The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics - Robert Oerter (2006)
Chapter 8. The Color of Quarks
You boil it in sawdust: you salt it in glue:
You condense it with locusts and tape:
Still keeping one principle object in view—
To preserve its symmetrical shape.
—Lewis Carroll, The Hunting of the Snark
By 1960, fundamental physics had gotten ugly. The beautiful simplicity of the earlier years, with every atom made of just protons, neutrons, and electrons, had yielded to the confusion of the subatomic zoo. Before 20 more years had passed, though, a new beauty would be revealed. In his novel Perelandra, C. S. Lewis describes a man writing by an open window who looks up in horror to see what he thinks is a hideous beetle crawling across his desk. “A second glance showed him that it was a dead leaf, moved by the breeze; and instantly the very curves and re-entrants which had made its ugliness turned into its beauties.” Something much like that was to happen to elementary particle physics, the ugly riot of new particles metamorphosing into the clear signs of a deeper order in the world, a hitherto unsuspected symmetry at the heart of matter.
The new picture of the subatomic world would be the result of an intimate dialogue between experimenters and theorists. As the experimenters were bagging more specimens for the subatomic zoo throughout the 1950s, theorists were struggling to catch up. The first task was to classify the particles that were being discovered—were there groups of particles that shared some characteristics?
The first rough classification was by mass. The particles in the lightweight division, called leptons, were the electron, with mass about 1/2000 of the proton mass, and the neutrino, with mass of zero, as far as anyone could tell. Then there were particles with intermediate mass between the electron mass and the proton mass, like the muon and the pion. These middleweight particles were called mesons. The heavyweight division comprised the proton, the neutron, and all the heavier particles, which were named baryons.
A second classification was by spin. Particles with half-integer spin (equal to 1/2 or 1 1/2 or 2 1/2 ...) are called fermions, and they obey the Pauli exclusion principle: No two identical fermions can be in the same quantum state. We saw the importance of this property earlier; it was the property that forced electrons to arrange themselves in different energy levels and the reason the elements arranged themselves into a periodic table. Particles with integer spin (like the pion, with spin 0, or the photon, with spin 1) are called bosons. Many bosons can occupy the same state: this fact is responsible for laser light, in which all the photons of the beam act in harmony. The fermion/boson distinction reflects, to some degree, the earlier particle/field distinction. All of the particles that are normally considered matter—protons, neutrons, and electrons—are fermions. All of the intermediate force-carrying particles, such as the photon that carries the electromagnetic force and the pion that carries the nuclear force, are bosons.
The Strong, the Weak, and the Strange
By 1950, physicists had come to realize that they needed yet another classification to deal with the nuclear forces. On the one hand, there was the muon. It clearly had something to do with nuclear forces since it was produced when a nucleus suffered beta decay. However, this interaction was seemingly very weak: this was the conclusion of the famous Italian experiment discussed in the previous chapter, which showed that muons were absorbed very slowly in matter. Whatever force was involved in these muon processes must be a very weak one. On the other hand, there was the pion, which was absorbed very rapidly in matter in a manner completely consistent with Yukawa’s predictions. The force carried by pions must be extremely strong, as it must hold the protons together in the nucleus while their electromagnetic repulsion is trying to tear them apart. Physicists began to speak of two different nuclear forces, called (prosaically but practically) the strong force and the weak force.
Confirmation of the strong/weak distinction came from the newly discovered subatomic particles. Some of these had extremely short lifetimes, around 10-24 second; comparable to the lifetime we calculated earlier for virtual pions. This was a good indication that the force involved with the decay of these particles was the same as the force involved with the pions. Other particles, the muon, for instance, had lifetimes of a few microseconds. This is very short in everyday terms, but many trillions of times longer than the lifetimes associated with the strong force. According to the Heisenberg uncertainty principle, ΔE Δt ≥ ℏ, a short lifetime corresponds to a large energy difference, and hence a large force; whereas a longer lifetime corresponds to a smaller energy and smaller force. So it makes sense that the strongly interacting particles should have shorter lifetimes and the weakly interacting particles should have longer lifetimes.
Some particles, like the muon, never participate in strong interactions. Other particles participate in both the strong and the weak interactions. Take the pion, for example. It certainly figures in the strong force: it’s the glue that holds the nucleus together. Its lifetime, however, is around 10-8 second—much too long to be explained by the strong force. In fact, when it decays it produces a muon and an antineutrino, both of which are particles that interact only via the weak (or electromagnetic) force, never the strong force. There must be some reason that the pion, a strongly interacting particle, can only decay by the weak force. This explains both its relatively long lifetime and the particles that result from the decay. A deeper understanding of the nature of the pion had to await the development of the Standard Model.
One more classification we need to know about was invented for the strange new particles that left V-shaped tracks in the cloud chambers. Like the pion, their lifetimes were too long—around 10-10 second, rather than the 10-24second expected from the strong interaction. But the solution found for the pion wouldn’t work for the new particles. The particles they decay into are strongly interacting, so it is no good to suppose they decay via the weak interaction. How then could they be so long lived? Another strange thing about them: They always seemed to be produced in pairs, never alone. A young theorist, Murray Gell-Mann, invented a new property to help explain the peculiar properties of these new particles, which he dubbed strangeness. The editors of the Physical Review considered this name too frivolous, and Gell-Mann was forced to substitute the clunky phrase “new unstable particles,” which was, according to Gell-Mann, the only phrase “sufficiently pompous” for the editors.1 But physicists continued to call them strange particles, and eventually even the Physical Review had to accept that label.
Strangeness worked like this: If a strange particle decayed into a normal particle, say a proton, it was given a strangeness value of -1. A strange particle that decayed into an antiproton was given a strangeness value of +1. A strange particle that decayed into another strange particle by a slow route (10-10 second or so) was doubly strange, so was assigned a strangeness value of -2; whereas one that decayed by a fast route (10-24 second or so) was assigned the same strangeness value as the particle it decayed into. Thus, the abnormally long lifetime was explained by the fact that the strangeness value changed by 1. This ad hoc solution to the problem of the long particle lifetimes would eventually lead Gell-Mann to a crucial breakthrough.
Now that there were ways to classify the new particles, some patterns started to emerge. For instance, the leptons, the lightweight particles, are all fermions (they all have spin 1/2) and are all weakly interacting. What’s more, in any interaction, the number of leptons before the interaction is equal to the number of leptons after the interaction, if we count antiparticles as having negative lepton number. For instance, in beta decay, a neutron (n) decays into a proton (p+), an electron (e-), and an antineutrino (e).
Physicists say that lepton number is conserved. Similarly, it was discovered that isospin is conserved in strong interactions, but not in weak interactions.
These patterns are not mere curiosities. From Emmy Noether’s work back in the 1910s, physicists were aware that symmetry in any theory led to an invariance, that is, to a conserved quantity. Slowly, throughout the 1960s, they came to realize that the argument could also run the other way. Find the conserved quantities, and you will learn something about the symmetries of the underlying theory. It is like someone who is trying to figure out the rules of chess by looking at many different board positions, to use a favorite illustration of Richard Feynman’s. They might notice that whenever one player has two bishops on the board, they are never on the same color square. This is a “conservation law” that gives a hint about what moves the bishop can make. When the observer comes up with a theory of the bishop’s “interactions” (the bishop always moves on a diagonal line), the observed conservation law is seen to be a result of the interactions. As in chess, it is not necessarily easy to guess the particle interactions from the symmetries. (You can probably think up other theories about the bishop’s motion that would still keep the two bishops on opposite-colored squares.) In 1959, Murray Gell-Mann began to tackle the problem of the strong interactions from the point of view of symmetry.
A New Periodic Table
As a young man, Gell-Mann was every bit the precocious genius that Schwinger had been, but even more impressive was the breadth of his interests and knowledge. He was as likely to hold forth on linguistics, history, archaeology, or exotic birds as on physics. He had a tremendous talent for languages and was famous for correcting people on the pronunciation of their own names. For all his intellectual arrogance, he was often curiously reluctant to publish his ideas. He said once that a theoretical physicist should be judged by the number of right ideas he published minus twice the number of wrong ones. His paper introducing the idea of strangeness was circulated to colleagues, but never published. His was unquestionably one of the most fertile minds of his generation and his enthusiasm for physics was unbounded. He once told an interviewer, “If a child grows up to be a scientist, he finds that he is paid to play all day the most exciting game ever devised by mankind.”2
As the count of fundamental particles blossomed from three in 1932 to 16 in 1958, physicists found themselves in the same position as Mendeleev in 1869, who had had 62 chemical elements and no good classification scheme. The scheme that Mendeleev developed, known to us as the periodic table of the elements, not only classified the elements according to their chemical properties but allowed Mendeleev to predict the existence of as yet undiscovered elements by looking at the gaps in his table. As we have seen, the whole structure of the periodic table would ultimately be explained in terms of the three particles that are the building blocks of the elements, the proton, the neutron, and the electron. What physicists needed was a new periodic table for the fundamental particles. In 1961, Murray Gell-Mann gave them one.
Gell-Mann’s initial step seems simple enough in retrospect: He plotted the known particles on a diagram with a particle’s isospin on one axis, and the newly invented property, strangeness, on the other. For the eight lightest mesons, the result came out like this:
The result: a perfect hexagon. There are two particles at the center, both with isospin 0 and strangeness 0, so these particles form an octuplet, leading Gell-Mann to dub his scheme the Eightfold Way, a light-hearted reference to the Buddhist teaching:
Now this, 0 monks, is the noble truth that leads to the cessation of pain, this is the noble Eightfold Way: namely, right news, right intention, right speech, right action, right living, right effort, right mindfulness, right concentration.3
To get his scheme to work, Gell-Mann had to assume that the Ko had strangeness +1, but its antiparticle, the0, had strangeness -1, in other words, they were two distinct particles. The referees reviewing his paper for publication objected: Neutral mesons like K° were supposed to be their own antiparticle. “It’s all right,” Gell-Mann replied, “they can be like that.”4 As it turned out, he was right; they could be like that.
What about the other particles? The lightest baryons fell out like this:
Another octuplet. The Eightfold Way was working. It was all very well to see the particles falling into pretty patterns on the strangeness-isospin diagram, but what did it mean? Was there some mathematical relationship that determined these particle multiplets? And, did this new periodic table hint at some substructure for the particles in the same way that the periodic table of the elements was explained, many years later, by the discovery of atomic structure?
Gell-Mann tackled the mathematical question first. Working by analogy to the well-understood example of spin, he tried to build up his octuplets, but without success. A chance conversation with a mathematician colleague led him to an obscure bit of nineteenth century mathematics called Lie groups, after the Norwegian mathematician Sophus Lie (pronounced “Lee”). Here he found what he wanted: a Lie group that had an octuplet representation. This group was called SU(3). The mathematics of group theory (which we will skip over) guaranteed that the masses of different particles in the octuplets had to be related in certain ways. Gell-Mann checked these relationships and found them to be satisfied for the octuplets he had constructed. These mass rules were to play a crucial role in a dramatic discovery.
One of the triumphs of Mendeleev’s periodic table was his ability to predict new elements from the gaps in his table. At a conference of particle physicists in Geneva in 1962, Gell-Mann got the opportunity to predict a new particle using the Eightfold Way. The Lie group of the Eightfold Way, SU(3) allows other representations besides the octet. There is a representation with 10 particles (decuplet), one with 27 particles, and so on. Gell-Mann and his colleagues had been worrying about what to do with a set of four particles, called the delta particles (Δ-, Δ0, Δ+, Δ++), that had been known since 1952. They wouldn’t fit in an octet, but they would fit either the decuplet or the 27-particle multiplet. At the 1962 conference, two new particles were reported that allowed Gell-Mann to create this diagram:
This was the expected form for the decuplet, and with the other newly discovered particles, only the bottom corner of the triangle was missing. On the spot, Gell-Mann went to the blackboard and predicted a new particle, which he called the omega-minus (Ω-), and described what its properties should be: charge -1, spin 3/2, mass about 1670 million electron-volts. By 1963 it had been detected, with the predicted properties, at an accelerator in Brookhaven, NY. The Eightfold Way was a success, and Gell-Mann was the new Mendeleev. He had to share the glory, however, which he did readily. An Israeli politician, Yuval Ne‘eman, who studied physics when he could get away from his job of defense attaché, had come up with the same prediction at the same 1962 conference. The two had never met before the conference, but, according to Ne’eman, “from then on, they became close friends.”5
Three Quarks for Muster Mark
With the successful prediction of the existence and properties of the omega-minus, it became clear to everyone that the Eightfold Way, or, more properly, SU(3) symmetry, was indeed the right way to classify the particles of the subatomic zoo. Gell-Mann hardly hesitated before plunging deeper. Why did the particles follow that symmetry? It had taken scientists more than 50 years from Mendeleev’s discovery of the periodic table of the elements to come to an understanding of the structure of atoms that answered the question: Why is there a periodic table? Gell-Mann didn’t intend to wait that long.
He began with the observation that, although all the known heavy particles could be arranged in SU(3) multiplets, the simplest possible multiplet, a three-particle triplet, was nowhere to be found in the sub-atomic zoo. Why should Nature ignore the simplest solution? It was unlike her. Perhaps the triplet was there all along, right under the physicists’ noses. Perhaps all the particles in the subatomic zoo were built out of these three fundamental particles. He decided to call the quirky little things quarks, and was delighted to find support for the name in a passage from James Joyce’s Finnegan’s Wake:
Three quarks for Muster Mark.
Sure he hasn’t got much of a bark
And sure as any he has it’s all beside the mark.
To make the scheme work, though, Gell-Mann had to make a radical assumption. Every particle ever detected had an electric charge that was a whole multiple of the electron charge. Reluctantly, Gell-Mann concluded that his quarks had to have electric charges that were fractions of the electron charge. The quarks, which he named up, down (in analogy with spin-up and spin-down), and strange (because it was a constituent of the strange particles) had charges of +2/3, -1/3, -1/3, and isospins of +1/2, -1/2, 0, respectively.
Gell-Mann was well aware of the objections his colleagues would raise: Why have we not seen these particles? Why have we never seen any fractionally charged particle? He was uncharacteristically timid in the paper he wrote proposing this model, giving just the barest outline, and ending the paper with the enigmatic phrase: “A search for stable quarks... would help to reassure us of the non-existence of real quarks.”6 He seemed to be saying that quarks were just a mathematical abstraction that allowed the properties of the known particles to be explained. His reluctance to say clearly whether or not quarks were real physical entities was summarized by a colleague like this: “If quarks are not found, remember I never said they would be, if they are found, remember I thought of them first.”7 8
Actually, someone else had thought of them independently. George Zweig had written an 80-page paper that worked out many of the consequences of the quark model (he called them aces), which was not published until years later. Zweig, like Gell-Mann, was cautious about claiming these bizarre particles actually existed, but he was bold enough to end his paper on an optimistic note: “There is also the outside chance that the model is a closer approximation to nature than we may think, and that fractionally charged aces abound within us.” Today, both are given credit for the model, but it is Gell-Mann’s names that are used.
The difficulty in deciding whether quarks were real lay in the very idea of a fundamental particle. The term “fundamental” was being used in two different senses. One meaning is basic constituent: a particle that is a building block for more complex objects. A second meaning is particle that cannot be broken apart into smaller particles. It had long been accepted that protons, neutrons, and electrons were the basic constituents of atoms, a view that was confirmed by experiments that split atoms apart, yielding the particles themselves. It was natural to think that, if protons and neutrons were made of still smaller constituents, it should be possible to split the proton and observe a free, fractionally charged quark. Since no such particle had ever been detected in all the years of accelerator experiments, Gell-Mann’s reluctance to predict the existence of quarks as physical particles is understandable. As we will see, it would take a better understanding of the interactions between quarks to explain why quarks could be basic constituents of protons and neutrons but nonetheless be trapped forever inside them, unable to be knocked out as free particles regardless of how energetically the protons and neutrons were slammed into each other.
With the quark model in hand, the entire subatomic zoo suddenly started to make sense. First off, all of the baryons (the heavyweight particles like the proton and neutron) are composed of three quarks. For instance, the proton is made of two up quarks and one down quark. This gives the correct electric charge, since 2/3 + 2/3 - 1/3 = +1, as well as the correct isospin: 1/2 + 1/2 - 1/2 = 1/2. The neutron has one up quark and two down quarks: Its charge is 2/3 - 1/3 - 1/3 = 0, and its isospin 1/2 - 1/2 - 1/2 = - 1/2, as it must be. Strange particles contain a strange or antistrange quark, and doubly strange particles contain two, and so on. The quark structure of particles is discussed in more detail in Appendix A.
The mesons (the middleweight division) are built from one quark and one antiquark. The three pions, for example, are made of various combinations of up and down quarks and their antiquarks.
The leptons (the lightweight division) are the particles that are not built from quarks. In this new understanding of leptons, the muon had to be reclassified. Even though its mass put it in the middleweight division, it didn’t participate in the strong interaction. In the Gell-Mann-Zweig quark model, all quarks participate in the strong interaction. The muon therefore could not be built of quarks. Even though it is 200 times heavier than the electron, it must be considered a fundamental particle with no structure. In this new understanding, the muon is a lepton, not a meson.
The quark model not only explained the observed properties of the particles in the subatomic zoo, it also gave a clear picture of their interactions. Physicists had known since the 1930s that the pion held neutrons and protons together in the atomic nucleus in much the same way that photons cause the attraction of oppositely charged particles. This was the premise of Yukawa’s theory of the strong interactions. Recall how pion exchange looks in terms of Feynman diagrams. The proton emits a pi-plus and changes into a neutron. The neutron then absorbs the pion and changes into a proton.
The quark model gives a deeper understanding of the pion-exchange process.
Here, we see a proton (duu) and a neutron (dud) coming in from the left. (In this notation, which we will continue to use, d is a down quark, u an up quark, and an antiparticle is represented with a bar over its letter or symbol.) At the upper kink in the diagram, a virtual dd pair is created, in the same way that virtual electron-positron pairs are created from empty space. (There must, of course, be a photon or some other particle, not shown in the figure, that provides the energy to create this quark-antiquark pair. For now, we’ll set aside the question of what sort of particle this might be.) The ucombination is emitted, leaving a neutron (dud) on the right. The pion (u) is then absorbed by the original neutron. This, we now see, is nothing more than dannihilation. What’s left (uud) is a proton. The result is the same as in Yukawa’s theory, but it is now understood in terms of the production and annihilation of quark-antiquark pairs.
It’s all very well that the particles and their (strong) interactions can be understood in terms of the quark model, but what about the question that Gell-Mann was so ambivalent about: Are quarks real? In favor of the affirmative, Gell-Mann and Zweig could point out that all of the known strongly interacting particles could be explained in terms of three fundamental quarks. We now know that there are actually six quarks, called up, down, strange, charm, top, and bottom, which are known as the quark flavors. We can still say today that all known strongly interacting particles can be built out of these six quarks and, of course, their antiquarks. On the side of caution, however, it should be noted that in the 1960s, no one had ever detected any particle with fractional electric charge, nor was there any evidence that the proton and neutron had any structure—that is, that there was anything inside them. Worse, no one was at all certain that relativistic quantum field theory was the right approach for understanding the strong interaction. There was a plethora of alternatives: the S-matrix, Regge poles, the SU(6) group. No one, not even the quarks’ inventors, would have bet money that they were real, physical particles.
Evidence that quarks actually existed began showing up in experiments at Stanford University in 1968. The SLAC machine accelerated a beam of electrons and fired it into a vat of liquid hydrogen, a procedure considered uninteresting by physicists on the East coast, who had already begun colliding protons with each other head-on. The proton-proton collisions were more energetic, but they were messy; it was the cleaner electron-proton collisions at SLAC that would be the first to reveal the structure of the proton.
Think back to the example of the BBs fired at the Nerf ball. The electrons (the BBs) were deflected by the protons (the Nerf ball) and the pattern of the deflection told experimenters about the internal structure of the proton. The interpretation of the results can be quite tricky, however, especially when there is more than one object inside the target particle. There is no way to hold the quarks in place while firing many electrons to map out the locations of the quarks. Each scattering event involves a potentially different arrangement of quarks inside the proton. The most that experimenters could say was that the size of the proton was about 1/1000 the size of a typical atom, and that the proton had no hard core; there was no “pit” inside the “peach.” At the tremendously high energies (for the time) reached by SLAC, there was another kind of scattering that could occur. The energy that the electron carried could be converted into other particles, a process known as inelastic scattering. The two scattering possibilities, elastic and inelastic, can be diagrammed like this:
Surprisingly, it was the messier inelastic collisions that were shown to have a simple property, called scaling, that provided the evidence that protons were really made of point-like constituents: the quarks. In any scattering process, the probability of the incoming electron scattering in a particular direction depends on two quantities: the energy of the incoming electron and the amount of energy the electron loses. Very roughly, scaling refers to the fact that at high enough energy, the scattering probability no longer depends on the energy loss. This was a surprise to the experimenters who discovered it. If the proton had some complicated internal structure, you would expect the scattering probability to get more complicated as you go to higher energy and probe the interior more deeply. Instead, things got simpler. Why?
Although he didn’t invent the idea, Richard Feynman was the person who drew attention to scaling in inelastic collisions, and he was the one who explained the phenomenon in a simple and convincing way. Feynman didn’t want to rely on the quark model; he didn’t think that there was sufficient evidence for quarks in 1968 to take them as proven. He decided to start from the assumption that the proton was made of some collection of point particles, while remaining uncommitted about their numbers and interactions, and see what predictions would follow from these minimal assumptions. He didn’t want to confuse his simple model with the more sophisticated quark theory, so he called his hypothetical point particles partons, as they were the parts of the proton. Feynman found that the parton model was enough to derive scaling. To put it another way, the scaling that experimenters were finding in their data was evidence that the proton contained point-like particles of some kind. Did this mean scaling was evidence of quarks? Feynman thought not, but Gell-Mann vehemently disagreed. “The whole idea of saying they weren’t quarks and anti-quarks but some new thing called ‘put-ons’ seemed to me an insult to the whole idea that we had developed,” Gell-Mann said later. “It made me furious, all this talk about put-ons.”9
Physicists did not immediately rush to embrace the quark model when evidence of scaling showed up in the SLAC experiments. A great deal of effort had been invested in alternate approaches, and those who had invested it were understandably reluctant to throw it all away for something as iffy as field theory. The quark model was not without its problems, either. For one thing, the scaling idea depended on the assumption that the quarks were weakly bound, nearly uninteracting. But in that case, it should be easy to knock a quark out of the proton and detect it on its own. In spite of much intense searching, nothing resembling a free quark had ever been seen. How could quarks be nearly uninteracting and yet be confined inside the proton?
Another problem with the quark model can be seen in the famous omega-minus (Ω-) particle that Gell-Mann predicted using the Eightfold Way. In the quark model, it should be made of three strange quarks, each with a charge of -1/3 and spin of 1/2. The omega-minus has spin 3/2, so the spins of the three quarks must be aligned (that is, all must be spin up or all must be spin down). To understand why the very existence of such a particle was puzzling, recall the Pauli exclusion principle: You can never have two identical fermions in the same quantum state. The exclusion principle was the reason each energy state of an atom can only accommodate two electrons: the electrons are spin 1/2 fermions, and so have only two possible states, spin up or spin down. Now, strange quarks are also spin 1/2 fermions, so they also can only be spin-up or spin-down. But that means that the quark picture of the omega-minus is impossible. Three identical quarks can never have their spins in the same direction.
Finally, and perhaps most importantly, the quark model said nothing about the forces that held the quarks together in the proton and the neutron. The strong force that bound protons and neutrons in the nucleus was now understood to be caused by an exchange of pions, which is the same thing as exchanging a quark-antiquark pair, as we have seen. But there had to be yet another force that operated inside the proton that kept its quarks from flying apart.
The solution to all three puzzles came in 1972 from an old hand applying an old idea with a new twist. The old hand was Murray Gell-Mann, working together with his colleagues Harold Fritsch and William Bardeen. The old idea was the same SU(3) group that had explained the Eightfold Way classification of the subatomic particles. Gell-Mann and colleagues, however, this time used it in a completely new way. The basic idea is this: Each flavor of quark, up, down, strange, and so on, comes in three colors, which were given the names red, green, and blue, after the primary colors of light. So there is a red up quark, a blue up quark, and a green up quark, and so on for each quark flavor. This is not a claim that the quarks would actually look those colors if you could see them—rather, the quarks have an additional, and heretofore undiscovered, property, which is given the arbitrary name color. It could just as well have been called anything else that comes in threes. Gender (he, she, it), for instance, or porridge (hot, cold, just right). Color, however, turns out to be a particularly apt metaphor.
Straightaway we can see how the new quantity, color, solves the omega-minus puzzle: simply require that each strange quark in the omega-minus have a different color. The Pauli exclusion principle requires that the three quarks all be in different quantum states. The new property, color, allows us to give them different color states, so the fact that they all have the same spin state is no longer a problem.
just as the three primary colors of light combine to make white light, the three quark colors combine to make “colorless” particles. We can also make an analogy with electric charge. A hydrogen atom is made of a negatively charged electron and a positively charged proton. From a distance, the positive and negative charges appear to cancel, and the atom looks neutral, or uncharged. It is only when you probe deeply into the atom—for instance, by shooting electrons at it as Rutherford did—that you discover the charged particles hidden inside. In the same way, a proton might be made up of a red up quark, a blue up quark, and a green down quark. From a distance, the three color charges cancel each other, and the proton appears “white,” or color-neutral.
The mesons work a little differently. Each meson is made of a quark and an antiquark, and the antiquarks come in the colors antired, antiblue, and antigreen. So a pion, the pi-plus, for instance, might be composed of a red up quark and an antired antidown quark.
According to Gell-Mann & Co., only color-neutral combinations appear in free particles. This was why color had never been detected. An electrically neutral particle doesn’t produce or respond to an electric field. In the same way, a colorless particle doesn’t produce any external signature. Since all free particles are, by fiat, colorless, no color force has ever been observed. This may seem like a cheat: introduce a new quantity that solves the immediate problem but is otherwise unobservable. However, in the form introduced by Gell-Mann, Fritsch, and Bardeen, it was much more than that. The color theory also describes the force holding the quarks together inside the proton. The theory predicted that this force, the glue that holds the proton together, would be carried by a set of new, massless particles, in the same way that the electromagnetic force is carried by photons. With Gell-Mann’s typical flair for names, he dubbed these new particles gluons. The whole theory of interacting quarks and gluons he called quantum chromodynamics or QCD.
The discovery of scaling, together with Feynman’s parton explanation of it, gave theorists and experimenters alike reason to think that the proton was built of smaller point-like particles. About the whole apparatus of color theory and QCD, though, they remained skeptical. Particularly troubling was the claim that these quarks were confined forever inside the protons and neutrons. How could anyone believe in particles that could never be observed on their own? Everything changed in the November Revolution of 1974.
At the time, three quark flavors were all that were needed to explain the properties of the known particles. Protons and neutrons were composed of up and down quarks, and strange particles required a third flavor called, logically enough, the strange quark. A few theorists played around with the idea that quarks should be organized into two-quark families. The lightest quark family consisted of the up quark and the down quark. To complete the second family, a fourth quark was needed to go along with the strange quark. They whimsically termed this hypothetical new quark charm.
The charm quark seemed to solve some difficulties of the weak interactions. It all seemed very tenuous, however. If you believed in quarks, and if you believed they could be described using color theory, and if the weak interactions could also be described using color theory, and if, on top of all that, you bought into the idea of a fourth quark that was otherwise completely unnecessary, then a few little theoretical puzzles went away. Then, in September 1974, Samuel Ting and his experimental group at Brookhaven National Accelerator Laboratory on Long Island found a bump in their data that indicated the existence of a new particle, which Ting named the J. A meticulous experimenter, Ting had been taking data using very small steps in energy, and so had caught sight of a narrow resonance that other, more powerful accelerators had missed. But now Ting’s natural caution tripped him up. He passed up several chances to announce the discovery, wanting first to eliminate any possibility of error. As he waited, word leaked out about the bump in the data at an energy of 3.1 billion electron-volts. A team at Stanford Linear Accelerator Center (SLAC) found the same bump in early November, assigning it the Greek letter psi. When Ting heard that the SLAC group was about to announce its discovery, he scrambled his group to make its own announcement. The two groups’ papers were published simultaneously in the December 2 issue of Physical Review Letters, and the particle is now known as the J/psi, pronounced “Jay-sigh.”
The importance of the J/psi discovery lay in its theoretical interpretation: It was charmonium, a charm quark tightly bound to an anticharm quark. The evidence for this interpretation lay first of all in the narrowness of the bump in the energy spectrum (see the graph shown in the previous chapter, in the section “Building a Better BB Gun”), which implied a lifetime about a thousand times longer than expected for a strongly interacting particle. Secondly, charmonium should theoretically exist in several different configurations. Experimentally, this meant that the big bump at 3.1 billion electron-volts should consist of several separate bumps. When experimenters confirmed the existence of some of these individual resonances, the charmonium model quickly became accepted as the correct explanation of the J/ psi.
After the November Revolution, interest in the quark model exploded. Experimenters competed for the glory of discovering particles that combined a charm quark with an up, down, or strange quark, as theorists frantically set about calculating their expected properties. In 1977, another narrow resonance suggested the existence of a fifth quark. This in turn implied a third quark family. Some pushed for the fifth and sixth quarks to be called “beauty” and “truth,” but eventually the names “bottom” and “top” won out. In experiment after experiment, the quark model proved its worth. By the time the discovery of the top quark was announced in 1994, there was no longer any doubt that quarks were real.
The World According to Quarks
QCD tells us that each flavor of quark comes in three colors. We can depict this as a color triangle, here drawn for the up quark:
The SU(3) symmetry of QCD says that we can rotate the triangle, and the theory will remain unchanged. In other words, if we could reach inside every proton and neutron in the universe and instantaneously replace every red up quark with a green up quark, every green up quark with a blue up quark, and every blue up quark with a red up quark, and simultaneously do the same with all the other quark flavors, there would be no way to tell that we had done so. The universe would continue on exactly as before the change.
According to Noether’s theorem, this kind of symmetry guarantees that color is a conserved quantity. That means that in any interaction, the amount of color going into the reaction equals the amount coming out. Now, QCD tells us that a quark can emit a gluon and change its color:
Here the double wavy line represents the gluon. But color is not conserved in this diagram unless the gluon carries color. In fact, the gluon has to carry two kinds of color: It must carry red (so that the outgoing colors include the red of the incoming quark) and antiblue (to cancel out the blue of the outgoing quark). Let’s add color to the Quark and gluon lines, using a thick line for red, a medium for green, and a thin for blue. The antiblue in the gluon double line is represented by a backward arrow:
Now we can see that color is conserved: red comes in, and (red + blue + antiblue = red) comes out.
This is a major difference between QED and QCD. In QED, the photon that mediates the interaction between electrically charged particles is not itself electrically charged. In contrast, the gluon of QCD, which mediates the interaction between the colorful quarks, itself carries color. As a result, gluons can interact with each other, something photons can’t do.
QCD doesn’t tell us anything about the possible flavors of quarks; we simply have to go looking for them among the particles of the sub-atomic zoo. We now know that there are six quark flavors. Together with the three colors, this gives us 18 different quarks. Of course, there are 18 antiquarks as well.
We are now ready to write down the Feynman diagrams for QCD that show all the possible processes.
■ A quark can go from one place to another.
■ A gluon can go from one place to another.
■ A quark can absorb or emit a gluon.
So far, the rules look just like those for QED. But in QCD there are two more possible processes.
■ A gluon can split into two gluons.
■ Two gluons can collide and form two new gluons.
These additional interactions fundamentally change the behavior of the theory and ultimately explain why we never see free quarks in nature.
Now two of the three major chunks of the Standard Model are in place. The first chunk is QED, the relativistic quantum field theory that describes the interactions of charged particles and photons. The second chunk is QCD, the relativistic quantum field theory of quarks and gluons. The only thing missing from our Theory of Almost Everything is a description of the weak interactions—the subject of the next chapter.
For now, let’s see where our description of the world has brought us. Everything around us is composed of atoms, which consist of a small nucleus of protons and neutrons surrounded by a cloud of electrons. The electrons are bound to the nucleus via photon exchange, as described by QED. In the nucleus, protons and neutrons are bound together via pion exchange, which we now know is actually the exchange of a quark-antiquark pair. Each proton or neutron is composed of three quarks, which are bound together by gluon exchange, in other words, the color force. Inside the proton there is a whirlwind of activity: gluons being exchanged, virtual quark-antiquark pairs being created and annihilating. The quarks themselves come in six flavors and three colors, for 18 versions, or 36 versions if you count the anti-quarks as well.
We are now ready to tackle the remaining puzzle of the quark model: why do quarks behave as if they are weakly bound in scattering experiments, yet they can never be knocked free? Here is the basic gluon-exchange interaction between two quarks:
The rules of relativistic quantum field theory tell us that this interaction will be modified by the creation of virtual quark-antiquark pairs, virtual gluons, and so forth. Remember the totalitarian theorem: Anything that is not forbidden is compulsory. For QED, we discovered that the cloud of virtual particles has the effect of screening the electric field. This means that as we go to higher energy and penetrate deeper into the virtual cloud the electric force increases more than we would have expected had we not known about the virtual particles. For QCD, we find exactly the opposite effect. That is, as we go to higher energy and shorter distances, the strength of the color force decreases. (The details are worked out in Appendix B.) Conversely, at longer distances, the strength of the color force increases. It’s like putting two fingers inside a rubber band to stretch it. The farther apart you pull your fingers, the larger the force. But if you move your fingers together, the rubber band goes slack. This property of QCD is called asymptotic freedom, meaning that at the extremes of large energy the quarks behave like free, non-interacting particles. The discovery of asymptotic freedom earned David Gross, David Politzer, and Frank Wilczek the 2004 Nobel Prize in Physics.
At last we can understand why quarks can act like free particles in high-energy scattering experiments, yet remain bound in the proton and neutron. At the high energies of the scattering experiments, the interaction strength is’ less, and the quarks behave like free particles. On their own inside a proton, the quarks have much lower energy, so the interaction strength is higher, and the quarks remain bound. Roughly speaking, the strong force is like stretching a spring: When the quarks are close to each other, the spring is unstretched, and the force is small. As we try to pull the quarks apart, the force gets larger and larger, making it impossible to pull a quark out of a proton far enough to detect it as a free, fractionally charged particle. The strength of the QCD interaction has now been measured over a wide range of interaction energies, and the results are in striking agreement with the theoretical prediction.
How does this explain why we never see a lone quark? Let’s start by picturing a pion, say, as a quark and an antiquark connected by a tube of color, like two marbles connected by a rubber band (top, in the diagram below). Just as two electrically charged particles have a tube of electric field connecting them, the two quarks have a tube of color field. Just as an electric field can be thought of as made up of virtual photons, the tube of color can be thought of as a stream of virtual gluons. As we pull the quarks apart, we have to add more and more energy until the tube eventually snaps (middle). The breaking point occurs when the added energy becomes sufficient to create a quark-antiquark pair, so that instead of two free quarks, we end up with two new mesons (bottom).
Physicists call this color confinement: Particles with color can only occur in color-neutral combinations. Free particles with color are never seen.
The process shown here is not the only one possible. Usually, there is so much energy in the gluon tube when it snaps that numerous particle-antiparticle pairs are produced, resulting in particle jets in the directions that the original quarks were moving. Jets like these have actually been observed at several accelerators, providing dramatic (but indirect) evidence for the existence of the elusive quarks.
Other, more subtle effects predicted by QCD have been tested at many different accelerators, and the results all support the picture that QCD describes: Quarks are point-like, spin-1/2 particles, with electric charges of ± 1/3 or ± 2/3, that are bound together by the gluons of QCD. Still, neither quarks nor gluons have ever been directly observed as tracks in a cloud chamber or particle detector. How then can we be so confident of the existence of entities that we have never seen (and according to the theory of QCD, will never see)?
Leon Lederman, speaking to an audience of nonphysicists, was once confronted by an irate questioner who demanded an answer to that question. The physicist replied, “Have you ever seen the Pope?”
“No,” was the reply.
“Then how do you know he exists?”
“Well, I’ve seen him on TV,” the interlocutor responded.10 Pause for a moment and think what this answer implies. A device (the TV camera) admits light and converts it into a code involving tiny magnetic areas on a piece of videotape. Some time later, a TV station takes that tape and converts it into a stream of electromagnetic waves or a cable signal, which carries the information to your TV. Your TV then turns this code into a series of minute variations in the sweep of an electron beam, resulting in an image on the phosphorescent screen of the TV. By comparison, the indirect evidence for quarks and gluons is rather straightforward. The point is this: If each step in the chain of evidence is well understood, then indirect evidence carries nearly as much weight as direct evidence. If we can believe there is a Pope because we’ve seen him indirectly on TV, then we can believe in quarks because we’ve “seen” them indirectly through particle jets, through scaling, and through their amazing capability to explain the properties of strongly interacting particles.
Ignorance Is Strength
The history of theories of the strong force reveals how important the concept of symmetry has become in physics. The early isospin theory was an expression of the (inexact) symmetry between neutrons and protons. The Eightfold Way extended that symmetry in order to include the different types of heavy particles that were turning up in accelerator experiments. In the triumphant version of the strong force theory, QCD, symmetry and force are intimately and inextricably intertwined.
Call it the principle of ignorance is strength. Color SU(3) symmetry declares that there is no way to tell the difference between, say, a red up quark and a blue up quark. Now, suppose I could isolate a single quark and store it in my lab in some kind of box. I then declare that this is a color standard; this quark is the definition of the color red. (The particle property, not, of course, the visible color.) In the same way that anyone can determine if they have a kilogram of mass by comparing it to the standard kilogram in Paris, anyone who wants to know the color of a quark has only to compare it to my standard quark. Let the two quarks interact, and it will be possible, in principle at least, to determine the color of the second quark.
Now, suppose that experimenters at another laboratory on a different continent isolate their own quark and declare it the definition of the color red. They can perform any experiments they like using their definition of red and obtain results that are completely consistent with the results coming out of my laboratory, whether or not their “red” is the same as my “red.” In order to find out if we are talking about the same red, I only need to pack my standard quark and fly to their laboratory to compare with their standard quark.
In other words, since red, blue, and green quarks are completely equivalent, the term red can have different meanings at different locations. It is only when the two quarks are at the same point in space that they can interact and so be compared. There is nothing to prevent us, then, from defining red differently at every point in space. We only need to keep track of how the definition of red changes from point to point. The mathematical function that keeps track of the changes in the definition is something we have encountered before—it is a field. In fact, for QCD, it is the gluon field. Gluons, therefore, are a manifestation of our inability to distinguish a red quark from a blue quark. That is, the color force is a consequence of the color symmetry. Ignorance is strength.
The ignorance is strength principle is the basis of all the forces in the Standard Model. Theories that work this way are called Yang-Mills theories or gauge theories. At the root of a Yang-Mills theory is a symmetry. If we make one assumption—that the symmetry transformation can be applied differently at different points in space—then we find mathematically that the symmetry guarantees the existence of a quantum field that mediates a force. In QCD, the symmetry is color symmetry, and the quantum field that arises from this symmetry is the gluon field that binds the quarks together into particles. Ultimately, color symmetry is the reason that matter as we know it can exist.
QED is another example of a Yang-Mills theory. The terms positive and negative for electric charge are just as arbitrary as the terms red, blue, and green for the color force. Our inability to define the charge in any absolute sense is the ignorance that gives rise to a quantum field: the photon field. This symmetry (called U(1) symmetry) guarantees that electric charge will be conserved—Noether’s theorem at work. But it does even more; it guarantees the existence of the photon, the quantum of light. This symmetry is the reason light can travel across a billion light-years of empty space, bringing us news of distant galaxies.
The crucial idea is that QED and QCD are the same type of theory, that both the electromagnetic force and the strong force are related to the symmetries of the fundamental particles involved (the electrons and quarks). The reason light and electromagnetic forces exist is the underlying U(1) symmetry of charged particles. The reason quarks stick together in protons and neutrons is the underlying color symmetry. As we will see shortly, the Standard Model is built on the same central idea. In the Standard Model, symmetry is force and force is symmetry.