgs "rug" (below). The bottom illustration shows a pair of monopoles. Although there have been scattered reports of finding monopoles, none of them has been substantiated to date.
Illustration by Hank Iken
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A further smattering of evidence suggests that nature has been sparing in its u
se of the Higgs fields-if they have been used at all. As it happens, in the electroweak theory the employment of only the simplest type of Higgs field leads to a relation between the masses of the W bosons and the Z0 boson. The relation is expressed in terms of a factor called the rho-parameter, which is essentially the ratio of the mass of the W bosons to the mass of the Z0 boson. (There are correction factors that need not bother us here.) The expected value of the rho-parameter is 1; experimentally it is found to be 1.03, with an estimated error of 5 percent. If there is more than one Higgs field, the rho-parameter can take on virtually any value. Assuming that the agreement between theory and experiment is not accidental, the implication is that only one Higgs field exists.
At this point it becomes necessary to question seriously whether the Higgs boson exists in nature. I mentioned above that the only legitimate reason for postulating the Higgs boson is to make the standard model mathematically consistent. Historically the introduction of the Higgs boson to give such consistency had nothing to do with its introduction to account for mass. The introduction of the Higgs boson to account for mass came out of a "model building" line, in which theories were explicitly constructed to model nature as closely as possible. Workers in this line include Sidney A. Bludman of the University of Pennsylvania, who proposed the bulk of the model containing W bosons, and Sheldon Lee Glashow of Harvard University, who incorporated electromagnetism into Bludman's model. Steven Weinberg of the University of Texas at Austin, using methods developed by Thomas W.B. Kibble of the Imperial College of Science and Technology in London, replaced the part of the model concerning particle masses with the Higgs mechanism for generating mass. The integration of quarks into the vector-boson theory was achieved by Nicola Cabibbo and Luciano Maiani of the University of Rome, Y. Hara of the University of Tsukuba, Glashow and John Iliopoulos of the Ecole Normale Superieure in Paris.
All these papers were prod uced over a rather long period, from 1959 through 1970. In that same period many other suggested attempts at model building were also published, but none of them, including the ones I have cited, drew any attention in the physics community. In fact, most of the authors did not believe their own work either, and they did not pursue the subject any further (with the exception of Glashow and Iliopoulos). The reason for the disbelief was obvious: no one could compute anything. The methods and mathematics known at the time led to nonsensical answers. There was no way to predict experimental results.
While I was considering the body of available evidence in 1968, I decided that Yang-Mills theories (a general class of theories of which the standard model is a specific example) were relevant in understanding weak interactions and that no progress could be made unless the mathematical difficulties were resolved. I therefore started to work on what I call the "mathematical theory" line, in which little attention is paid to the extent theory corresponds to experimental observations. One focuses instead on mathematical content. In this line I was by no means the first investigator. It was started by C. N. Yang and Robert L. Mills of the Brookhaven National Laboratory. Richard Feynman of the California Institute of Technology, L. Faddeev of the University of Leningrad, Bryce S. DeWitt of the University of North Carolina and Stanley Mandelstam of the University of California at Berkeley had already made considerable inroads in this very difficult subject.
I did not finish the work either. The concluding publication was the 1971 thesis of my former student Gerard 't Hooft, who was then at the University of Utrecht. In that period few researchers believed in the subject. More than once I was told politely or not so politely that I was, in the words of Sidney R. Coleman of Harvard University, "sweeping an odd corner of weak interactions." A noted exception was a Russian group, led by E.S. Fradkin of the University of Moscow, that made substantial contributions.
Interestingly enough, the modelbuilding line and the mathematicaltheory line proceeded simultaneously for many years with little overlap. I confess that up to 1971 I knew nothing about the introduction of the Higgs boson in the model-building line. For that matter neither did 't Hooft. At one point, in fact, I distinctly remember saying to him that I thought his work had something to do with the Goldstone theorem (a concept that came out of the model-building line). Since neither of us knew the theorem, we stared blankly at each other for a few minutes and then decided not to worry about it. Once again progress arose from "Don't know how," a phrase coined by Weisskopf.
Progress in the mathematical-theory line would ultimately show that the electroweak theory becomes betterbehaved mathematically and has more predictive power when the Higgs boson is incorporated into it. Specifically, the Higgs boson makes the theory renormalizable: given a few parameters, one can in principle calculate experimentally observable quantities to any desired precision. A nonrenormalizable theory, in contrast, has no predictive power beyond a certain limit: the theory is incomplete and the solutions to certain problems are nonsense.
I must point out, however, that the electroweak theory can make powerful predictions even without the Higgs boson. The predictions concern the forces among elementary particles. Those forces are investigated in highenergy- physics laboratories by means of scattering experiments. In such experiments beams of high-energy particles are directed at a "target" particle. A beam of electrons might, for instance, be scattered off a proton. By analyzing the scattering pattern of the incident particles, knowledge of the forces can be gleaned.
The electroweak theory successfully predicts the scattering pattern when electrons interact with protons. It also successfully predicts the interactions of electrons with photons, with W bosons and with particles called neutrinos. The theory runs into trouble, however, when it tries to predict the interaction of W bosons with one another. In particular, the theory indicates that at sufficiently high energies the probability of scattering one W boson off another W boson is greater than 1. Such a result is clearly nonsense. The statement is analogous to saying that even if a dart thrower is aiming in the opposite direction from a target, he or she will still score a bull's-eye.
It is here that the Higgs boson enters as a savior. The Higgs boson couples with the W bosons in such a way that the probability of scattering falls within allowable bounds: a certain fixed value between 0 and 1. In other words, incorporating the Higgs boson in the electroweak theory "subtracts off" the bad behavior. A more thorough description of the way in which the Higgs boson makes the electroweak theory renormalizable requires a special notation known as Feynman diagrams.
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FEYNMAN DIAGRAMS are shorthand representations of a well-defined mathematical procedure for determining the probability that one particle will scatter off another. In the top illustration an electorn scatters off a proton by exchanging a photon, the carrier of the electromagnetic force. The particles can also scatter off each other by exchanging two or more photons (not shown); such exchanges are statistically less likely, so that the one-photon exchange is a good approximation of reality. A photon can scatter off an electron. Two diagrams are necessary to approximate such an interaction (bottom). In this case it is hard to think of scattering in terms of a force. Instead one must think in terms of elementary processes: the photon can be absorbed or emitted by an electron. There is, however, no fundamental difference between electron-proton scattering and electron-photon scattering; one can think of both types of event as elementary processes.
Illustration by Andrew Christie
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Illustration by Andrew Christie
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Armed with the insight that the Higgs boson is necessary to make the electroweak theory renormalizable, it is easy to see how the search for the elusive particle should proceed: weak vector bosons must be scattered off one another at extremely high energies, at or above one trillion electronvolts (TeV). The necessary energies could be achieved at the proposed 20-TeV Superconducting Supercollider (ssc), which is currently under consideration in the U.S. If the pattern of the scattered particles fo
llows the predictions of the renormalized electroweak theory, then there must be a compensating force, for which the Higgs boson would be the obvious candidate. If the pattern does not follow the prediction, then the weak vector bosons would most likely be interacting through a strong force, and an entire new area of physics would be opened up.
A difficulty in searching for the Higgs boson is that its mass is virtually unconstrained. As determined by experiment, the mass must be greater than about 5 GeV. Theory presents no clue as to how heavy the Higgs boson could be, except the particle would generate some of the same difficulties it has been designed to solve if its mass were 1 TeV, which is approximately 1,000 times the mass of the proton. At that point theory suggests the weak vector bosons could no longer be viewed as elementary particles; they could be composite structures made of smaller particles.
The notion of a composite structure is, of course, nothing new in the history of physics. At the beginning of the article I mentioned five known layers of structure: molecules, atoms, nuclei, nucleons (protons and neutrons) and quarks and leptons.
In considering the Higgs boson as a composite structure it is only a small step to suppose such "fundamental" particles as quarks and leptons are really composite structures made from still smaller particles. In a sense the notion of a sixth layer of structure, one beyond quarks and leptons, brings me full circle. Traditionally the way to account for free parameters has been to go to a deeper layer of structure. The success of composite models in predicting energy levels of atoms and nuclei suggests that mass could also be predicted by going to a deeper layer of structure. The fact that in the standard model the Higgs boson is responsible for all observed masses implies that, even if in the end there is no such thing as a Higgs boson, there is at least a common source for all masses. Searching for the Higgs boson could ultimately be the same as searching for a deeper structure of elementary particles.
The Higgs Boson: Searching for the God Particle Page 15
