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What We Have Learned in the Past Two Decades DEVELOPMENT OF THE QUARK MODEL OF HADRONS The Beginnings of the Quark Model It was first recognized in 1964 that all the known hadrons fell into the particular symmetry scheme, or pattern, expected if all hadrons are formed from three fundamental constituents. These were called quarks, and they were given the names u, d, and s for up, down, and strange. Each hadron would be composed of either three quarks [such as the ten-member group shown in Figure 3. 1(A)] or of quark-antiquark pairs [such as the octet group shown in Figure 3el(B)~. Note that for each of these states the total charge of the particle is the sum of the charges of the quarks of which it is composed. For example, the A+ + (pronounced delta plus plus) shown in Figure 3.1(A) consists of 3 u quarks, so its total charge is 3 x (+ 2/3) = ~ 2 (hence the + + superscript). Similarly, the ~ + is composed of uad and has a charge of 2 x (+2/3) + (-1/3) = +1. Each of these quarks is in a particular orbit or state of motion relative to the other two quarks. If we were able to reach into the A+ + and magically transform one of the u quarks into a d quark, without altering the orbit of the quark, then we would have a A+ (delta plus) particle. Similarly, if we were to change one of the two u quarks in the ~ + into a d quark, then we would have a At (delta zero) and so on. The similar 48

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WHAT WE HAVE f EARNED IN THE PAST ~0 DECADES 49 is- (ddd) ~(ddu) BAA ~~ \ \ co-eds) (B) -(dub \ K-(su) / / _~ K( sd) * (dus) .~s*-(dss) \ / \ / \ ~ n~ (Sss' / / K(ds) K+(us) ~~ / ~+(duu) ^++(uuu ) ~ 7 / , *US) / / /'*(USS \ \ 77 7~ ~ 7~+(ud) / FIGURE 3.1 Hadrons are made out of quarks. (A) shows how the delta, sigma-star, xi-star, and omega family of hadrons are made out of three quarks; (B) shows how the meson family, which contains the plan and kaon, is made of a quark and an antiquark. The positive pion, Tr+, and the positive kaon, K', have different properties because the 1r~ consists of an up quark (u) and a down antiquark (d), while the K+ consists of an up quark (a) and a strange antiquark (s). The ~ and A are made up of combinations of uu, dd, and ss quarks.

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50 ELEMENTARY-PARTICLE PHYSICS masses of all the As indicate that the u and d quarks have about the same mass. However, if we were to change one of the u quarks in the ~ + + into an s quark, again without changing the orbit, we would then have a I* + (sigma-star plus), which has a mass about 150 MeV greater than the A+ +. This indicates that the s quark is about 150 MeV heavier than the u or d quarks. If we were to change one of the two u quarks in the I;* + into an s, we would get the _* (xi-star zero), about 150 MeV heavier than the I* +. And finally, if we were to change the remaining u into an s, we would have the Q~ (omega minus). The Q- had not been seen when the quark model was first proposed. Its discovery the following year, with the predicted mass and the predicted charge, gave strong support to the quark picture. But even then many physicists emphasized that the symmetry did not necessarily imply the actual physical existence of quarks. In particular, the charge of the quarks had to be fractional (2/3 of the standard unit for the u quark and -1/3 for the d and s quarks)' but no fractionally charged particles had ever been observed. Thus although the hadron classification scheme based on quarks was widely accepted, the actual physical existence of quarks was questioned. The Discovery of the Charmed Quark During the years from 1964 through 1973, considerable progress was made, both experimentally and theoretically, in support of the idea of physical quarks. Some of this is described in Chapter 3 in the section on How Quarks Interact. But perhaps the most important and compel- ling new evidence for quarks began in 1974 with the discovery of a new particle, the J/ ('~jay-psi"), which was discovered simultaneously at Brookhaven National Laboratory (where it was called the J) and at Stanford Linear Accelerator Center (where it was called the Off. The J/ was unusually heavy (3.1 GeV in mass) and had a very long lifetime, uncharacteristic of strongly interacting particles. Indeed, heavy particles in general tend to be more unstable and therefore to have shorter lifetimes. Thus the J/ definitely did not fit into the symmetry scheme that had been so successful in classifying other hadrons. Physicists hypothesized that it contained a new kind of quark, called c or charm, which had in fact been predicted earlier. The J/ was believed to be a bound state of a charmed quark and a charmed antiquark. In order for the J/ to have such a large mass, the mass of the new quark would also have to be large (about 1.5 GeV). Thus the

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WHAT WE HAVE LEARNED IN THE PAST ~0 DECADES 51 mass of the J/ would be about the mass of a c quark plus the mass of a c antiquary. [An antiparticle is often symbolized by drawing a short bar above the symbol for the corresponding particle. Thus c (pro- nounced c bar) is the symbol for the charmed antiquark.] If this hypothesis were correct, it would mean that a whole family of new charmed particles would exist, consisting of a charmed quark bound together with one or more other kinds of quarks. For example, there would be a cu state (called the Do, with a mass of about 1.8 GeV), a cd state (called the D+, with a similar mass), a cs (called the F+, with a mass of about 2.0 GeV), and a uric state (a charmed baryon, with a mass of about 2.2 GeV). All these states, and others, have since been discovered! All have had the masses, charges, decay modes, and other properties predicted from the idea of constituent quarks. The excellent agreement between prediction and experiment has established the validity of the quark picture beyond any reasonable doubt. Charmonium States The discovery of the J/ was also important in establishing the existence of quarks in a second way, since it was the first of several states, referred to as '~charmonium" states, that are composed of a cc pair. All these states have masses in the range 3.0 to 3.6 GeV. All are believed to consist of a charmed quark bound together with a charmed antiquary. The heavier ones are excited states in the sense that the two quarks have more energetic orbits. The existence of these distinct but similar particles, each formed by the same constituent quarks but in different energy states, provided an important quantitative confi~n~a- tion that quarks do indeed exist. Such a range of different energy states in a two-body system is very familiar to physicists. An analogous two-body system is the hydrogen atom, composed of a single electron orbiting around a single proton. The different energy levels of the excited states of hydrogen account for the discrete lines in the spectrum of light emitted by hydrogen; the spectral lines are produced by photons emitted in a transition from an excited level to a less-excited level, and their energy is equal to the difference in energy levels of the initial and final states. Spectral lines were first observed in 1802, and the spectrum of excited states was first quantitatively explained by the Bohr model of the hydrogen atom in 1913. A similar set of different energy levels is seen in positronium, which is a bound state of an electron and its antiparticle, the positron. Since

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52 EfEMENTARY-PARTIC~E PHYSICS POSIT RObJ ~ UM 7 2 ._ _ , o D'ssoclotion E net gy I< 23S, 23P2 2'P, 23P 23Po 2'So X ~OtOOO x 1000 n: 1 ~ l3S ~ 1lSo AS Stotes ~PStctes IS Stotes UP Stotes CHARMObJ\UM 000 800 200 - 33s, 1 o c o - - 600 -E 400 2iS ~' 21p' 25P2X c, - 0 0 c, cr - 23s. ' So Tic 15s,* IS Stotes UP Stoles 25P,X,/2 PoXo c ED AS Stotes UP Stotes FIGURE 3.2 The spectrum of energy states is similar in positronium and charmonium, but the scale of the energy differences in charmonium is greater by a factor of roughly 100 million. The energy of a state is determined by the principal quantum number n and by the orientation of the particle spins and the orbital angular momentum. The arrangement of the energy levels is similar because both pairs of particles obey the same laws of quantum mechanics. In positronium the venous combinations of angular momentum cause only minuscule shifts in energy (shown by expanding the vertical scale), but in charmonium the shifts are much larger. All energies are given with reference to the 135' state. At 6.8 electron volts positronium dissociates. At 633 MeV above the energy of the charmonium becomes quasi-bound because it can decay into D and D mesons. charmonium states are also bound states of a particle (the c quark) and its antiparticle, they should show a spectrum of energy levels similar to those of positronium. However, since the charmed quark is about 3000 times more massive than the electron, and since the force holding the quarks together in charmonium is the nuclear force (about 100 times stronger than the electric force), one would expect the masses and the mass difference between charmonium states to be much larger than those of the positronium states. This is exactly what is observed. Seven different charmonium bound states have been found. These states are shown in Figure 3.2(b). The similar states for positronium are shown in Figure 3.2(a). Note that the energy spacing between the charmonium levels is about 100 million times larger than the spacing between the positronium levels. But aside from this expected difference, the close similarity of the structure of the splittings speaks for itself and provides another strong proof of the

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WHA T WE lIA VE LEARNED IN THE PAST TWO DECADES 53 physical existence of quarks and of the universality of quantum mechanics. DISCOVERY OF THE THIRD GENERATION OF LEPIONS AND QUARKS With the discovery of the charmed quark in 1974, the second generation of quarks was completed. At that time, two generations of leptons were also known: the electron and its neutrino, and the muon and its neutrino. It is interesting to go back to 1974 to understand the significance of the two generations and to give a brief history of how the third generation was accidentally discovered in both the lepton and the quark areas. In 1974 there was no explanation of why there was more than one generation of either leptons or quarks, and indeed we still have no explanation of this fact. As discussed in the next chapter, this is one of the outstanding puzzles facing elementary-particle physicists. The Discovery of the Tau Lepton The generations puzzle is most easily seen in terms of the charged- lepton situation in 1974. At that time we knew that both the electron and the muon existed, that the muon was about 200 times heavier than the electron, and that botn the muon and the electron had the same kind of behavior with respect to the electromagnetic force and the weak force. We also knew that the muon was very different from the electron in the sense that it could not decay into an electron in any simple way. But there was absolutely no theoretical understanding of why both particles existed or of how the mass of the muon was related to the mass of the electron. Experimenters at the SPEAR electron-positron collider at the Stanford Linear Accelerator Center (SLAC) began to look at the particles being produced in this machine to see if there might be charged leptons other than the electron or muon being created in the collisions. This was purely an experimental search, since there was no theoretical motivation for it. This is an illustration of a theme that we shall return to again and again in this report that experimenters often explore the unknown without theoretical guidance. And such explora- tions can be very fruitful, particularly at new accelerator facilities. SPEAR was such a facility in 1974. In 1975 these experimenters began to accumulate evidence for the existence of the third charged lepton, now called the taut The tau has

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54 ELEMENTARY-PARTICLE PHYSICS Muon (It) r A\ I / Yet Electron (e) /~. \ l - FIGURE 3.3 One of the electron-muon two-prong events that led to the discovery of the tau lepton in 1975. At the time such events were unusual and could not be explained by the production of any of the then known particles. a mass of a little over 1780 MeV; hence it is about 3500 times heavier than the electron. The discovery was made through the finding of electron-muon two-charged-particle events as shown in Figure 3.3. The tau lepton had too short a lifetime to be detected directly at that time, but in an electron-positron collision a tau-antitau pair can be produced, and this pair can then decay to an electron and a muon, plus unseen neutrinos. Subsequent studies of the tau lepton at SPEAR and other electron- positron colliders showed that it behaved the same way as the electron and muon with respect to the weak and electromagnetic force and that it did not respond to the strong force. Further studies of the decay of the tau lepton demonstrated that it had its own unique neutrino associated with it. That is, the neutrino associated with the tau lepton is not the same as the neutrino associated with the electron, nor as the neutrino associated with a muon. Thus two

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WHAT WE HAVE LEARNED IN THE PAST ~0 DECADES 55 new leptons were actually found, the tau lepton and its associated neutrino. It is still necessary for us to learn how the tan neutrino interacts, i.e., to see if it interacts in a manner similar to the way in which the electron neutrino and the muon neutrino interact. Such an experiment cannot be carried out in an electron-positron collider, where all other studies of the tau and its neutrino have been done, but rather must make use of a secondary neutrino beam produced at a proton accelerator. The Discovery of the Bottom Quark The discovery of the b or bottom quark was made at Fermilab in 1977. As in the case of the tau, this was a purely experimental discovery. There was little theoretical guidance in looking for the b quark and no indication of what energy might be required to find it. The experiment at Fe~ilab that found the b quark was studying pairs of electrons and pairs of muons produced in the collisions of the primary proton beam of the 400-GeV proton accelerator with a fixed target. The experimenters measured the masses of the pairs of electrons or muons produced, and they plotted the frequency of occurrence of those masses, as shown in the historic curve of Figure 3.4. A peak in that mass frequency plot appears between 9 and 10 GeV. This peak turned out to be due to the production of a new kind of particle called the upsilon. Each of the upsilon particles consists of a bottom quark bound together with its corresponding antiquary. Hence the mass of the bottom quark is about half of 10 GeV, namely, 5 GeV. This is how the bottom quark was discovered. Information about the bottom quark can be obtained by studying the upsilon family of particles or by studying mesons that consist of one bottom quark and one of the lighter antiquarks (or vice versa). Such particles are called B mesons. Extensive studies of upsilon particles and B mesons have been and are being made, particularly at electron- positron colliders. For example, Figure 3.5 shows the spectrum of the upsilon family of particles, obtained at the Cornell Electron Storage Ring (CESR) and DORIS [at the Deutsches Electronen Synchrotron (DESY)] electron-positron colliders. B mesons are probably also copiously produced in hadron-hadron collisions, either in fixed-target experiments or at particle colliders. At present, the large background of ordinary mesons also produced in hadron-hadron collisions makes the detailed study of B mesons difficult when produced in this way. But as particle detectors improve, it should become possible to make detailed studies of B mesons at proton

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56 ELEMENTARY-PARTICLE PHYSICS , , ~ ._ CL ~ 100 o o Q i,_ 10 o c a) or a' ._ ~ O cr _ ~ t 1 1, 1 1 1 ~ . rfL 6 8 10 12 Muon Pair Mass (GeV) FIGURE 3.4 The upsilon was discovered in 1977 by studying the production of muon pairs or electron pairs in proton collisions. Here the relative frequency of production of muon pairs is shown to decrease as the muon pair mass increases. The bump in the curve at 9-10 GeV is due to the upsilon. accelerators as well as those currently done at electron-positron colliders. The Third Generation As shown in Figure 3.6, we can now see how the third generation of leptons and half of the third generation of quarks was added to our basic

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WHAT WE HAVE LEARNED IN THE PAST ~0 DECADES 57 system of elementary particles. Most physicists believe that there is a second member of the third generation of quarks, which is called the t or top quark. The expectation for the existence of the top quark comes from two sources: first is our belief that nature is simple, so that in each gen- eration quarks like leptons should come in pairs; second, measure- ments of the b quark lifetime give an indirect indication that there should be a top quark associated with the bottom quark. As this report was being completed in 1984, initial direct evidence was reported for the existence of the top quark. 3S' states in ~ family lo' 3.69 3.10 ~ 3S' stotes in T family Mass (GeV) , 10.55 To' , ' 10.32 10.00 T; 9.43 FIGURE 3.5 The triplet 5 states (351) of the upsilon (Y) family are shown on the right. Each of these states consists of a b quark bound to a ~ quark. For comparison the two 35~ states of the ~ family are shown on the left. Although the masses are very different, the level separations are nearly equal.

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58 ELEMENTARY-PARTICLE PHYSICS Generation Particle Charge Mass ~ electron (e) I ~ electron neutrino (~e) 0.51 MeV I O less than 50 eV 1 2 .4 muon (id) | muon neutrino (v,,) O 106 MeV=0.106 GeV I less then O.S MeV | 3 ~ tau ( T) -1 1784 MeV = 1.784 GeV tau neutrinos (V') O less then 160 MeV = 0. 160 GeV *indirect evidence Generation Porticle Charge Moss Tup (u) down(d) ~ 2/3 about 300 MeV - 0.3 GeV - 1/3 about 300 MeV= 0.3 GeV 2 ~ charm (c) strange (s) +2/3 aboutl50OMeV= 1.5GeV -1 /3 about 500 MeV= 0 5 GeV 36 bottom (b) - 1/3 about 5,000 MeV= S.O GeV | 1 ' - - . _ FIGURE 3.6 Our present knowledge of the lepton and quark families of particles. Although nature does seem to be simple, that does not mean that we understand it. Just as in 1974 we did not know why there were two generations of leptons and quarks, so in 1985 we do not know why there are three generations of leptons and quarks. What has been gained, of course, is the experimental demonstration that there can be more than two generations of leptons and quarks. Indeed, there may be more than the present three generations. Some theoretical arguments and some deductions from astrophysical considerations can be inter- preted to mean that there are not more than four generations of leptons and quarks. But physics is, in the end, an experimental science, and the search for more than four generations of leptons and quarks will be carried on by experimenters. There is probably nothing more challeng- ing to a scientist than to be told that, theoretically, something cannot exist.

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70 ELEMENTARY-PARTICLE PHYSICS STRONG INTERACTION AMONG QUARKS We have seen already how the idea that the strongly interacting particles are built up of quarks brought new order to hadron spectros- copy and suggested new relations among mesons and baryons. But this constituent description also brought with it a number of puzzles. These seemed at first to indicate that the quark model was nothing more than a convenient mnemonic recipe. In pursuing and resolving these puz- zles' physicists have found a dynamical basis for the quark model that promises to give a complete description of the strong interactions. An obvious question concerns the rules by which the hadrons are built up out of quarks. Mesons are composed of one quark and one antiquary, while baryons are made of three quarks. What prevents two-quark or four-quark combinations? Within this innocent question lurks a serious problem of principle. The Pauli exclusion principle of quantum mechanics is the basis for our understanding of the periodic table of the elements. It restricts the configurations of electrons within atoms and of protons and neutrons within nuclei. We should expect it to be a reliable guide to the spectrum of hadrons as well. But according to the Pauli principle, the observed baryons such as ~ + + (uuu) and Q~ (sss), which would be composed of three identical quarks in the same state, cannot exist. To comply with the Pauli principle, it is necessary to make the three otherwise identical quarks distinguishable by supposing that every type of quark exists in three varieties, fancifully labeled by the colors red, green, and blue. Then each baryon can be constructed as a colorless (or white) state of a red quark, a green quark, and a blue quark. Similarly, a meson will be a colorless quark-antiquark combination. The rule for constructing hadrons may then be rephrased as the statement that only colorless states can be isolated. A second issue is raised by the fact that free quarks have not been observed. This suggests that the interaction between quarks must be extraordinarily strong, and perhaps permanently confining. That free quarks are not seen is of course consistent with the idea that colored states cannot exist in isolation. On the other hand, the quark model description of violent collisions rests on the assumption that quarks within hadrons may be regarded as essentially free. This paradoxical state of affairs may be visualized as follows. We may think of a hadron as a bubble within which the constituent quarks are imprisoned. The quarks move freely within the bubble but cannot escape from it. This picturesque representation yields an operational understanding of many aspects of hadron structure and interactions,

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WHAT WE HAVE [EARNED IN THE PAST TWO DECADES 71 ma) 3~O (O ) iota (b) FIGURE 3.13 Electrically polarized molecules weaken the effect of an electric charge. In (a) the molecules point in random directions. In (b) a negative charge is present, and the positive ends of the molecules point toward this charge and partially cancel it. Outside of this area the electric charge will appear weaker. but it falls far short of a dynamical explanation for the puzzling behavior of quarks. We still do not understand completely why quarks apparently interact only weakly when they are close together and yet cannot be pulled apart. To see why this is surprising, and to learn how it might come about, it is helpful to consider the interactions of electrically charged objects. We customarily speak of the electric charge carried by an object as a fixed and definite quantity, as indeed it is. However, if a charge is placed in surroundings in which other charges are free to move about, the effect of the charge may be modified. An example is a medium composed of many molecules, each of which has a positively charged end and a negatively charged end. In the absence of an intruding charged particle, the molecules are oriented randomly [Figure 3.13(a)], and the medium is electrically neutral not only in the large, but locally as well, down to the submolecular scale. Placing an electron in the medium polarizes the molecules [Figure 3.13(b)~: the negatively charged ends of the molecules are repelled by the electron, while the positively charged ends are attracted to it. The effect of this orientation of the molecules is that at finite distances from the electron its influence is screened, or reduced, by the opposite charges it has attracted. Only when we inspect the electron at very close rangesmaller than molecular size is the full magnitude of the electron's charge apparent. We may say that the effective charge is larger at short distances than at long distances. We normally think of the vacuum, or empty space, as the essence of nothingness. However, in quantum theory the vacuum is a complicated and seething medium in which virtual pairs of charged particles, most

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72 ELEMENTARY-PARTICLE PHYSICS blue Time quork~_ ( a ) (~)_ gluon green",> quark ,~ ( b ) green '~ quark blue quork oll gluons q = quark it) 9=gluon FIGURE 3.14 How quarks and gluons interact. In (a) quarks change their color through the emission and absorption of a gluon. In (b) gluons interact with each other. importantly electrons and positrons, have a fleeting existence. These ephemeral vacuum fluctuations are polarizable in the same way as the molecules of our example. Consequently in QED it is also expected that the effective electric charge should increase at short distances, and indeed the consequences of this variation are observed in atomic spectra. The behavior of the effective charge in QED is opposite to that required in the realm of the strong interactions, where the interaction between quarks must diminish in strength at short distances. An explanation for the contrary behavior of the strong force emerged unexpectedly from the ideas that had proved so fruitful for the electroweak interactions: the strategy of gauge theories. Since color is an attribute of quarks but not of leptons, it can be considered as a strong-interaction charge. When the color symmetry among red, blue, and green quarks is taken as the basis for a gauge theory, the resulting interactions among quarks are mediated by force particles called gluons. There are eight gluons corresponding to the distinct color- anticolor combinations. (The white combination corresponding to an equal mixture of red-antired, blue-antiblue, and green-antigreen is not included.) In quantum chromodynamics, or QCD as the theory is called, quarks may interact as shown in Figure 3.14(a), where a blue

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WHAT WE HAVE LEARNED IN THE PAST TWO DECADES 73 quark and a green quark exchange color. Because the gluons carry color, they can interact among themselves as well, as shown in Figure 3.14(b). The photons of QED, being electrically neutral, have no such self-interactions. The fact that the gluons are (color) charged is responsible for the crucial difference between the behavior of the effective charge in QED and QCD. In the strong-interaction theory there are two competing effects: a screening brought about by the color charges in the fluctu- ating vacuum and a camouflage effect that is not present in QED. The screening, or vacuum polarization, may be understood just as in electrodynamics. This time we think of the vacuum as a collection of randomly oriented three-cornered objects, as shown in Figure 3.15(a). By placing a green quark in the vacuum, we orient the triangles [Figure 3.15(b)] and screen the color charge. The behavior of the strong interaction charge is the result of a competition between these two opposing effects. In QCD, the outcome is that the effective color charge does have the properties necessary to reconcile the simple quark model and quark confinement. The steady weakening of the charge at short distances is known as asymptotic freedom because quarks become effectively free at very small separa- tions. In the regime of short distances probed in violent high-energy collisions, the strong interactions are sufficiently feeble that reaction rates may be calculated using the diagrammatic methods developed for QED. In some measure these calculations reproduce the simple quark model results as first approximations. This is the case, for example, in electron-positron annihilations into hadrons. The quark-antiquark pro- duction rate, represented by the diagram in Figure 3.16(a), correctly anticipates both the structure of the dominant twojet events and the D V R/\B <0 5o eG Dm eVa 9 (a) ~ b) FIGURE 3.15 An illustration of how the force exerted by a quark owing to its color charge can be weakened by vacuum effects.

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74 ELEMENTARY-PARTICLE PHYSICS Time Q (b) Q:(,* ,~ `~> ~ becomes _` I hod rons (a) W{~)*~( (/ Am) ~ h o d ro n s ~~ ~ becomes ,,~J J hod rons ~ ~ ~ becomes i!} ~ hadrons becomes ~! hodrons e~- electron r = photon q = antiquark q = quark g = g loon FIGURE 3.16 An example of how interactions of gluons with quarks lead to more complicated processes. In (a) an electron-positron pair annihilate to produce a virtual photon, which in turn produces a quark-antiquark pair. In (b) one of those quarks also emits a gluon. approximate rate of hadron production. The strong-interaction correc- tions to this process include the diagram shown in Figure 3.16(b)' in which a gluon is radiated by one of the outgoing quarks. Like the quarks, the gluon materializes as a jet of hadrons. The resulting threejet events are commonplace in the electron-positron annihilations studied at the PEP and PETRA storage rings. The highest energies yet attained in collisions of the fundamental constituents are those reached in proton-antiproton interactions at the CERN SppS machine. Already collisions among quarks and gluons have been recorded at energies approaching 300 GeV. The hard scatterings of these particles lead to striking jets of hadrons at large angles to the direction defined by the incident proton and antiproton beams. Events of this kind are observed at approximately the fre- quency suggested by QCD. While diagrammatic methods are of great value in the study of strong interactions, several considerations prevent the resulting calculations from being as precise as those long familiar in the electroweak domain. The first is that at the energies currently accessible (or, in other words, at the distances currently probed), the strong interaction is still con- siderably stronger than electromagnetism. A more serious sticking point is that the diagrammatic methods

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WHAT WE HAVE LEARNED IN THE PAST TWO DECADES 75 describe reactions that involve isolated quarks and gluons, whereas in the laboratory quarks and gluons are found only within hadrons. We have not yet succeeded in solving the theory in the regime of potent strong interactions characteristic of hadron structure. In some cases this problem may be circumvented by using QCD only to predict how observables change from one energy to the next and not the value they take at one particular energy. This is the case, for example, in deeply inelastic electron-proton scattering, for which the reaction rate de- pends in an essential way on the internal structure of the proton. This prediction and observation of gradual but systematic change is one of the notable successes of the theory. To deal with the existence and properties of the hadrons themselves it is necessary to devise a new computational approach that does not break down when the interaction becomes strong. The most promising approach has been the crystal-lattice formulation of the theory, in which space-time is accorded a discrete, rather than continuous, structure. By considering the values of the color field only on individ- ual lattice sites, one is able to make use of many of the techniques developed in statistical physics for the study of spin systems such as magnetic substances. One of the most valuable methods has been the use of computer simulations in which different gluon configurations are explored by random sampling (Monte Carlo) techniques. This program makes extremely heavy demands on computer time and has spurred the de- velopment and implementation of new computer architectures. Already calculations of this sort have yielded suggestive evidence that quarks and gluons are indeed permanently confined in QCD. Work is continu- ing actively, with the eventual goal of computing the spectrum and properties of hadrons ab initio. Attempts to understand confinement and the nature of the QCD vacuum have led to the prediction of new phenomena. It seems likely that when hadronic matter is compressed to very great densities and heated to extremely high temperatures hadrons will lose their individ- ual identities. When the hadronic bubbles of our earlier image overlap and merge, quarks and gluons may be free to migrate over great distances. A similar phenomenon occurs when atoms are squashed together in stars. The resulting new state of matter, called quark-gluon plasma, may exist in the cores of collapsing supernovas and neutron stars. The possibility of creating QCD plasma in the laboratory in collisions of energetic heavy ions is under active study.

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76 ELEMENTARY-PARTICLE PHYSICS UNIFIED THEORIES We have seen in this chapter that developments in elementary- particle physics during the past decade have brought us to a new level of understanding of fundamental physical laws. The establishment- tentative though it beef the electroweak theory and QCD has brought us a coherent point of view and a single language appropriate for the description of all subnuclear phenomena. The new maturity of elemen- tary-particle physics has made more fruitful the interaction with other areas of physics and promises new insights into the origin of our world. With QCD and the electroweak theory in hand, what remains to be understood? If both theories are correct, can they also be complete? There are, in fact, many observations that are explained only in part, if at all, by the separate theories of the strong and electroweak interactions. Many of these seem to invite a further unification of the strong, weak, and electromagnetic interactions. This has important consequences not only for our worldview but also for experimental initiatives. Let us examine a few of the patterns unexplained by the separate strong and electroweak theories. First, there is the striking resemblance among quarks and leptons. Both classes of particles appear fundamental, in that they are struc- tureless at our present limits of resolution. Apart from the fact that quarks carry color but leptons do not, they appear nearly identical. Is this a coincidence, or are quarks and leptons related? The hint of a connection between quarks and leptons comes from the electroweak theory itself. Unless each lepton family like (e,v~) is matched by a color-triplet quark family such as (u,d), the theory will be beset with mathematical inconsistencies. These matched sets are known as quark-lepton generations. The second puzzling aspect of the theory has to do with the existence of distinct forces of diverse strengths. Here we recall that the electro- magnetic interaction, which is of only modest strength between ele- mentary particles, becomes stronger and stronger at short distances. In contrast, the strong interaction becomes increasingly feeble at short distances. Could all the interactions become comparable at some tiny distance, which is to say at some gigantic energy? This would raise the possibility of a common origin for the strong, weak, and electromag- netic interactions. A unification is also suggested by the fact that both QCD and the electroweak theory are gauge theories, with similar mathematical structure. The strategy for constructing a unified theory is to treat the quarks and leptons symmetrically by joining the quark and lepton families into

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WHAT WE HAVE LEARNED IN THE PAST TWO DECADES 77 extended families of fundamental constituents. In the simplest example of a unified theory, each quark and lepton generation is identified with a different extended family. In this way the long-standing mystery of the electric neutrality of stable matter is explained, because the proton and electron must have equal and opposite charges if quarks are combined with leptons in extended families. One branch of the first extended family is the set (dreg Doreen dare ever. In a gauge theory, each particle in a set can be transformed into any other. Some of these transformations are familiar, such as dreg ~ dgreen ~ ~ gluons dblue ~ e: ~1 Low+ but others are novel. The transformations between quarks and leptons, such as ~ dred ~ r ~ dgreen ~ ~ Y dhtlle X '~~ ~ pe can enable protons and bound neutrons to decay. One of the mecha- nisms for proton decay is shown in Figure 3.17. Here X and Y are hypothetical particles that connect the quarks with the leptons. In a specific gauge theory, we can compute precisely how the effective interaction strengths change with energy or distance. The evolution of the interaction strengths in the theory is depicted in Figure 3.18. The strong, weak, and electromagnetic interactions strengths are calculated to become comparable at an energy of approximately 10'5 GeV. The predictions of the theory for the relative strengths of the interactions at current energies agree with precision measurements of

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78 ELEMENTARY-PARTICLE PHYSICS IS ~3 - d t U , U tO u in a;< or _ i~ FIGURE 3.17 An example of how a proton might decay in some proposed theories that connect quarks and leptons. In the top diagram, two up quarks unite, leading to the production of a positron and a down antiquark. The down antiquark unites with a down quark to form a neutral pion. Thus in this proposed theory a proton could decay to a positron plus a neutral pion. X and Y are hypothetical particles that connect the quarks and leptons. the weak interactions and with the masses of the W+ and Z bosons recently observed. Some unified theories also successfully relate the masses of some quarks and leptons in the same generation, but the meaning of these partial successes is less clear. The prediction of proton instability is a key consequence of unified theories, and dedicated experiments have been mounted to search for proton decay. The large unification energy implies that the mean pro- ton lifetime must be extraordinarily long about 103 years or more. Since it is not practical to observe a single proton for such a long period (102 times the age of the universe), it is necessary to monitor extremely large numbers of protons. The largest experiment mounted to date is an instrumented tank of 8000 cubic meters of purified water in a salt mine near Cleveland (Figure 3.191. Currently the searches have yielded negative results that seem to conflict with the predictions of the simplest unified theories. While the specific prediction of proton decay is a dramatic conse- quence of unification, the difficulty of studying quark-lepton transitions

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WHAT WE HAVE LEARNED IN THE PAST TWO DECADES 79 in the laboratory is apparent. We live in a world in which energies- even in the most powerful accelerators that we can contemplate are very low compared with the unification scale. However, the discovery of the cosmic microwave background radiation (together with many supporting pieces of evidence) makes it likely that the universe began in a hot big bang of extremely high-energy density. Many aspects of the observed universe find natural explanations in terms of this cosmolog- ical model. Other features of the universe are not so easily understood. Among these, the net baryon number of the universe is of particular interest. The prediction of baryon-number-violating processes, such as proton decay, in unified theories opens the way to understanding why matter dominates over antimatter in the universe. The phenomenon, technically known as CP violation in K-meson decay, was discovered almost two decades ago. We have no basic explanation for this phenomenon; it may or may not have anything to do with the unified theories discussed in this section. But we should not end this brief survey of what we know in elementary-particle physics without mentioning CP violation. Briefly the phenomenon is as follows. When a K meson, that is, a neutral K meson, is produced, it goes into 0.15 at 0.10 .0s is H o (OLD) Weoh Unificotion Point Electromognelic (x8/3) 10 105 101 lol5 ENERGY ( GeV ) FIGURE 3.18 Example of how in some proposed theories the strong interaction can eventually be combined with the electromagnetic and weak interactions. The idea is that the strength of the interactions depends on the energy at which the interaction occurs. The proposal is that at very high energies say 10'5 GeV, all three interactions would have the same strength. This is far beyond any energy that we know how to achieve with present accelerator technology or even with advanced accelerator concepts (see Chapter 5, section on Research on Advanced Concepts for Accelerators and Colliders).

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80 ELEMENTARY-PARTICLE PHYSICS ~ .. - .= .~, . . = . . - ~ FIGURE 3.19 The lrvine-Michigan-Brookhaven experiment searching for proton de- cay uses 2000 photomultiplier tubes arrayed in an 8000-cubic-meter tank of very pure water. The tank is located deep underground in a large chamber of a working salt mine. A physicist working under water to adjust the tubes wears a special diver's suit to avoid contaminating the water through contact with his skin. two different states, called ~~ and K`s, with different lifetimes. The K~ has the longer lifetime, 500 times that of the KOs. The KOs decays through the weak interaction into two pions. According to a general invariance principle called CP symmetry, the K0r should never decay into two pions, but it does, about 0.002 of the time. This is the only reaction or decay in all of elementary-particle physics where CP symmetry has been observed to be violated. We do not know what is special about the decay of the Ki,. Perhaps it is an indication of another basic force that is very weak and is so far manifest only in this decay process; perhaps it has another explanation. One of the basic principles of relativistic quantum mechanics is that all physical phenomena must be invariant under a combination of CP symmetry and time-reversal symmetry. Therefore this CP violation also represents a violation of time-reversal symmetry.