Quark-Gluon Plasma

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QUARK-GLUON PLASMA

Quark-gluon plasma is a novel form of matter whose existence and properties are predicted by quantum chromodynamics (QCD). QCD is the theory of quarks and gluons and their interactions. QCD describes protons, neutrons, pions, kaons, and many other subatomic particles collectively known as hadrons. Hadrons are quite complicated bound states of many quarks, antiquarks, and gluons that are "color-neutral" and are much heavier than the quarks inside them. Why do the hadrons that QCD describes turn out to be so complicated, relative to the elementary quarks and gluons? The answer to this question relies on the properties of the vacuum in QCD. Furthermore, answering this question reveals that at high enough temperatures, QCD simplifies. At temperatures above 2 × 1012 Kelvin, the complex hadrons fall apart into a plasma of unconfined quarks and gluons. For the first 10 microseconds after the Big Bang, the entire universe was hot enough that it was filled with this quark-gluon plasma. Current experiments at the Brookhaven National Laboratory (BNL) in Brookhaven, New York, and at the European Laboratory for Particle Physics (CERN) in Geneva, Switzerland, seek to recreate these extraordinarily high temperatures last seen during the Big Bang, in order to study QCD by simplifying it.

According to the laws of quantum mechanics, the vacuum is not empty. All states are characterized by quantum mechanical fluctuations, and the vacuum is just the state in which these fluctuations happen to yield the lowest possible energy. In QCD, the vacuum is a sea of quarks, antiquarks, and gluons arranged precisely so as to have the minimum possible energy. QCD describes the excitations of this vacuum, which turn out to be the colorless and heavy hadrons, instead of colorful and light quarks and gluons.

To understand why hadrons are colorless, one must first understand how the QCD vacuum responds to the presence of a single "extra" quark. This quark disturbs (polarizes) the surrounding vacuum, which responds by surrounding it with a cloud of many quark-antiquark pairs and gluons. QCD predicts that the force between quarks is weak when they are close together, much closer than about 1 Fermi (10-15 m, about the diameter of a proton). At distances of about 1 Fermi, however, the cloud surrounding a quark acts to ensure that the force between this quark and another quark (surrounded by its own cloud) does not lessen as one tries to separate the quarks. Pulling a single, isolated quark completely out of a colorless hadron requires working against a force that does not weaken with increasing separation—and therefore costs infinite energy. Thus, the energy of a single quark (or of any colored excitation) is infinite, once one includes the energy cost of the resulting disturbance of the vacuum. Adding a colorless combination of quarks to the vacuum disturbs it much less, creating a finite-energy excitation. This explains why the excitations of the QCD vacuum must be colorless.

Understanding why hadrons are heavy requires a second crucial feature of the QCD vacuum. Part of the description of the vacuum is a specification of what fraction of the quark-antiquark pairs at any location is ūu , d̄d , ūd , or d̄u . At each point in space, the vacuum is therefore described by a "vector" that can point any direction in an abstract four-dimensional space with axes labeled ūu , d̄d , etc. QCD predicts that in order to achieve the lowest energy, all these vectors must be aligned. A sea of quark-antiquark pairs so ordered is called a condensate. The fact that the arrows must pick one among many otherwise equivalent directions is known as symmetry breaking. The condensate that characterizes the QCD vacuum is much like a ferromagnet, within which all the microscopic spin vectors are aligned (see Figure 1). The presence of a hadron disturbs this condensate, and the largest contribution to the mass of the hadron is the energy of this disturbance. In effect, the condensate that fills the vacuum slows down the quarks, and because of its presence, hadrons are much heavier than the quarks of which they are made.

There is one exception to the dictum that hadrons must be heavy. Because QCD does not specify in which direction the arrows point, it should be relatively easy to excite "waves" in which the directions of the arrows ripple as a wave passes by. In quantum mechanics, all such waves are associated with particles, and because these waves are easily excited, the related particles should not have much mass. The requisite particles, called pions, are indeed light, as they have a mass only about one-seventh that of a proton.

Thus, the QCD vacuum is a complex state of matter. The laws describing it are written in terms of colored quarks and gluons, but its natural excitations are colorless hadrons, which are heavy because of their interaction with a symmetry-breaking condensate that pervades all of space. One good way of testing understanding of the QCD vacuum is to create new states of matter that are simpler than the vacuum, although they must, of course, be more energetic. Is there a phase of matter in which quarks can roam free? In which the excitations are individual quarks and gluons rather than complicated hadrons?

QCD provides two methods of deconfining (freeing) the quarks. The first is to squeeze nuclei together until their protons and neutrons overlap. In the resulting dense quark matter the quarks are close together and therefore interact only weakly. The second approach is to take a chunk of matter and heat it. When a magnet is heated, by analogy, the spins in the magnet start to oscillate; eventually, above some critical temperature, they oscillate so wildly that the spins all point in random directions, and the magnet loses its magnetization. Something similar happens in QCD. At low temperatures, the arrows that describe the QCD condensate ripple, yielding a gas of pions. Above a critical temperature, the arrows oscillate so wildly that they point randomly, and the condensate "melts." Above its critical temperature, the matter described by QCD is more disordered but more symmetric (no direction favored in Figure 1) than the QCD vacuum. Theoretical calculations that challenge the world's fastest supercomputers show that at a temperature of about 2 × 1012 K, a phase transition occurs in which the QCD condensate melts and the hadrons "ionize," yielding a quark-gluon plasma in which the quarks are light and free (as shown in Figure 2). At low temperatures, QCD describes a gas of hadrons, mostly pions. Once the condensate melts, the pions ionize, releasing quarks and gluons that are lighter and more numerous (three colors of each of up, down, and strange quarks plus their antiquarks and eight types of gluons) and therefore have a much larger energy density at a given temperature.

The prominent features on the phase diagram of QCD are shown in Figure 3. At low densities and temperatures, QCD describes hadrons. The only known place in which nuclei are squeezed together without being heated is the center of neutron stars. The cores of these extraordinarily dense cinders, with masses about that of the Sun but with radii of only approximately 10 km, may be made of super-conducting quark matter. Finding a phase of matter in which QCD simplifies completely requires exploring the high temperature region of the phase diagram. Upon heating any chunk of matter to trillions of degrees, the vacuum condensate melts, the hadrons ionize, and the quarks and gluons are free

FIGURE 1

FIGURE 2

to move in the resulting quark-gluon plasma. The universe began far up the vertical axis of the diagram: at its earliest moments, shortly after the Big Bang, it was filled with a hot quark-gluon plasma that expanded and cooled, moving down the vertical axis, falling below 2 × 1012 K after about 10 microseconds. Since then, quarks have been confined in hadrons—with the possible exception of quarks at the centers of neutron stars and those that are briefly liberated in heavy-ion collisions.

In a heavy-ion collision, two nuclei accelerated to enormous energies are collided in an attempt to create a tiny, ultrahot region within which matter enters the quark-gluon plasma phase. As in the Big Bang (but much more quickly), this quark-gluon plasma droplet expands and cools, moving downward on the phase diagram. For a brief instant the quarks are free, but their liberation is short-lived. After about 10-22s they recombine to form an expanding gas of hadrons, which expands for approximately another 10-22 s. After that these hadrons are so dilute that they fly outward without further scattering, to be seen in a detector. Detectors record many thousands of hadrons—the end products of a collision in which quark-gluon plasma may have been created. The purpose of these heavy-ion collision experiments is twofold. First, they seek to create a region of quark-gluon plasma—the stuff of the Big Bang—and measure its properties to see whether the complexities of the QCD vacuum have truly melted away. And, second, they seek to study how matter behaves as it undergoes the transition from this plasma back to a mundane hadron gas.

In June 2000, the first collisions occurred at Brookhaven's new Relativistic Heavy Ion Collider (RHIC) whose collisions are about ten times more energetic than those achieved previously at CERN. This increases the initial energy density, and thus the initial temperature, pushing further upward into the expected quark-gluon plasma region of the phase diagram. In addition, these higher-energy collisions produce many more pions, diluting the net quark density. More energetic heavy-ion colliders therefore explore upward and to the left on the phase diagram, more and more closely recreating the conditions of the Big Bang. To date, only the first, simplest analyses of collisions at RHIC have been performed, but it is already clear that these collisions have higher initial energy densities and lower net quark densities than ever before.

Near the vertical axis of the phase diagram (traversed by the Big Bang and by the highest-energy collisions), the phase transition from quarks to hadrons occurs smoothly and continuously. In this way, it is like the ionization of a gas and is quite unlike the boiling of water. The latter phase transition occurs discontinuously at a single sharply defined temperature. Theoretical arguments indicate that at higher net quark density, the phase transition between quark-gluon plasma and hadrons is similarly discontinuous and can be shown in Figure 3 as a sharp line. This line ends at what is called the critical point.

There are phenomena that occur at the critical point and nowhere else on the phase diagram. At this point, the arrows of Figure 1 undulate in a unique, precisely calculable manner. Consequently, distinctive fluctuations occur in the momentum of the pions produced in those heavy-ion collisions that pass near the critical point as they cool. Experiments move leftward in the phase diagram as the collision energy increases and search for the telltale signatures of the critical point.

In addition to studying the transition between quark-gluon plasma and hadrons, the goal of heavyion collisions is to measure properties of the quark-gluon plasma itself. This requires observables that reveal something about the earliest, hottest moments of a collision. One method would be to shoot a very fast quark through the plasma and watch how rapidly it loses energy. Estimates suggest that a quark plowing through such a plasma loses much more energy than it would if it encounters only heavy, colorless hadrons. The sign of this rapid energy loss is a paucity of 5 to 10 GeV pions emerging from a heavy-ion collision. Any such energetic pions must have originated as a fast quark. If these quarks have to fight their way through a quark-gluon plasma, they will lose energy and thermalize, and consequently very few pions of 5 to 10 GeV will be seen, relative to what occurs in proton collisions. No evidence of such a deficit has been seen in the lower-energy collisions at CERN. One of the most exciting features of the first, preliminary data from the RHIC experiments is an indication that they yield about five times fewer energetic pions than expected. With time, this measurement should become a quantitative measure that will allow one to test whether high-temperature QCD indeed describes a quark-gluon plasma—and to test predictions of its properties.

FIGURE 3

The study of the quark-gluon plasma has to date been largely accomplished by theoretical methods, working deductively beginning from the laws of QCD. Experimenters hope to soon confirm that they are regularly recreating the material of the Big Bang. As they then begin to measure its properties, scientists shall learn whether QCD behaves as expected. If the vacuum condensate melts and hadrons ionize, freeing the quarks, the simplicity implicit in the laws of QCD will have been realized.

See also:Cosmology; Phase Transitions; Quantum Chromodynamics

Bibliography

Brookhaven National Laboratory. "RHIC." <http://www.bnl.gov/RHIC>.

Hallman, T. J.; Kharzeev, D. E.; Mitchell, J. T.; and Ullrich, T., eds. Quark Matter 2001, Proceedings of the 15th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions. (Elsevier, Amsterdam, 2002).

Rajagopal, K., and Wilczek, F. "The Condensed Matter Physics of QCD" in At the Frontiers of Particle Physics, edited by M. Shifman (World Scientific, Singapore, 2001).

Krishna Rajagopal