The search for squarks and winos will go on as the Tevatron increases its power through the 1990s and the machines of the year 2000 come on-line. The Super Collider being built in Texas will enable exploration of the "mass domain" up to about 2 TeV. The definition of mass domain is very loose and depends on the details of the reaction that makes a new particle. However, a sign of the power of the Super Collider is that if no Susy particles are found in this machine, most Susy protagonists have agreed to abandon the theory in a public ceremony in which they break all their wooden pencils.
But the SSC has a more immediate goal, a quarry more pressing than the squarks and sleptons. As a compact summary of everything we know, the standard model has two major defects, one aesthetic, one concrete. Our aesthetic sense tells us that there are too many particles, too many forces. Worse, the many particles are distinguished by the seemingly random masses assigned to quarks and leptons. Even the forces differ largely because of the masses of the messenger particles. The concrete problem is one of inconsistency. When the force-field theories, in impressive agreement with all of the data, are asked to predict the results of experiments carried out at very high energies, they churn out physical absurdities. Both problems can be illuminated and possibly solved by an object (and a force) that must be added gingerly to the standard model. The object and the force go by the same name: Higgs.
AT LAST...
All visible objects, man, are but as pasteboard masks. But in each event ... some unknown but still reasoning thing puts forth the mouldings of its features from behind the unreasoning mask. If man will strike, strike through the mask!
—Captain Ahab
One of the finest novels in American literature is Herman Melville's Moby Dick. It is also one of the most disappointing—at least for the captain. For hundreds of pages we hear about Ahab's quest to find and harpoon a large white oceangoing mammal named Moby Dick. Ahab is pissed. This whale has bitten off his leg, and he wants revenge. Some critics suggest that the whale bit oft a lot more than leg, which would explain more adequately the good captain's pique. Ahab explains to his first mate, Starbuck, that Moby Dick is more than a whale. He is a pasteboard mask; he represents a deeper force in nature that Ahab must confront. So for hundreds of pages Ahab and his men scurry furiously around the ocean, having adventures and misadventures, killing lots of smaller whales of various masses. Finally, thar she blows: the great white whale. And then, in quick succession, the whale drowns Ahab, kills all the other harpooners, then sinks the ship for good measure. End of story. Bummer. Perhaps Ahab needed a bigger harpoon, one denied by nineteenth-century budgetary restraints. Let's not let that happen to us. Moby Particle is within striking distance.
We have to ask this question about our standard model: is it simply a pasteboard mask? How can a theory be in accordance with all the data at low energy and predict nonsensical effects at high energy? The answer is to suggest that the theory is leaving something out, some new phenomenon which, when installed in the theory, will contribute negligibly to the data at, say, Fermilab energies and therefore will not spoil agreement with experimental data. Examples of what's left out might be a new particle or a change in the behavior of a force. These postulated new phenomena must contribute negligibly at low energy but massively at Super Collider or higher energy. When a theory does not include these terms (because we don't know about them) we get mathematically inconsistent results at these high energies.
This is somewhat like Newtonian physics, which works very successfully for ordinary phenomena but predicts that we can accelerate an object to infinite velocity; this implausible consequence is totally contradicted when Einstein's special theory of relativity is installed. Relativity theory has infinitesimally tiny effects at the velocities of bullets and rockets. However, as the velocities approach that of light, a new effect appears: the masses of the speeding objects begin to increase, and infinite velocities become impossible. What happens is that special relativity merges into Newtonian results at velocities that are small compared to the velocity of light. The weakness of this example is that whereas the concept of infinite velocity may have been disturbing to Newtonians, it was not nearly as traumatic as what happens to the standard model at high energies. We'll return to this soon.
THE MASS CRISIS
I have hinted at the function of the Higgs particle in giving mass to massless particles and thereby disguising the true symmetry of the world. This is a new and bizarre idea. Heretofore, as we have seen in our myth-history, simplicity was gained by finding substructures—the Democritan idea of atomos. And so we went from molecules to chemical atoms to nuclei to protons and neutrons (and their numerous Greek relatives) to quarks. History would lead one to expect that now we reveal the little people inside the quark, and indeed this may still happen. But we really don't think that is the way the long-awaited complete theory of the world will come out. Perhaps it's more like the kaleidoscope I referred to earlier, in which some split mirrors convert a few bits of colored glass into a myriad of seemingly complex designs. Higgs's ultimate purpose (this isn't science, it's philosophy) may be to create a more amusing, more complex world as suggested in the parable that started this chapter.
The new idea is that all of space contains a field, the Higgs field, which permeates the vacuum and is the same everywhere. This means that when you look up at the stars on a clear night you are looking through the Higgs field. Particles, influenced by this field, acquire mass. This by itself is not remarkable since particles can acquire energy from the (gauge) fields we have discussed, the gravitational field or the electromagnetic field. For example, if you carry a lead block to the top of the Eiffel Tower, the block acquires potential energy because of its altered position in the earth's gravitational field. Since E = mc2, this increase in potential energy is equivalent to an increment in mass, in this case the mass of the earth-lead-block system. Here we have to gently add a small complexity to Einstein's hoary equation. The mass, m, actually has two parts. One is the rest mass, m0, which is what is measured in the laboratory when the particle is at rest. The other part of the mass is "acquired" by the particle by virtue of its motion (like the protons in the Tevatron) or by virtue of its potential energy in a field. We see a similar dynamic in atomic nuclei. For example, if you separate the proton and neutron that make up the deuterium nucleus, the sum of the masses increases.
But the potential energy acquired from the Higgs field differs in several ways from the action of the more familiar fields. The Higgs-acquired mass is actually rest mass. In fact, in what may be the most intriguing version of the Higgs theory, all rest mass is generated by the Higgs field. Another difference is that the amount of mass soaked up from the field differs for various particles. Theorists say that the masses of the particles in our standard model are a measure of how strongly they are coupled to the Higgs field.
The Higgs influence on the masses of quarks and leptons reminds one of Pieter Zeeman's discovery, in 1896, of the splitting of the energy levels of an electron in an atom when a magnetic field is applied to the atom. The field (playing the metaphoric role of Higgs) breaks the symmetry of space that the electron had enjoyed. For example, one energy level, influenced by the magnet, splits into three; level A gains energy from the field, level B loses energy, and level C doesn't change at all. Of course, we now understand completely how all of this happens. It is simple quantum electromagnetism.
So far we have no idea what the rules are that control the Higgsgenerated mass increments. But the question nags: why only these masses—the masses of the W+, W−, and Z0, and the up, down, charm, strange, top, and bottom, as well as the leptons—which form no obvious pattern? The masses vary from that of the electron, at .0005 GeV, to the top quark's, which must be greater than 91 GeV. We should recall that this bizarre idea—Higgs—was used with great success in formulating the electroweak theory. There the Higgs field was proposed as a way of hiding the unity of the electromagnetic and the weak force. In unity there are four ma
ssless messenger particles—the W+, W−, Z0, and the photon—that carry the electroweak force. Along comes the Higgs field, and presto, the W's and Z soak up the essence of Higgs and grow heavy; the photon is untouched. The electroweak shatters into the weak (weak because the messengers are so fat) and the electromagnetic force, whose properties are determined by the massless photon. The symmetry is spontaneously broken, the theorists say. I prefer the description that Higgs hides the symmetry by its mass-giving power. The masses of the W's and the Z were successfully predicted from the parameters of the electroweak theory. And the relaxed smiles of the theorists remind us that't Hooft and Veltman established that this whole theory has no infinities.
I dwell on this issue of mass in part because it has been with me all during my professional life. In the 1940s the issue seemed well focused. We had two particles that exemplified the puzzle of mass: the electron and the muon. They seemed to be in all respects identical except that the muon weighed two hundred times more than its puny cousin. The fact that these were leptons, ignoring the strong force, made it more intriguing. I became obsessed with the problem and made the muon my favorite object of study. The aim was to try to find some difference, other than mass, in the behavior of the muon and the electron as a clue to the mechanism of mass differences.
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.
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