33-6. Quarks: Is That All There Is?
Quarks have been mentioned at various points in this text as fundamental building blocks and members of the exclusive club of truly elementary particles. Note that an elementary or
Conception of Quarks
Quarks were first proposed independently by American physicists Murray Gell-Mann and George Zweig in 1963. Their quaint name was taken by Gell-Mann from a James Joyce novel—Gell-Mann was also largely responsible for the concept and name of strangeness. (Whimsical names are common in particle physics, reflecting the personalities of modern physicists.) Originally, three quark types—or
How Does it Work?
To understand how these quark substructures work, let us specifically examine the proton, neutron, and the two pions pictured in Figure 1 before moving on to more general considerations. First, the proton p is composed of the three quarks uud, so that its total charge is , as expected. With the spins aligned as in the figure, the proton’s intrinsic spin is , also as expected. Note that the spins of the up quarks are aligned, so that they would be in the same state except that they have different colors (another quantum number to be elaborated upon a little later). Quarks obey the Pauli exclusion principle. Similar comments apply to the neutron n, which is composed of the three quarks udd. Note also that the neutron is made of charges that add to zero but move internally, producing its well-known magnetic moment. When the neutron decays, it does so by changing the flavor of one of its quarks. Writing neutron decay in terms of quarks,
We see that this is equivalent to a down quark changing flavor to become an up quark:
Table 1: Quarks and Antiquarks1
1. The lower of the symbols are the values for antiquarks.
Table 2: Quark Composition of Selected Hadrons4
4. These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
This is an example of the general fact that the weak nuclear force can change the flavor of a quark. By general, we mean that any quark can be converted to any other (change flavor) by the weak nuclear force. Not only can we get , we can also get . Furthermore, the strange quark can be changed by the weak force, too, making and possible. This explains the violation of the conservation of strangeness by the weak force noted in the preceding section. Another general fact is that the strong nuclear force cannot change the flavor of a quark.
Again, from Figure 1, we see that the meson (one of the three pions) is composed of an up quark plus an antidown quark, or . Its total charge is thus , as expected. Its baryon number is 0, since it has a quark and an antiquark with baryon numbers . The half-life is relatively long since, although it is composed of matter and antimatter, the quarks are different flavors and the weak force should cause the decay by changing the flavor of one into that of the other. The spins of the and quarks are antiparallel, enabling the pion to have spin zero, as observed experimentally. Finally, the meson shown in Figure 1 is the antiparticle of the meson, and it is composed of the corresponding quark antiparticles. That is, the meson is , while the meson is . These two pions annihilate each other quickly, because their constituent quarks are each other’s antiparticles.
Two general rules for combining quarks to form hadrons are:
One of the clever things about this scheme is that only integral charges result, even though the quarks have fractional charge.
All Combinations are Possible
All quark combinations are possible. Table 2 lists some of these combinations. When Gell-Mann and Zweig proposed the original three quark flavors, particles corresponding to all combinations of those three had not been observed. The pattern was there, but it was incomplete—much as had been the case in the periodic table of the elements and the chart of nuclides. The particle, in particular, had not been discovered but was predicted by quark theory. Its combination of three strange quarks, , gives it a strangeness of (Table: Selected Particle Characteristics) and other predictable characteristics, such as spin, charge, approximate mass, and lifetime. If the quark picture is complete, the should exist. It was first observed in 1964 at Brookhaven National Laboratory and had the predicted characteristics as seen in Figure 2. The discovery of the was convincing indirect evidence for the existence of the three original quark flavors and boosted theoretical and experimental efforts to further explore particle physics in terms of quarks.
Patterns and Puzzles: Atoms, Nuclei, and Quarks
Patterns in the properties of atoms allowed the periodic table to be developed. From it, previously unknown elements were predicted and observed. Similarly, patterns were observed in the properties of nuclei, leading to the chart of nuclides and successful predictions of previously unknown nuclides. Now with particle physics, patterns imply a quark substructure that, if taken literally, predicts previously unknown particles. These have now been observed in another triumph of underlying unity.
Example 1: Quantum Numbers From Quark Composition
Verify the quantum numbers given for the particle in Table: Selected Particle Characteristics by adding the quantum numbers for its quark composition as given in Table 2.
The composition of the is given as in Table 2. The quantum numbers for the constituent quarks are given in Table 1. We will not consider spin, because that is not given for the . But we can check on charge and the other quantum numbers given for the quarks.
The total charge of uss is , which is correct for the . The baryon number is , also correct since the is a matter baryon and has , as listed in Table: Selected Particle Characteristics. Its strangeness is , also as expected from Table: Selected Particle Characteristics. Its charm, bottomness, and topness are 0, as are its lepton family numbers (it is not a lepton).
This procedure is similar to what the inventors of the quark hypothesis did when checking to see if their solution to the puzzle of particle patterns was correct. They also checked to see if all combinations were known, thereby predicting the previously unobserved as the completion of a pattern.
Now, Let Us Talk About Direct Evidence
At first, physicists expected that, with sufficient energy, we should be able to free quarks and observe them directly. This has not proved possible. There is still no direct observation of a fractional charge or any isolated quark. When large energies are put into collisions, other particles are created—but no quarks emerge. There is nearly direct evidence for quarks that is quite compelling. By 1967, experiments at SLAC scattering 20-GeV electrons from protons had produced results like Rutherford had obtained for the nucleus nearly 60 years earlier. The SLAC scattering experiments showed unambiguously that there were three pointlike (meaning they had sizes considerably smaller than the probe’s wavelength) charges inside the proton as seen in Figure 3. This evidence made all but the most skeptical admit that there was validity to the quark substructure of hadrons.
More recent and higher-energy experiments have produced jets of particles in collisions, highly suggestive of three quarks in a nucleon. Since the quarks are very tightly bound, energy put into separating them pulls them only so far apart before it starts being converted into other particles. More energy produces more particles, not a separation of quarks. Conservation of momentum requires that the particles come out in jets along the three paths in which the quarks were being pulled. Note that there are only three jets, and that other characteristics of the particles are consistent with the three-quark substructure.
Quarks Have Their Ups and Downs
The quark model actually lost some of its early popularity because the original model with three quarks had to be modified. The up and down quarks seemed to compose normal matter as seen in
Table 2, while the single strange quark explained strangeness. Why didn’t it have a counterpart? A fourth quark flavor called
History quickly repeated itself. In 1975, the tau () was discovered, and a third family of leptons emerged as seen in Table: Selected Particle Characteristics. Theorists quickly proposed two more quark flavors called
What’s Color got to do with it?—A Whiter Shade of Pale
As mentioned and shown in Figure 1, quarks carry another quantum number, which we call
Why must hadrons be white? The color scheme is intentionally devised to explain why baryons have three quarks and mesons have a quark and an antiquark. Quark color is thought to be similar to charge, but with more values. An ion, by analogy, exerts much stronger forces than a neutral molecule. When the color of a combination of quarks is white, it is like a neutral atom. The forces a white particle exerts are like the polarization forces in molecules, but in hadrons these leftovers are the strong nuclear force. When a combination of quarks has color other than white, it exerts extremely large forces—even larger than the strong force—and perhaps cannot be stable or permanently separated. This is part of the
The Three Families
Fundamental particles are thought to be one of three types—leptons, quarks, or carrier particles. Each of those three types is further divided into three analogous families as illustrated in Figure 6. We have examined leptons and quarks in some detail. Each has six members (and their six antiparticles) divided into three analogous families. The first family is normal matter, of which most things are composed. The second is exotic, and the third more exotic and more massive than the second. The only stable particles are in the first family, which also has unstable members.
Always searching for symmetry and similarity, physicists have also divided the carrier particles into three families, omitting the graviton. Gravity is special among the four forces in that it affects the space and time in which the other forces exist and is proving most difficult to include in a Theory of Everything or TOE (to stub the pretension of such a theory). Gravity is thus often set apart. It is not certain that there is meaning in the groupings shown in Figure 6, but the analogies are tempting. In the past, we have been able to make significant advances by looking for analogies and patterns, and this is an example of one under current scrutiny. There are connections between the families of leptons, in that the decays into the and the into the e. Similarly for quarks, the higher families eventually decay into the lowest, leaving only u and d quarks. We have long sought connections between the forces in nature. Since these are carried by particles, we will explore connections between gluons, and , and photons as part of the search for unification of forces discussed in GUTs: The Unification of Forces..
The quark flavor change takes place in decay. Does this mean that the reverse quark flavor change takes place in decay? Justify your response by writing the decay in terms of the quark constituents, noting that it looks as if a proton is converted into a neutron in decay.
Explain how the weak force can change strangeness by changing quark flavor.
Beta decay is caused by the weak force, as are all reactions in which strangeness changes. Does this imply that the weak force can change quark flavor? Explain.
Why is it easier to see the properties of the c, b, and t quarks in mesons having composition or rather than in baryons having a mixture of quarks, such as udb?
How can quarks, which are fermions, combine to form bosons? Why must an even number combine to form a boson? Give one example by stating the quark substructure of a boson.
What evidence is cited to support the contention that the gluon force between quarks is greater than the strong nuclear force between hadrons? How is this related to color? Is it also related to quark confinement?
Discuss how we know that () are not fundamental particles and are not the basic carriers of the strong force.
An antibaryon has three antiquarks with colors . What is its color?
Suppose leptons are created in a reaction. Does this imply the weak force is acting? (for example, consider decay.)
How can the lifetime of a particle indicate that its decay is caused by the strong nuclear force? How can a change in strangeness imply which force is responsible for a reaction? What does a change in quark flavor imply about the force that is responsible?
(a) Do all particles having strangeness also have at least one strange quark in them?
(b) Do all hadrons with a strange quark also have nonzero strangeness?
The sigma-zero particle decays mostly via the reaction . Explain how this decay and the respective quark compositions imply that the is an excited state of the .
What do the quark compositions and other quantum numbers imply about the relationships between the and the proton? The and the neutron?
Discuss the similarities and differences between the photon and the in terms of particle properties, including forces felt.
Identify evidence for electroweak unification.
The quarks in a particle are confined, meaning individual quarks cannot be directly observed. Are gluons confined as well? Explain
Problems & Exercises
(a) Verify from its quark composition that the particle could be an excited state of the proton.
(b) There is a spread of about 100 MeV in the decay energy of the , interpreted as uncertainty due to its short lifetime. What is its approximate lifetime?
(c) Does its decay proceed via the strong or weak force?
(a) The composition is the same as for a proton.
(c) Strong (short lifetime)
Accelerators such as the Triangle Universities Meson Facility (TRIUMF) in British Columbia produce secondary beams of pions by having an intense primary proton beam strike a target. Such “meson factories” have been used for many years to study the interaction of pions with nuclei and, hence, the strong nuclear force. One reaction that occurs is , where the is a very short-lived particle. The graph in Figure 7 shows the probability of this reaction as a function of energy. The width of the bump is the uncertainty in energy due to the short lifetime of the .
(a) Find this lifetime.
(b) Verify from the quark composition of the particles that this reaction annihilates and then re-creates a d quark and a antiquark by writing the reaction and decay in terms of quarks.
(c) Draw a Feynman diagram of the production and decay of the showing the individual quarks involved.
The reaction (described in the preceding problem) takes place via the strong force. (a) What is the baryon number of the particle?
(b) Draw a Feynman diagram of the reaction showing the individual quarks involved.
One of the decay modes of the omega minus is .
(a) What is the change in strangeness?
(b) Verify that baryon number and charge are conserved, while lepton numbers are unaffected.
(c) Write the equation in terms of the constituent quarks, indicating that the weak force is responsible.
Repeat the previous problem for the decay mode
(b) , all lepton numbers are 0 before and after
One decay mode for the eta-zero meson is
(a) Find the energy released.
(b) What is the uncertainty in the energy due to the short lifetime?
(c) Write the decay in terms of the constituent quarks.
(d) Verify that baryon number, lepton numbers, and charge are conserved.
One decay mode for the eta-zero meson is .
(a) Write the decay in terms of the quark constituents.
(b) How much energy is released?
(c) What is the ultimate release of energy, given the decay mode for the pi zero is ?
(b) 277.9 MeV
(c) 547.9 MeV
Is the decay possible considering the appropriate conservation laws? State why or why not.
Is the decay possible considering the appropriate conservation laws? State why or why not.
No. is conserved. is not conserved. is conserved.
(a) Is the decay possible considering the appropriate conservation laws? State why or why not.
(b) Write the decay in terms of the quark constituents of the particles.
(a) Is the decay possible considering the appropriate conservation laws? State why or why not. (b) Write the decay in terms of the quark constituents of the particles.
(a)Yes. , , all lepton family numbers are 0 before and after, spontaneous since mass greater before reaction.
The only combination of quark colors that produces a white baryon is RGB. Identify all the color combinations that can produce a white meson.
(a) Three quarks form a baryon. How many combinations of the six known quarks are there if all combinations are possible?
(b) This number is less than the number of known baryons. Explain why.
(b) There are more baryons observed because we have the 6 antiquarks and various mixtures of quarks (as for the π-meson) as well.
(a) Show that the conjectured decay of the proton, , violates conservation of baryon number and conservation of lepton number.
(b) What is the analogous decay process for the antiproton?
Verify the quantum numbers given for the in Table: Selected Particle Characteristics by adding the quantum numbers for its quark constituents as inferred from Table 2.
Verify the quantum numbers given for the proton and neutron in Table: Selected Particle Characteristics by adding the quantum numbers for their quark constituents as given in Table 2.
(a) How much energy would be released if the proton did decay via the conjectured reaction ?
(b) Given that the decays to two s and that the will find an electron to annihilate, what total energy is ultimately produced in proton decay?
(c) Why is this energy greater than the proton’s total mass (converted to energy)?
(a) 803 MeV
(b) 938.8 MeV
(c) The annihilation energy of an extra electron is included in the total energy.
(a) Find the charge, baryon number, strangeness, charm, and bottomness of the particle from its quark composition.
(b) Do the same for the particle.
There are particles called D-mesons. One of them is the meson, which has a single positive charge and a baryon number of zero, also the value of its strangeness, topness, and bottomness. It has a charm of What is its quark configuration?
There are particles called bottom mesons or B-mesons. One of them is the meson, which has a single negative charge; its baryon number is zero, as are its strangeness, charm, and topness. It has a bottomness of . What is its quark configuration?
(a) What particle has the quark composition ?
(b) What should its decay mode be?
a) The antiproton
(a) Show that all combinations of three quarks produce integral charges. Thus baryons must have integral charge.
(b) Show that all combinations of a quark and an antiquark produce only integral charges. Thus mesons must have integral charge.