The electron is occasionally captured by a nucleus, giving rise to a neutrino and a recoiling nucleus. Can the muon do this? We measured the process of muon capture—bingo, same process! A high-energy electron beam scatters protons. (This reaction was studied at Stanford.) We measured the same reaction at Brookhaven with muons. A small difference in rates enticed us for years, but nothing came of it. We even discovered that the electron and the muon have separate neutrino partners. And we have already discussed the superprecise g minus 2 experiment, in which the magnetism of the muon was measured and compared to that of the electron. Except for the extra mass effect, they were the same.
All efforts to find a clue to the origin of mass failed. Along the way, Feynman wrote his famous inquiry: "Why does the muon weigh?" Now, at least, we have a partial, by no means complete, answer. A stentorian voice says, "Higgs!" For fifty or so years we have been puzzling about the origin of mass, and now the Higgs field presents the problem in a new context; it is not only the muon. It provides, at the least, a common source for all masses. The new Feynmanian question could be: how does the Higgs field determine the sequence of seemingly patternless masses that is given to the matter particles?
The variation of mass with state of motion, the change of mass with system configuration, and the fact that some particles—the photon surely and the neutrinos possibly—have zero rest mass all challenge the concept of mass as a fundamental attribute of matter. Then we must recall the calculation of mass that came out infinite, which we never solved—just "‹normalized" away. This is the background with which we face the problem of the quarks, leptons, and force carriers, which are differentiated by masses. It makes our Higgs story tenable—that mass is not an intrinsic property of particles but a property acquired by the interaction of particles and their environment. The idea that mass is not intrinsic like charge or spin is made even more plausible by the idyllic notion of zero mass for all quarks and leptons. In this case, they would obey a satisfying symmetry, chiral symmetry, in which their spins would forever be associated with their direction of motion. But that idyll is hidden by the Higgs phenomenon.
Oh, one more thing. We talked about gauge bosons and their one-unit spin; we also discussed fermion matter particles (spin of one half unit). What breed of cat is the Higgs? It is a spin-zero boson. Spin implies directionality in space, but the Higgs field gives mass to objects at every location and with no directionality. Higgs is sometimes called a "scalar [no direction] boson" for that reason.
THE UNITARITY CRISIS
Much as we are intrigued by the mass-endowing attributes of this new field, one of my favorite theorists, Tini Veltman, rates that job of the Higgs far below its major obligation, which is nothing less than making our standard model consistent. Without Higgs, the model fails a simple test of consistency.
Here's what I mean. We have talked a lot about collisions. Let's aim one hundred particles at a specific target, say a piece of iron with one square inch of area. A theorist of modest ability can calculate the probability (remember, quantum theory permits us to predict only probability) that there will be a scattering. For example, the theory may predict that ten particles will scatter out of the one hundred that we direct at our target, for a probability of 10 percent. Now many theories predict that the probability of scattering depends on the energy of the beam we are using. At low energy all of the force theories we know—strong, weak, and electromagnetic—predict probabilities that are in agreement with the actual experiments. However, it is known that for the weak force the probability increases with energy. For example, at medium energy the scattering probability may increase to 40 percent. If the theory predicts that the scattering probability is greater than 100 percent, then clearly the theory ceases to be valid. Something is wrong, since a probability of more than 100 percent makes no sense. It literally means that more particles are scattered than were in the beam in the first place. When this happens we say the theory violates unitarity (exceeds unit probability).
In our history, the puzzle was that the theory of the weak force was in good agreement with the experimental data at low energy but predicted nonsense at high energy. This crisis was discovered when the energy at which disaster was predicted was outside the energy reach of the existing accelerators. But the failure of the theory indicated that something was being left out, some new process, some new particle perhaps, which, if we only knew what it was, would have the effect of preventing the increase of probability to nonsense values. The weak force, you will remember was invented by Fermi to describe the radioactive decay of nuclei. These decays are basically low-energy phenomena, and as the Fermi theory evolved, it became very accurate at predicting a huge number of processes in the 100 MeV energy domain. One motivation of the two-neutrino experiment was to test the theory at higher energies, because the predictions were that a unitarity crisis would occur at about 300 GeV. Our experiment, carried out at a few GeV, confirmed that the theory was heading toward a crisis. This turned out to be an indicator that the theorists had left out of the theory a W particle of approximately 100 GeV mass. The original Fermi theory, which did not include W's, was mathematically equivalent to using an infinitely massive force carrier, and 100 GeV is so extremely large compared to the early experiments (below 100 MeV) that the old theory worked well. But when we asked the theory what 100 GeV neutrinos would do, the 100 GeV W had to be included to avoid a unitarity crisis—but more is needed.
Well, this review is simply to explain that our standard model suffers from a unitarity disease in its most virulent form. The disaster now strikes at an energy of about 1 TeV. The object that would avoid disaster if ... if it existed is a neutral heavy particle with special properties that we call—you guessed it—a Higgs particle. (Earlier we referred to the Higgs field, but we should remember that the quanta of a field are a set of particles.) It might be the very same object that creates the diversity of masses or it might be a similar object. There might be one Higgs particle or there might be a family of Higgs particles.
THE HIGGS CRISIS
Lots of questions must be answered. What are the properties of the Higgs particles and, most important, what is their mass? How will we recognize one if we meet it in a collision? How many types are there? Does Higgs generate all masses or only some increment to masses? And how do we learn more about it? Since it is Her particle, we can wait, and if we lead an exemplary life, we'll find out when we ascend to Her kingdom. Or we can spend $8 billion and build us a Super Collider in Waxahachie, Texas, which has been designed to produce the Higgs particle.
The cosmologists are also fascinated by the Higgs idea, since they sort of stumbled on the need for scalar fields to participate in the complex process of expanding the universe, thus adding to the burden Higgs must bear. More about this in Chapter 9.
The Higgs field as it is now contrived can be destroyed by high energy (or high temperatures). These generate quantum fluctuations that can neutralize the Higgs field. Thus the joint particle-cosmology picture of an early universe, pure and with dazzling symmetry, is too hot for Higgs. But as temperature/energy drops below 1015 degrees Kelvin or 100 GeV, the Higgs acts up and does its mass-generating thing. So, for example, before Higgs we have massless W's, Z's, and photons and a unified electroweak force. The universe expands and cools and along comes the Higgs—making the W and Z fat, for some reason ignoring the photon—and this results in breaking the electroweak symmetry. We get a weak force, mediated by massive force carriers W+, W−, Z0, and we get a separate electromagnetic force, carried by photons. It is as if to some particles the Higgs field is like a heavy oil through which they move sluggishly, seeming to be massive. To other particles the Higgs is like water, and to still others, such as photons and perhaps neutrinos, it is invisible.
I should probably review the origin of the Higgs idea, since I've been a bit coy about letting the cat out of the bag. It is also called hidden symmetry or "spontaneous symmetry breaking." The idea was introduced into particle physics
by Peter Higgs of the University of Edinburgh. It was used by theorists Steven Weinberg and Abdus Salam, working independently, to understand the conversion of a unified and symmetric electroweak force, transmitted by a happy family of four zero-mass messenger particles, into two very different forces: QED with its massless photon and the weak force with massive W+, W−, and Z0's. Weinberg and Salam built on the earlier work of Sheldon Glashow, who, following Julian Schwinger, just knew that there was a consistent, unified electroweak theory but didn't put all the details together. And there were Jeffrey Goldstone and Martinus Veltman and Gerard't Hooft. And there are others who should be mentioned, but that's life. Besides, how many theorists does it take to light up a light bulb?
Another way of looking at Higgs is from the point of view of symmetry. At high temperatures the symmetry is exposed—regal, pure simplicity. At lower temperatures the symmetry is broken. Time for some more metaphors.
Consider a magnet. A magnet is a magnet because, at low temperatures, its atomic magnets are aligned. A magnet has a special direction, its north-south axis. Thus it has lost the symmetry of a piece of nonmagnetic iron in which all spatial directions are equivalent. We can "fix" the magnet. By raising the temperature, we go from magnetic iron to nonmagnetic iron. The heat generates molecular agitation, which eventually destroys the alignment, and we have a purer symmetry. Another popular metaphor is the Mexican hat: a symmetric dome surrounded by a symmetric turned-up brim. A marble is perched on the top of the dome. Perfect rotational symmetry, but no stability. When the marble falls to a more stable (lower-energy) position, somewhere on the brim, the symmetry is destroyed even though the basic structure is symmetric.
In another metaphor we imagine a perfect sphere filled with water vapor at very high temperature. The symmetry is perfect. If we let the system cool, eventually we get a pool of water with some ice floating in it and residual water vapor above. The symmetry has been totally destroyed by the simple act of cooling, which in this metaphor allows the gravitational field to exert itself. However, paradise can be regained by simply heating up the system.
So: before Higgs, symmetry and boredom; after Higgs, complexity and excitement. When you next look out at the night sky you should be aware that all of space is filled with this mysterious Higgs influence, which is responsible, so this theory holds, for the complexity of the world we know and love.
Now picture the formulas (ugh!) that give correct predictions and postdictions of the properties of particles and forces we measure at Fermilab and in our accelerator labs of the 1990s. When we plug in reactions to be carried out at much higher energies, the formulas churn out nonsense. Aha, but if we include the Higgs field, then we modify the theory and get a consistent theory even at energies of 1 TeV. Higgs saves the day, saves the standard model with all its virtues. Does all this prove that it is correct? Not at all. It's only the best the theorists can do. Perhaps She is even more clever.
A DIGRESSION ON NOTHING
Back in the days of Maxwell, physicists felt that they needed a medium that would pervade all space and through which light and other electromagnetic waves could travel. They called it an aether and established properties so that it could do its job. Aether also provided an absolute coordinate system that enabled measurement of the velocity of light. Einstein's flash of insight showed that aether was an unnecessary burden on space. Here one is tampering with a venerable concept, none other than the "void" invented (or discovered) by Democritus. Today the void, or more precisely, the "vacuum state," is front and center.
The vacuum state consists of those regions of the universe where all matter has been removed and no energy or momentum exists. It is "nothing at all." James Bjorken, in talking about this state, said that he was tempted to do for particle physics what John Cage did for music: a four-minute-and-twenty-two-second ... nothing. Only fear of the conference chairman dissuaded him. Bjorken, expert as he is on the properties of the vacuum state, doesn't compare to't Hooft, who understands nothing at all much better.
The sad part of the story is that the pristine absoluteness of the vacuum state (as a concept) has been so polluted (wait until the Sierra Club finds out!) by twentieth-century theorists that it is vastly more complicated than the discarded nineteenth-century aether. What replaces the aether, in addition to all the ghostly virtual particles, is the Higgs field, whose full dimensions we do not yet know. To do its job, there must exist, and experiments must reveal, at least one Higgs particle, electrically neutral. This may be only the tip of the iceberg; a zoo of Higgs boson quanta may be needed to completely describe the new aether. Clearly there are new forces here and new processes. We can summarize the little we know: at least some of the particles that represent the Higgs aether must have zero spin, must be intimately and mysteriously connected to mass, and must manifest themselves at temperatures equivalent to an energy of less than 1 TeV. There is controversy also about the Higgs structure. One school says it's a fundamental particle. Another idea is that it is composed of new, quarklike objects, which could eventually be seen in the laboratory. A third camp is intrigued by the huge mass of the top quark and believes that Higgs is a bound state of top and antitop. Only data will tell. Meanwhile, it's a miracle that we can see the stars at all.
The new aether is then a reference frame for energy, in this case potential energy. And Higgs alone doesn't explain the other debris and theoretical garbage that is dumped in the vacuum state. The gauge theories deposit their requirements, the cosmologists exploit "false" vacuum energy, and in the evolution of the universe, the vacuum can stretch and expand.
One longs for a new Einstein who will, in a flash of insight, give us back our lovely nothingness.
FIND THE HIGGS!
So Higgs is great. Why, then, hasn't it been universally embraced? Peter Higgs, who loaned his name to the concept (not willingly), works on other things. Veltman, one of the Higgs architects, calls it a rug under which we sweep our ignorance. Glashow is less kind, calling it a toilet in which we flush away the inconsistencies of our present theories. And the other overriding objection is that there isn't a single shred of experimental evidence.
How does one prove the existence of this field? Higgs, just like QED, QCD, or the weak force, has its own messenger particle, the Higgs boson. Prove Higgs exists? Just find the particle. The standard model is strong enough to tell us that the Higgs particle with the lowest mass (there may be many) must "weigh" less than 1 TeV. Why? If it is more than 1 TeV, the standard model becomes inconsistent, and we have the unitarity crisis.
The Higgs field, the standard model, and our picture of how God made the universe depend on finding the Higgs boson. There is no accelerator on earth, unfortunately, that has the energy to create a particle as heavy as 1 TeV.
You could, however, build one.
THE DESERTRON
In 1981 we at Fermilab were deeply involved in building the Tevatron and the p-bar/p collider. We were, of course, paying some attention to what was going on in the world and especially to the CERN quest for the W. By late spring of that year we were getting confident that superconducting magnets could work and could be mass-produced with the required stringent specifications. We were convinced, or at least 90 percent convinced, that the 1 TeV mass scale, the terra incognita of particle physics, could be reached at relatively modest cost.
Thus it made sense to start thinking of the "next machine" (whatever would follow the Tevatron), as an even bigger ring of superconducting magnets. But in 1981 the future of particle research in this country was mortgaged to a machine struggling to survive at the Brookhaven lab. This was the Isabelle project, a proton-proton collider of modest energy that should have been working by 1980 but had been delayed by technical problems. In the interval the physics frontier had moved on.
At the annual Fermilab users' meeting in May of 1981, after duly reporting on the State of the Laboratory, I ventured a guess about the future of the field, especially "the energy frontier at 1 TeV." I remarked that Carl
o Rubbia, already a dominating influence at CERN, would soon "pave the LEP tunnel with superconducting magnets." The LEP ring, about seventeen miles in circumference, contained conventional magnets for its e+ e− collider. LEP needed that huge radius to reduce the energy lost by the electrons. These radiate energy when they are constrained into a circular orbit by magnets. (The smaller the radius, remember, the more the radiation.) So CERN's LEP machine used weak fields and a large radius. This also made it ideal for accelerating protons, which because of their much larger mass don't radiate very much energy. The farsighted LEP designers surely had this in mind as an eventual application of the big tunnel. Such a machine with superconducting magnets could easily go to about 5 TeV in each ring, or 10 TeV in the collision. And all the United States had to offer in competition beyond the Tevatron at 2 TeV was the ailing Isabelle, a 400 GeV collider (0.8 TeV in total), although it did have a very high collision rate.
By the summer of 1982, both the Fermilab superconducting-magnet program and the CERN proton-antiproton collider looked as if they would be successful. When American high-energy physicists gathered at Snowmass, Colorado, in August to discuss the status and the future of the field, I made my move. In a talk entitled "The Machine-in-the-Desert," I proposed that the community seriously consider making its number-one priority the building of a huge new accelerator based on the "proven" technology of supermagnets and forge ahead to the 1 TeV mass domain. Let's recall that to produce particles that might have a mass of 1 TeV, the quarks participating in the collision must contribute at least this amount of energy. The protons, carrying the quarks and gluons, must have much higher energy. My guess in 1982 was 10 TeV in each beam. I made a wild guesstimate at the cost and rested my case solidly on the premise that the lure of the Higgs was too attractive to pass up.
There was a moderately lively debate at Snowmass over the Desertron, as it was initially called. The name was based on the idea that a machine so large could be built only in a place devoid of people and land value and hills and valleys. What was wrong about that idea was that I, a New York City kid, practically raised in the subways, had completely forgotten the power of deep tunneling. History rubbed it in. The German machine HERA goes under the densely populated city of Hamburg. CERN's LEP tunnel burrows under the Jura Mountains.
The God Particle: If the Universe Is the Answer, What Is the Question? Page 47
