A two-year-long calculation on a custom-made supercomputer has confirmed the existence of a long-theorized elementary particle, thereby validating the theory that predicted it .
In Brief:
IBM physicist Don Weingarten and his colleagues spent eight years building a supercomputer designed to solve the equations of a theory known as quantum chromodynamics, or QCD. Now, after carrying out the largest single numerical calculation in the history of computing, his results confirm the existence of a long-sought elementary particle, called the glueball, and thereby provide the strongest confirmation to date of the basic tenets of the theory.
It is a strange way to do elementary particle physics. In step one, you build a supercomputer rather than an atom smasher. For step two, you program in the equations of the theory to be tested. And step three requires running a few hundred-quadrillion calculations until you've come up with a prediction that you can match to reality.
That is how physicist Don Weingarten of the Thomas J. Watson Research Center has spent the last dozen years of his life. His latest result, achieved in collaboration with Jim Sexton, now at Trinity College, Dublin, and Alessandro Vaccarino, now working in Italy, is a prediction of the mass and decay properties of an esoteric subatomic phenomenon known as a glueball. Weingarten's calculation, published in Physical Review Letters (December 18, 1995), represents one of the most stringent tests ever of the theory known as quantum chromodynamics, or QCD. If the physics community accepts the work, Weingarten may also be acclaimed the "discoverer" of the glueball - quite an accomplishment for a man who rarely strays near a high-energy physics laboratory.
At issue is the theory of the "strong force," one of the four fundamental forces of nature (along with electromagnetism, the weak force and gravity). The strong force binds the truly elementary particles, known as quarks, together into protons and neutrons, and holds the protons and neutrons together in the nuclei of atoms.
Since 1973, physicists have accepted that QCD explains the strong force. However, it is an odd theoretical construct by any account. Notably, QCD accounts for the strong force in terms of a field known as the chromoelectric field, which is transmitted by quanta known as gluons. In this chromoelectric field, quarks and gluons interact in such a way that neither entity can ever be seen as an independent particle (see "How QCD Solves the Mystery of the Particle Zoo"). Try to pull two quarks or gluons apart, or shoot a single quark out of a proton using an accelerator, and the effort will merely create new pairs of quarks and antiquarks.
One of the remarkable predictions of the theory of QCD is that, while gluons carry the chromoelectric field in the same way that photons carry electromagnetic fields, gluons can exist bound together in particlelike states known as glueballs. These glueballs also can be thought of as infinitesimal bundles of the chromoelectric field. If physicists could ever create them in their accelerators, they would have discovered direct evidence of the existence of the chromoelectric field.
"Since the early 1970s," says Weingarten, "people have been looking for glueballs with ambiguous results. The problem is that the properties of the lightest glueballs are not drastically different from the properties of ordinary particles composed of quarks and antiquarks. So, when you observe some particle in an experiment, and you find some number for its mass and its lifetime, that still doesn't tell you a priori whether you've got a glueball or not."
To nail down the glueball, physicists need to use the equations of QCD to obtain accurate calculations of the mass of a glueball and the precise way in which it decays into other particles. Until very recently, they hadn't been able to do so.
The quagmire of QCD
The inability to carry out these calculations exists, Weingarten explains, because QCD doesn't respond to the techniques that physicists apply to calculate physical processes in their other quantum theories. Because of the complexity intrinsic to the quantum world, none of these theories provides exact solutions. That complexity requires that any theory attempting to describe the interactions of particles and forces must account for infinite possible interactions. That demand makes the "raw" theories, in Weingarten's words, "intractable problems."
To solve the equations, therefore, physicists have turned to approximation schemes, known as perturbation theory, or perturbation expansions, in which the quantity that one wishes to calculate is expressed as a sum of terms that becomes more accurate as the number of terms increases. But expansions work only when the interactions between particles are very weak. Not surprisingly, that doesn't normally apply to the strong force. In fact, physicists have been able to use the equations of QCD to predict phenomena that might be seen in accelerators at very high energy, where the strong interactions are relatively weak. But all predictions have failed at low energies - the range at which glueballs, among other things, might manifest themselves.
Since 1981, Weingarten has worked on a technique, known as the valence approximation, to finesse - or force, if necessary - accurate calculations out of QCD. As his theoretical tool, he has used lattice gauge theory, originally developed by Nobel Laureate Kenneth Wilson at Cornell University in 1974.
Instead of working with an infinite space, explains Weingarten, lattice gauge theory approximates space and time as a four-dimensional lattice of finite volume. The good news is that this makes solving the theory a finite problem, rather than an infinite one. The bad news, he says, "is you now have a defined theory that doesn't have anything to do with the real world. The real world is continuous; it doesn't have a lattice."
So how do you connect this with the real world? "The answer," responds Weingarten, "is that you calculate your favorite physical quantity with a lattice of finite volume, and then you calculate over and over again with smaller lattice spacing and a bigger volume, and at the end you take the limit of your predictions as the lattice goes to zero and the volume goes to infinity." The result is a theoretical method of making predictions with QCD.
In the 1970s, that result did little in practical terms for QCD, because, says Weingarten, "the expressions one encounters to obtain predictions are still hopelessly nasty." But in the past 10 years, Weingarten and other physicists have been able to come up with variations on lattice QCD that can be solved on computers in less than the lifetime of the physicists involved. Even so, the solutions demanded computers that would work at extraordinary speeds.
"The biggest machine we could build"
In 1983, Weingarten left the University of Indiana to join IBM and build a computer specifically designed to run his QCD algorithms. He planned to build the fastest possible computer, a machine, he recalls, "big enough to get real numbers out of QCD - the biggest machine we could build and have any chance that we would get it to work."
Along with Monty Denneau and a handful of other collaborators from the computer science department at Watson, Weingarten set out to design and build one of the world's first massively parallel supercomputers, with 566 processors. They called it the GF11, because they calculated that it would perform QCD calculations at roughly 11 gigaflops (a gigaflop is equal to 1 billion floating point operations per second). That would make the machine 40,000 times faster than the VAX computer Weingarten had been using at the University of Indiana, and 250 times faster than the fastest supercomputers then available, built by Cray.
It took Weingarten and his collaborators nearly three times as long as he had planned to get GF11 up and running. Not until 1991 did he begin to believe that the machine would work at all. "There were a whole bunch of design problems," he says, "but in the end it got salvaged."
Finally, in 1993, a decade after he had begun the project, GF11 produced its first publishable QCD calculation. The work, which alone took a year and a half of computer time, was a calculation of the mass of the nucleon (a proton or a neutron) and some half-dozen other hadrons (particles, like the nucleon, that interact via the strong force). Weingarten saw it as a test of how close his algorithms were to the real world. "What we found out," he says, "was a little bit surprising. The approximation was actually within 5 percent of the real world."
Is 5 percent really good enough for serious physics? Weingarten has a simple response: "Obviously," he says, "you would be very happy to find numbers much more accurate than this. On the other hand, in maybe 40 years, no one has ever come anywhere close to getting what looked like real numbers with that accuracy out of QCD or any other theory of strong interactions."
On to the glueball
With his computer and his algorithms performing better than expected, Weingarten went after the lightest glueball. "It was clear," he recalls, "that if you had correspondingly accurate numbers for the properties of glueballs you would be able to distinguish them from other quark-antiquark particles."
First, GF11 established the mass of the lightest possible glueball as 1,740 million electron volts, plus or minus 70. Intriguingly, that calculation was consistent with a resonance - a short-lived particle - at 1,710 million electron volts, first identified in an experiment at Brookhaven National Laboratory (BNL) in 1982, that appears to have some of the necessary quantum characteristics to be a glueball candidate.
"People had proposed that it might be a glueball," says Weingarten, "but not with very much conviction. The experiments are tough, the analyses of experiments are tough and, when people see something, they're not always completely satisfied that they know the properties of what they're seeing. And then to figure out whether one of these things is a quark-antiquark pair or a glueball, or anything else, you have to know the predictions of QCD with confidence. Until we did our calculations there was no way to get those predictions."
Despite the apparent good fit of its mass to Weingarten's calculated mass of the glueball, this particular resonance had problems. Although it decayed into three different pairs of subatomic particles, as theory predicted, it did so at uneven rates. Physicists assumed that a glueball should decay with equal probability into the three pairs of particles. In addition, some physicists doubted whether the glueball would even live long enough to be seen in an accelerator experiment.
Weingarten, therefore, worked out the particle's pattern of decay, to see if it would survive long enough to be detected. "We calculated the decay," he says, "and we got two results that I and some of my colleagues believe clinch this thing to be a glueball."
First, the team confirmed that the particle did live long enough to be observable. Then, Weingarten found that the glueball's decay rates, calculated by GF11, were compatible with the observations at BNL, despite theorists' previous doubts. "So the naive expectation that those three decay rates should be equal is just wrong," he says. "It doesn't follow from QCD."
In order to increase the accuracy of the approximation and raise its certainty level, Weingarten plans to do additional calculations. "I consider it already to be 99 percent certain," he says, "and some other people in the field agree with that - but I would like to convince the doubters."
Gary Taubes is a freelance science writer based in New York City. His latest book is entitled Bad Science: The Short Life and Weird Times of Cold Fusion.
How QCD Solves the Mystery of the Particle Zoo
Physicists of the 1960s referred to the mystery of the particle zoo: the plethora of elementary particles that had been created in their atom smashers or had appeared in cosmic rays falling from the heavens. This zoo could be explained, according to a model developed by Murray Gell-Mann and George Zweig, by the fact that most of these particles, including protons and neutrons, consisted of even smaller subatomic particles that Gell-Mann named "quarks." What the model didn't specify was how these quarks were held together.
The quark model also left physicists pondering two more "striking mysteries," in the words of IBM physicist Don Weingarten. On the one hand, if accelerator experiments were to be believed, the quarks that made up protons, neutrons and other "hadrons" behaved as if they were free particles that barely felt the presence of their neighbors. On the other hand, no amount of firing subatomic particles at protons had managed to knock one of those quarks out of the protons. "That was completely crazy," says Weingarten. "The natural candidates for these free charges are quarks. But having not seen a free quark, one would be very reluctant to suppose that they were barely interacting inside the proton. You'd expect them to be interacting so strongly that you couldn't pull them out."
The solution appeared in 1973. First, the theory of quantum chromodynamics added the "chromoelectric field" to the quark model; it suggested that this field, transmitted by quanta called gluons, held the quarks together inside the protons and neutrons. Then three physicists - David Gross, Frank Wilczek and David Pollitzer - proposed the solution to the mysteries, known as asymptotic freedom.
This concept turned conventional ideas about force fields upside down. In essence, it stated that the chromoelectric field between quarks was weak when the quarks were close together, but got increasingly stronger as the distance between quarks increased.
The field could be thought of as the quantum equivalent of a mechanical spring with a quark at each end. When the quarks are close together, as they are inside protons and neutrons, the force holding them together is virtually nonexistent, like that on a spring with no tension. Try to stretch the spring, however, by pulling the quarks apart, and the force grows greater. Eventually the spring will break, resulting in two new springs. In the case of QCD, when the spring breaks it results not in free quarks, but in the creation of new pairs of quarks and antiquarks, which are bound together inside new particles.
"Having resolved the paradox of the quark model in such a logical and simple way," says Weingarten, "QCD became the only candidate for strong interactions. Once it was born, it had no competition. Nonetheless it still
wasn't really confirmed. QCD makes all sorts of predictions, and we want to get those predictions out and test them to confirm the theory once and for all."
