FREE THE QUARKS by KRISHNA RAJAGOPAL UANTUM CHROMODYNAMICS, or QCD, is the theory of quarks and gluons 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 electrons— for example, those in the beams within any television set or computer monitor— and the photons they interact with. The laws of QCD describe particles called quarks, which are similar to electrons except that, in addi- tion to electric charge, they carry new charges whimsically called “ colors.” Their interactions involve eight new photon- 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 forces with macroscopic range, and gluon lasers. This fi rst impression would be wrong. QCD describes protons, neutrons, pions, kaons, and many other subatomic particles collectively known as hadrons. A hadron has two important properties: it is “ color-neutral,” and it is much heavier than the quarks inside it. For exam- ple, the proton is often described as made of two up quarks and one down quark. 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 neutron, 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 bound state 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 electron. Up quarks than antiquarks). QCD de- QCD describes excitations of this quarks, down quarks, and the scribes how the light quarks and vacuum; 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- down quark is about 20 MeV. The clei. Thus QCD describes the physics eral striking properties of the QCD strange quark 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 force 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, Frank Wilczek, 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 Big Bang. 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 Universe to recreate Henry Kendall, Richard Taylor, and these conditions in order to study their collaborators. QCD by simplifying it. Asymptotic freedom is a property of the QCD vacuum, which describes N A UNIVERSE governed by how it responds to an “ extra” quark. the laws of quantum mechanics, 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 matter. 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 symmetry breaking. 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 spin vec- OQCD vacuum is to create tors are aligned (see illustration above new, simpler, states of matter (often right).