The Higgs Boson: Searching for the God Particle (19 page)

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 10
¹⁶
to 10
¹⁷
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.

A further smattering of evidence suggests that nature has been sparing in its use 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
Z
⁰
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
Z
⁰
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.

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 follows 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.