FREE THE by KRISHNA RAJAGOPAL

UANTUM CHROMODYNAMICS, or QCD, is the theory of quarks and and their inter- actions. Its equations are simple enough to fi t on the back of an envelope. After a quick glance you Q might conclude that QCD is not very different from the theory of electricity and magnetism called quan- tum electrodynamics, or QED, which describes the behavior of — for example, those in the beams within any television set or computer monitor— and the they interact with. The laws of QCD describe called quarks, which are similar to electrons except that, in addi- tion to , they carry new charges whimsically called “ colors.” Their interactions involve eight new - like massless particles called gluons, representing eight new “ color-electric” and “ color-magnetic” fi elds. A glance at the equations of QCD suggests that they describe beams of quarks, new color with macroscopic range, and lasers. This fi rst impression would be wrong. QCD describes , , , , and many other subatomic particles collectively known as . A has two important properties: it is “ color-neutral,” and it is much heavier than the quarks inside it. For exam- ple, the is often described as made of two up quarks and one down . Indeed, this combination of quarks has

BEAM LINE 9 exactly the right electric charge (+1) mechanical fluctuations, and the vac- Six Different Quarks and color (0) to describe a proton. But, uum is just the state in which these a proton weighs about 50 times as fluctuations happen to yield the low- much as these three quarks! Thus a est possible energy. In QCD, the vac- ODATE, six different proton (or a , or any other uum is a frothing, seething sea of quarks have been discov- hadron) must be a very complicated quarks, antiquarks, and gluons ar- Tered. Two quarks—up and of many quarks, anti- ranged precisely so as to have the down—are light: only about 10 quarks, and gluons (with three more minimum possible energy. times heavier than the . Up quarks than antiquarks). QCD de- QCD describes excitations of this quarks, down quarks, and the scribes how the light quarks and ; indeed, we are made of massless gluons are the main con- massless gluons bind to form these these excitations. In order to under- stituents of pions, protons, and complicated but colorless packages stand how they turn out to be the neutrons. The proton mass is that turn out to be so heavy. It also colorless and heavy hadrons, instead 938 MeV while the sum of the describes how these hadrons them- of colorful and light quarks and glu- masses of two up quarks and one selves bind to form the atomic nu- ons, one must better understand sev- is about 20 MeV. The clei. Thus QCD describes the eral striking properties of the QCD is the next heaviest of everything that makes up our quo- vacuum. quark, with a mass about 20 times tidian world with the exception of According to QCD, the that of the up and down quarks. the electrons and photons. And yet between quarks is actually rather Although strange quarks do play we have never seen a beam of quarks weak as long as the quarks are close an important role in heavy ion colli- or a gluon laser. How, then, does the together, closer than 1 fermi. (One sions, this article focuses on the reality that QCD describes turn out fermi, or 1 F, equals 10−15 meters— or lighter up and down quarks. The three heaviest quarks—charm, to be so different from what a glance approximately the size of a proton.) bottom, and top—are heavy at its laws seems to suggest? This weakness of the force between enough to be left out of this article. The answer to this question relies nearby quarks, called “ asymptotic on our understanding of the proper- freedom” by its discoverers David Approximate ties of the vacuum. Furthermore, we Gross, , and David Quarks Mass(MeV/c) shall see that our naive fi rst impres- Politzer, explains how we can “ see” up (u)5sions are actually correct at temper- quarks at all. A microscope suffi- down (d)10atures above two trillion degrees ciently powerful that it can look strange (s) 150 kelvin. At such ultrahigh tempera- within a proton with a resolution charm (c) 1,300 tures, the stuff that QCD describes much smaller than 1Fallows one bottom (b) 4,200 top (t) 175,000 does indeed look like a plasma of free to observe weakly interacting quarks. quarks and gluons. The entire Uni- The first sufficiently powerful mi- verse was at least this hot for the fi rst croscope was the SLAC linear accel- 10 microseconds after the . erator; quarks were first seen using Thus the goal of heavy-ion collision this device in experiments conducted experiments is to heat up tiny por- in the late 1960s by Jerome Friedman, tions of the to recreate Henry Kendall, Richard Taylor, and these conditions in order to study their collaborators. QCD by simplifying it. is a property of the QCD vacuum, which describes N A UNIVERSE governed by how it responds to an “ extra” quark. the laws of , This quark disturbs (polarizes) the Ithe vacuum is not empty. All nearby vacuum, which responds by states are characterized by quantum- surrounding it with a cloud of many

10 SPRING/SUMMER 2001 quark-antiquark pairs and gluons. In If we add quarks to the QCD vac- T = 0 particular, this cloud acts so as to uum, they interact with this quark- u–u ensure that the force between this antiquark condensate, and the result – quark and another quark (surrounded is that they behave as if they have a dd by its own cloud) does not lessen as large mass. Thus the presence of a one tries to separate the quarks. hadron disturbs the condensate, and Pulling a single, isolated quark com- the largest contribution to the mass pletely out of a colorless hadron of the hadron is the energy of this dis- requires working against a force that turbance. In effect, the condensate 0 < T < Tc does not weaken with increasing slows the quarks down, and because separation—and therefore costs infi- of its presence, hadrons are much nite energy. Thus the energy of a sin- heavier than the quarks of which gle quark (or of any excitation of the they are made. (See the box “On the QCD vacuum that has nonzero color) Origin of Mass” on the next page.) is infinite, once one includes the There is one exception to the dic- energy cost of the resulting distur- tum that hadrons must be heavy. Be- bance of the vacuum. Adding a color- cause QCD does not specify in which T > Tc less combination of quarks to the direction the arrows point, it should vacuum disturbs it much less, cre- be relatively easy to excite “waves” ating a finite energy excitation. Real in which the directions of the arrows excitations of the QCD vacuum must ripple as a wave passes by. In quan- therefore be colorless. tum mechanics, all such waves are To understand why hadrons are associated with particles, and be- heavy, we need a second crucial, cause these waves are easily excited, qualitative, feature to describe the the related particles should not have QCD vacuum. We must specify what much mass. This exception was first Melting the Vacuum. (Top) The QCD vac- fraction of the quark-antiquark pairs understood in 1961 by Yoichiro uum is a condensate. At each location – – at any location is uu–, dd, ud or du–. Nambu and Jeffrey Goldstone. The are quark-antiquark pairs whose type must be specified by an arrow indicating At each point in space, the vacuum requisite particles, the well-known − what fraction of the pairs are uu versus is therefore described by a “vector” pions, weigh in at about one-seventh − − − that can point any direction in an of the proton’s mass. dd versus ud versus du . Only two of these four directions are shown. The abstract four-dimensional space with Thus the QCD vacuum is a com- – – central property of a condensate is that axes labeled uu, dd, etc. In order to plex state of . The laws de- all the arrows are aligned. (Middle) At achieve the lowest energy, QCD pre- scribing it are written in terms of col- non-zero temperatures, the arrows dicts that all these vectors must be ored quarks and gluons, but its describing the condensate begin to un- aligned. A sea of quark-antiquark natural excitations are colorless dulate. These waves can equally well be pairs so ordered is called a “conden- hadrons, which are heavy because of described as a gas of particles, called sate.” The fact that the arrows must their interaction with a symmetry- pions. (Bottom) As the temperature increases, the waves on the condensate pick one among many otherwise breaking condensate that pervades become more and more violent. Above equivalent directions is known as all of space. some critical temperature, the arrows . The condensate are completely scrambled, and the con- that characterizes the QCD vacuum NE GOOD WAY of test- densate has melted. is much like a ferromagnet, within ing our understanding of the which all the microscopic vec- OQCD vacuum is to create tors are aligned (see illustration above new, simpler, states of matter (often right). called phases) in which QCD behaves

BEAM LINE 11 as expected on first glance. Is there a apart. What actually occurs (see box On the Origin of Mass phase of matter in which quarks can on the opposite page) is a phase tran- roam free? In which the excitations sition to a plasma of quarks, anti- are closer to being individual quarks quarks, and gluons. At low temper- and gluons rather than the compli- atures, QCD describes a gas of pions. HE VACUUM in which we cated packages we call hadrons? Once the condensate melts, this live is actually filled with two Asymptotic freedom provides two gas ionizes, releasing quarks and glu- Tcondensates: a quark- antiquark condensate required by ways to free the quarks. The first is ons that are lighter, more numer- QCD and another of Higgs particles to squeeze nuclei together until their ous (three colors of each of up, down, required by the . If protons and neutrons overlap. In the and strange quarks plus their anti- neither condensate were present, resulting “quark matter” the quarks quarks and eight types of gluons) and both quarks and protons would be are close together, and therefore therefore have a much larger energy massless. The quarks get their interact only weakly. The second density at a given temperature. (light, but non-zero) mass from approach is to take a chunk of mat- their interaction with the Higgs ter and heat it. When you heat a mag- E NOW HAVE the nec- condensate; about 1/50th of the net, by analogy, the spins in the mag- essary tools to describe mass of protons and neutrons is net start to oscillate; eventually, Wthe prominent features on due to its presence. The remainder above some critical temperature, the phase diagram of QCD (see illus- of the mass of protons and neu- they oscillate so wildly that the spins tration on page 14). At low densi- trons (and of all hadrons) is due to all point in random directions, and ties and temperatures, we find the fa- the presence of the quark- the loses its magnetization. miliar world of hadrons. The only antiquark condensate. Something similar happens in QCD. known place in which nuclei are At low temperatures, the arrows that squeezed together without being describe the QCD condensate ripple, heated is the center of neutron stars. yielding a gas of pions. Above a crit- The cores of these extraordinarily ical temperature, the arrows oscil- dense cinders, with masses about late so wildly that they point ran- that of the Sun but with radii of only domly, and the condensate “melts.” about 10 km, may be made of super- Above its critical temperature, the conducting quark matter. matter described by QCD is more dis- To find a phase of matter in which ordered but more symmetric (no QCD simplifies completely and the direction favored in the illustration excitations are only quarks and on the previous page) than the QCD gluons, we must explore the high- vacuum. temperature regions of the phase Theoretical calculations that diagram. Upon heating any chunk of strain the world’s fastest supercom- matter to trillions of degrees, the vac- puters show that at a temperature of uum condensate melts, the hadrons about 2×1012 K the QCD condensate ionize, and the quarks and gluons are should melt and the hadrons “ion- free to roam in the resulting quark- ize,” yielding a plasma in which the gluon plasma. The Universe began quarks are free. Once the condensate far up the vertical axis of the diagram: melts, hadrons need no longer be at its earliest moments, shortly after heavy, and a putative gas of them the Big Bang, it was filled with a would have so many hadrons and very hot quark-gluon plasma that antihadrons that these would over- expanded and cooled, moving down lap, making it impossible to tell them the vertical axis, falling below

12 SPRING/SUMMER 2001 2×1012 K after about 10 microseconds. For the last fi ve years, the highest- diagram, more closely recreating the Since then, quarks have been con- energy heavy-ion collisions occurred conditions of the Big Bang. To date, fined in hadrons—with the possible in experiments done at the Super we have only the first, simplest exception of quarks at the centers of Proton Synchrotron (SPS) at CERN. analyses of collisions at RHIC, but neutron stars and those that are But in June 2000, the fi rst collisions it is already clear that these collisions briefly liberated in heavy-ion colli- occurred at Brookhaven’s new have higher initial energy densities sions. Relativistic Heavy Ion Collider and lower net quark densities than (RHIC) whose collisions are about 10 at the SPS. N A HEAVY-ION collision, times more energetic. What does this The intriguing SPS results reveal two nuclei accelerated to enor- big energy increase buy? It boosts the several aspects that are difficult to Imous energies are collided in an initial energy density, and thus the model using only the physics of attempt to create a tiny, ultrahot initial temperature, pushing further hadrons. One example is the paucity region within which matter enters upward into the expected quark- of J/Ψ particles, which include one the quark-gluon plasma phase. As in gluon plasma region of the phase charm and one anticharm quark. As the Big Bang (but much more diagram. In addition, these higher charm quarks are heavy, they are pro- quickly) this quark-gluon plasma energy collisions produce many more duced only rarely in a heavy-ion col- droplet expands and cools, moving pions, diluting the net quark density. lision. Those few that do occur arise downward on the phase diagram. For As we build more energetic heavy- from the earliest most energetic a brief instant the quarks are free, but ion colliders, therefore, we explore quark-quark collisions. If a charm their liberation is short lived. After upwards and to the left on the phase and anticharm quark are created in about 10−22 second they recombine to form an expanding gas of hadrons, which rattle around as they expand Melting the Vacuum for perhaps another 10−22 second. After that these hadrons are so dilute (Top) The strength of the condensate that they fly outwards without fur- (the “vector average” of all the ther scattering, to be seen in a Condensate colored arrows in the illustration on detector. The STAR and PHOBOS page 11) decreasing with increasing detectors at Brookhaven National temperature. The shape of this curve Laboratory (see previous article, mirrors that of an analogous curve “Creating a Little Big Bang on Long showing how magnetization vanishes Island,” by Frank Wolfs) record many when the spins in a magnet get T thousands of hadrons—the end prod- scrambled at a temperature of only a few hundred degrees. (Bottom) The ucts of a collision in which quark- Ideal Quark-Gluon higher the temperature (T), the more gluon plasma may have been created. Plasma ε energy per unit volume (ε). The ratio The purpose of these heavy-ion 4 T ε/T4 is a measure of how many differ- collision experiments is twofold. We ent types of particles are present. hope to create a region of quark-gluon ε/T4 rises rapidly from the value for a plasma—the stuff of the Big Bang— pion gas to close to the value for an and measure its properties to see ideal quark-gluon plasma in which the whether the complexities of the QCD Pion Gas interactions between quarks and vacuum have truly melted away. gluons have become weak. This rise T ~ 140– 190 MeV T And, we hope to study how matter c directly reflects the freeing of the ~ (1.6– 2.2) × 1012 K behaves as it undergoes the transi- quarks. tion from this plasma back to a mun- dane hadron gas.

BEAM LINE 13 by the Big Bang and by the highest T Heavy Ion Collisions energy collisions), the phase transi- tion from quarks to hadrons occurs smoothly and continuously. It is RHIC? therefore quite different from the boiling of water, which occurs at a sharply defi ned temperature at which Quark-Gluon Plasma ~ 150 MeV its properties change sharply. Theo- retical arguments suggest that at SPS? higher net quark density, the phase transition between quark-gluon Critical Point plasma and hadrons is similarly dis- continuous and can be shown in the illustration on the left as a sharp line. This line ends at what is called the Superconducting “ critical point.” Hadrons Quark Matter The Universe There are phenomena that occur ? at the critical point and nowhere else µ on the phase diagram. At this point, the arrows of the figure on page 13 Vacuum Nuclei Neutron Stars undulate in a unique, precisely cal- culable, manner. Consequently, dis- Phases of QCD as a function of tempera- a quark-gluon plasma (wherein they tinctive fluctuations occur in those ture and µ, a quantity that is a conve- nient measure of the net quark density, are free to wander), they are unlikely heavy-ion collisions that pass near Ψ namely the density of quarks minus that to fi nd each other and form a J/ . The the critical point as they cool. For of antiquarks. The vacuum is at the bot- striking paucity of J/Ψ particles in example, the mean momentum of tom left; nuclei have non-zero net quark measurements by the NA50 experi- the 100 lowest-energy pions in a col- density. Squeezing nuclei without heat- ment at the SPS is therefore quite lision should vary enormously from ing them pushes matter to the right on interesting. Further experiments by one collision to the next. The NA49 the diagram, while heating matter NA50 and the PHENIX experiment at experiment at the SPS has done a pushes it up. The colored line separat- RHIC ing the quark-gluon plasma from the should help to resolve remain- careful search for such fluctuations hadronic phase ends at a critical point. ing ambiguities in the interpretation but has not seen any. The search for of these data. One interpretation is the critical point continues, with that the SPS heavy-ion collisions are RHIC exploring to the left in the il- exploring the crossover region in the lustration above and new lower phase diagram (the colored “ in- energy SPS collisions exploring fur- between region” in the illustration ther to the right. Early indications on the previous page), where QCD are that fluctuations in RHIC colli- is not well described either as a gas sions are an order of magnitude larger of hadrons or as a quark-gluon plasma. than those at the SPS, but it remains How can we test this hypothesis? to be determined whether these have One idea uses the fact that higher the characteristic features that would energy collisions cool by passing signal the discovery of the critical through the phase transition region point. farther to the left. Near the vertical In addition to studying the tran- axis of the phase diagram (traversed sition between quark-gluon plasma

14 SPRING/SUMMER 2001 and hadrons, we wish to use heavy- expected. If the vacuum condensate ion collisions to measure properties melts and hadrons ionize, freeing the of the newly created quark-gluon quarks, we shall have realized the plasma itself. To do so, we need ob- dream of simplicity implicit in the servables that tell us about the ear- laws of QCD. liest, hottest, moments of a collision. One simple way is to shoot a very fast quark through the plasma and watch how rapidly it loses energy. Estimates suggest that a quark plow- ing through such a plasma loses much more energy than it would if it encounters only heavy, colorless hadrons. We search for signs of this rapid energy loss by looking for a paucity of 5– 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 5– 10 GeV pions will be seen, relative to what occurs in proton col- lisions. Despite best efforts, however, no evidence of such a deficit has been seen at the SPS. Perhaps the most exciting announcement at the recent Quark Matter conference was that preliminary data from both the STAR and PHENIX experiments show about 5 times fewer energetic pions than expected. With time, this observa- tion should become a quantitative measure that will allow us to test whether high temperature QCD in- deed describes a quark-gluon plasma— and to test predictions of its properties. We wait with great interest, hop- ing that experimenters soon confi rm they are regularly recreating the very stuff of the Big Bang. As they then begin to measure its properties, we shall learn whether QCD behaves as

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