135 Quarks: Is That All There Is?

Throughout this text we have encountered quarks as the building blocks of protons, neutrons, and many other particles. Quarks belong to the small group of particles that are currently considered fundamental, meaning that they show no evidence of being composed of smaller constituents. Like leptons, they behave as point-like particles down to the smallest distances that experiments can currently probe.

Not all particles are fundamental. Leptons, such as electrons and neutrinos, appear to have no internal structure, whereas hadrons—including protons, neutrons, and pions—are composite particles built from quarks. The Standard Model of particle physics classifies the known elementary particles into three broad groups: leptons, quarks, and the force-carrying particles (called gauge bosons). Together, these particles account for all known ordinary matter and the interactions between them.

In this chapter, we explore how quarks combine to form hadrons, how their properties explain the observed characteristics of particles, and why quarks have never been observed in isolation. These ideas provide one of the strongest examples of how simple underlying principles can explain an enormous variety of seemingly different particles.

Conception of Quarks

The quark model was proposed independently in 1964 by physicists Murray Gell-Mann and George Zweig to explain the growing number of particles being discovered in accelerator experiments. Instead of viewing every hadron as a separate elementary particle, they suggested that hadrons are combinations of a much smaller set of truly fundamental particles called quarks.

The original model contained three quark flavors: up (u), down (d), and strange (s). As experiments reached higher energies, three additional flavors—charm, bottom, and top—were discovered, completing the six-quark family recognized today.

Quarks are fermions, each having intrinsic spin [latex]1/2[/latex]. Their combinations explain the observed spins of hadrons. Baryons contain an odd number of quarks and therefore have half-integer spin, while mesons contain a quark and an antiquark, giving them integer spin.

Perhaps the most surprising feature of the quark model is that quarks possess fractional electric charge. Up-type quarks carry charge [latex]+\frac{2}{3}q_e[/latex], whereas down-type quarks carry charge [latex]-\frac{1}{3}q_e[/latex]. Antiquarks have equal but opposite charges. Although individual quarks have fractional charge, every observable particle has an integer charge because quarks always combine in specific ways that produce whole-number multiples of the elementary charge.

One of the strongest pieces of evidence supporting the quark model is that it naturally explains the properties of known hadrons. For example, the proton, neutron, and pions shown in Figure 135.1 all have quark compositions that correctly predict their electric charges, spins, and other quantum numbers. Later in this chapter, we will also see how quark combinations explain conservation laws and particle decays.

How Does It Work?

To understand the quark model, it is helpful to examine familiar particles such as the proton, neutron, and pions. The proton consists of two up quarks and one down quark, usually written as uud. Adding the charges of its constituent quarks gives

which is exactly the observed charge of the proton. Likewise, the orientations of the quark spins combine to produce the proton's measured intrinsic spin of [latex]\frac{1}{2}[/latex].

The neutron is composed of the quarks udd. Although its total charge is zero, its charged constituents move inside the particle, producing the neutron's magnetic moment. This provides direct evidence that the neutron is not a structureless particle.

An especially important feature of quarks is that the weak interaction can change one quark flavor into another. This process explains beta decay at the most fundamental level. In ordinary beta-minus decay, a neutron becomes a proton because one of its down quarks changes into an up quark:

Expressed in terms of quarks, the same process is

This is equivalent to the elementary quark-level reaction

This example illustrates a key property of the weak nuclear force: it is the only fundamental interaction capable of changing the flavor of a quark. The strong interaction, although much stronger, cannot alter quark flavor.

Note:

The upper signs apply to quarks and the lower signs apply to antiquarks. The quoted masses are approximate because free quarks cannot be isolated and measured directly.

One of the most important consequences of the quark model is that the weak interaction can change the flavor of a quark. In other words, one type of quark can transform into another through the weak nuclear force. For example, the down quark can change into an up quark, as occurs during beta decay. Likewise, up quarks can change into down quarks, and strange quarks can transform into either up or down quarks. These flavor-changing processes explain why quantities such as strangeness are not conserved in weak interactions.

By contrast, the strong nuclear force conserves quark flavor. Strong interactions can rearrange quarks among particles, create quark-antiquark pairs, or bind quarks into hadrons, but they cannot change one flavor of quark into another.

The quark model also explains the properties of mesons. For example, the positively charged pion is composed of an up quark and an antidown quark, [latex]u\bar{d}[/latex]. The total electric charge is

while its baryon number is

The quark and antiquark have opposite spins, allowing the pion to have total spin zero, consistent with experiment. Because the quark and antiquark have different flavors, the pion cannot simply annihilate internally. Instead, it decays through the weak interaction after one of the quarks changes flavor.

The negatively charged pion is the antiparticle of the positive pion. Its quark composition is [latex]\bar{u}d[/latex], meaning that each constituent is the antiparticle of the corresponding quark in the [latex]\pi^+[/latex]. When a [latex]\pi^+[/latex] and a [latex]\pi^-[/latex] meet, their constituent quarks and antiquarks can annihilate, producing other particles.

The quark model can be summarized by two simple rules:

1. Baryons are composed of three quarks, while antibaryons are composed of three antiquarks.
2. Mesons are composed of one quark and one antiquark.

These simple combinations explain why every observed hadron has an integer electric charge, even though the individual quarks themselves carry fractional charges.

All Combinations Are Possible

Once the quark model was proposed, physicists realized that every allowed combination of quarks should correspond to a possible particle. Some combinations had already been observed, while others had not yet been discovered. This situation resembled earlier developments in chemistry and nuclear physics, where patterns in the periodic table and the chart of nuclides successfully predicted previously unknown elements and isotopes.

The most striking prediction was the existence of the [latex]\Omega^-[/latex] baryon, composed of three strange quarks:

From this quark composition, physicists predicted that the particle would have a strangeness of [latex]S=-3[/latex], a charge of [latex]-1[/latex], baryon number [latex]B=1[/latex], and specific values for its mass, spin, and lifetime. In 1964, experiments at Brookhaven National Laboratory discovered the [latex]\Omega^-[/latex] with properties that closely matched these predictions.

The successful prediction and discovery of the [latex]\Omega^-[/latex] provided some of the strongest early evidence that the quark model correctly describes the internal structure of hadrons. It transformed quarks from an elegant mathematical idea into a powerful framework for understanding particle physics.

Direct Evidence for Quarks

When the quark model was first proposed, many physicists expected that sufficiently energetic collisions would eventually separate quarks so they could be observed directly. Despite decades of increasingly powerful particle accelerators, no isolated quark has ever been detected. Instead, whenever enough energy is supplied to pull quarks apart, that energy is converted into new quark–antiquark pairs, producing additional hadrons rather than free quarks. This phenomenon is known as quark confinement and is one of the defining features of the strong interaction.

Although free quarks have never been observed, the experimental evidence supporting their existence is overwhelming. One of the most important breakthroughs came in the late 1960s through deep inelastic scattering experiments at the Stanford Linear Accelerator Center (SLAC). In these experiments, electrons with energies of about 20 GeV were fired at protons. Much like Rutherford's scattering experiments revealed the compact nucleus inside the atom, the SLAC experiments showed that protons contain three small, point-like charged constituents. These scattering centers behave exactly as expected for quarks.

Modern particle accelerators provide even stronger evidence. In high-energy collisions, quarks are produced with enormous kinetic energies, but they never emerge as isolated particles. Instead, they generate narrow sprays of hadrons called jets. These jets preserve the momentum and direction of the original quarks, allowing physicists to reconstruct the underlying collision. The observed jet patterns agree remarkably well with predictions from quantum chromodynamics (QCD), the modern theory describing quarks and the strong interaction.

The Discovery of the Six Quark Flavors

The original quark model included only three flavors: up, down, and strange. While these successfully explained the known hadrons of the early 1960s, later discoveries showed that the particle family was larger than originally expected. Rather than disproving the quark model, each new discovery strengthened it by revealing additional quark flavors predicted by theory.

The first major breakthrough came in 1974 with the discovery of the J/ψ meson by two independent research teams led by Samuel C. C. Ting at Brookhaven National Laboratory and Burton Richter at SLAC. The particle was quickly identified as a bound state of a charm quark and a charm antiquark,

This discovery confirmed the existence of the charm quark and marked such a dramatic success for particle physics that the event became known as the November Revolution. Ting and Richter shared the 1976 Nobel Prize in Physics for this achievement.

The discovery of the tau lepton in 1975 suggested that nature contains three families of fundamental particles. To preserve this symmetry, theorists proposed two additional quark flavors: bottom and top. Evidence for the bottom quark soon followed with the discovery of the upsilon ([latex]\Upsilon[/latex]) meson, which consists of a bottom quark and a bottom antiquark:

The final member of the quark family, the top quark, proved much more difficult to observe because of its exceptionally large mass. It was finally discovered in 1995 at Fermilab, completing the six-flavor quark model that is now part of the Standard Model of particle physics.

Each newly discovered quark is heavier than the previous one, requiring increasingly energetic particle accelerators for its production. Because quarks are permanently confined inside hadrons, their masses cannot be measured directly. Instead, their values are inferred from the properties of the particles they form and from high-energy scattering experiments.

Color Charge and Quantum Chromodynamics

In addition to electric charge, quarks possess another fundamental property known as color charge, usually shortened to simply color. Despite its name, color has nothing to do with visible light. Instead, it is a quantum property that determines how quarks interact through the strong nuclear force.

Each quark can exist in one of three color states, conventionally called red, green, and blue. Antiquarks carry the corresponding anticolors, often called antired (cyan), antigreen (magenta), and antiblue (yellow). These names are used only as a convenient analogy with visible colors; they do not represent actual colors.

The color analogy is useful because combining red, green, and blue light produces white. Similarly, all observable hadrons must be color neutral, sometimes described as "white." A baryon contains one red, one green, and one blue quark, while a meson consists of a quark and an antiquark carrying matching color and anticolor.

Color charge explains one of the most puzzling features of quarks: why they are never observed individually. As two quarks are pulled farther apart, the strong force between them does not weaken as the electromagnetic force does. Instead, the interaction remains extremely strong, storing increasing amounts of energy. Eventually, enough energy is available to create an entirely new quark-antiquark pair, preventing the original quarks from becoming isolated. This phenomenon is known as quark confinement.

Color also resolves an apparent conflict with the Pauli exclusion principle. Particles such as the [latex]\Omega^-[/latex], which contains three strange quarks ([latex]sss[/latex]), or the [latex]\Delta^{++}[/latex], which contains three up quarks ([latex]uuu[/latex]), would seem to place identical fermions in the same quantum state. The additional color quantum number distinguishes the three quarks, allowing the exclusion principle to remain satisfied.

The modern theory describing the strong interaction between quarks is called quantum chromodynamics (QCD). In QCD, color charge plays a role analogous to electric charge in electromagnetism, except that the force is carried by particles called gluons, which themselves also carry color charge. QCD has been remarkably successful in explaining the behavior of quarks, hadrons, and the strong nuclear force.

The Three Families of Fundamental Particles

The Standard Model organizes fundamental particles into three broad categories: leptons, quarks, and force-carrying particles (also called gauge bosons). Both leptons and quarks are further arranged into three generations, or families, each containing particles with similar properties but progressively larger masses.

The first family contains the particles that make up nearly all ordinary matter, including electrons, electron neutrinos, and the up and down quarks that form protons and neutrons. The second and third families contain heavier particles that are unstable and quickly decay into members of the first family.

The force-carrying particles include the photon, which mediates the electromagnetic interaction; the [latex]W^\pm[/latex] and [latex]Z^0[/latex] bosons, responsible for the weak interaction; and the gluons, which carry the strong interaction. Although gravity is expected to have its own force carrier—the hypothetical graviton—it has not yet been experimentally observed and is therefore not included in the Standard Model.

One of the major goals of modern particle physics is to understand why nature contains three families and whether the different fundamental interactions can be unified into a single theoretical framework. While important progress has been made, these questions remain active areas of research.

Section Summary

• Quarks are fundamental particles that combine to form hadrons. Baryons contain three quarks, while mesons consist of a quark and an antiquark.
• The Standard Model includes six quark flavors: up, down, strange, charm, bottom, and top. Each flavor has a corresponding antiquark with opposite quantum numbers.
• The electric charge, baryon number, strangeness, charm, bottomness, and other quantum numbers of a hadron can be determined by adding the quantum numbers of its constituent quarks.
• The weak nuclear force can change one quark flavor into another, whereas the strong nuclear force conserves quark flavor.
• Deep inelastic scattering experiments and the observation of particle jets provide compelling experimental evidence for the existence of quarks, even though isolated quarks have never been observed.
• Quarks possess an additional quantum property called color charge. Observable hadrons are always color neutral, and color confinement explains why individual quarks cannot exist in isolation.
• Quantum chromodynamics (QCD) is the modern theory describing the strong interaction between quarks and gluons.
• Fundamental particles are organized into three categories—leptons, quarks, and force-carrying particles—with leptons and quarks each occurring in three generations.

Conceptual Questions

17. The quark flavor change [latex]d\to u[/latex] occurs in [latex]\beta^-[/latex] decay. Does the reverse flavor change, [latex]u\to d[/latex], occur in [latex]\beta^+[/latex] decay? Justify your answer by writing the decay in terms of the quark constituents. Note that, at the nucleon level, a proton is converted into a neutron during [latex]\beta^+[/latex] decay.
18. Explain how the weak interaction can change strangeness by changing quark flavor.
19. Beta decay is caused by the weak interaction, as are reactions in which strangeness changes. What does this imply about the ability of the weak interaction to change quark flavor? Explain.
20. Why is it easier to identify the properties of the charm, bottom, and top quarks in particles with compositions such as [latex]c\bar{c}[/latex], [latex]b\bar{b}[/latex], and [latex]t\bar{t}[/latex] than in hadrons containing mixtures of different quark flavors, such as [latex]udb[/latex]?
21. How can quarks, which are fermions, combine to form bosons? Why must an even number of fermions combine to produce a boson? Give one example by stating the quark composition of a boson.
22. What evidence supports the conclusion that the interaction between quarks is stronger than the residual strong nuclear force between hadrons? How is this related to color charge and quark confinement?
23. Discuss the evidence showing that the pion mesons [latex]\pi^+[/latex], [latex]\pi^-[/latex], and [latex]\pi^0[/latex] are not fundamental particles and are not the fundamental carriers of the strong interaction.
24. An antibaryon contains three antiquarks with anticolors [latex]\bar{R}\bar{G}\bar{B}[/latex]. What is the total color of the antibaryon?
25. Suppose leptons are created in a reaction. Does this necessarily imply that the weak interaction is responsible? Explain, using beta decay or another example.
26. How can the lifetime of a particle indicate whether its decay is caused by the strong interaction? How can a change in strangeness identify the interaction responsible for a reaction? What does a change in quark flavor imply about the responsible interaction?
27. (a) Do all particles with nonzero strangeness contain at least one strange quark or strange antiquark?(b) Do all hadrons containing a strange quark or strange antiquark necessarily have nonzero strangeness?
28. The sigma-zero particle decays primarily through
    [latex]\Sigma^0\to\Lambda^0+\gamma.[/latex]

    Explain how this decay and the quark compositions of the two baryons indicate that the [latex]\Sigma^0[/latex] is an excited state of the [latex]\Lambda^0[/latex].

29. What do their quark compositions and quantum numbers imply about the relationship between the [latex]\Delta^+[/latex] and the proton? What do they imply about the relationship between the [latex]\Delta^0[/latex] and the neutron?
30. Discuss the similarities and differences between the photon and the [latex]Z^0[/latex] boson, including their masses, electric charges, interactions, and the particles on which they act.
31. Identify experimental or theoretical evidence supporting electroweak unification.
32. Quarks are confined, meaning that isolated quarks cannot be directly observed. Are gluons also confined? Explain.

Problems and Exercises

23. (a) Use its quark composition to verify that the [latex]\Delta^+[/latex] particle could be an excited state of the proton.(b) The decay energy of the [latex]\Delta^+[/latex] has a spread of approximately 100 MeV. Interpreting this spread as an energy uncertainty caused by the particle’s short lifetime, estimate its lifetime.(c) Does the decay proceed through the strong or weak interaction? Explain.
24. Accelerators such as the TRIUMF facility in British Columbia produce secondary pion beams by directing an intense primary proton beam onto a target. These facilities have been used to study interactions between pions and nuclei and, therefore, the strong interaction.One reaction is
    [latex]\pi^+ + p \to \Delta^{++} \to \pi^+ + p,[/latex]

    where the [latex]\Delta^{++}[/latex] is a very short-lived particle. Figure 135.7 shows the probability of this reaction as a function of the pion’s kinetic energy. The width of the peak represents the uncertainty in energy associated with the short lifetime of the [latex]\Delta^{++}[/latex].

    

    • 1. Estimate the lifetime of the [latex]\Delta^{++}[/latex].
      2. Use the quark compositions of the particles to show that this reaction annihilates and then recreates a down quark and an antidown quark. Write both the production and decay reactions in terms of quarks.
      3. Draw a Feynman diagram for the production and decay of the [latex]\Delta^{++}[/latex], showing the individual quarks involved.
25. The reaction
    [latex]\pi^+ + p \to \Delta^{++}[/latex]

    occurs through the strong interaction.

    • 1. (a) What is the baryon number of the [latex]\Delta^{++}[/latex]?
      2. (b) Draw a Feynman diagram of the reaction showing the individual quarks involved.
26. One decay mode of the omega-minus particle is
    [latex]\Omega^- \to \Xi^0+\pi^-.[/latex]
    • • 1. What is the change in strangeness?
        2. Verify that baryon number and electric charge are conserved and that the lepton family numbers are unchanged.
        3. Write the decay in terms of the constituent quarks and indicate why the weak interaction must be responsible.
27. Repeat the preceding problem for the decay
    [latex]\Omega^- \to \Lambda^0+K^-.[/latex]
28. One decay mode of the eta-zero meson is
    [latex]\eta^0\to\gamma+\gamma.[/latex]
    • • 1. Find the energy released in the decay.
        2. What is the uncertainty in the energy associated with the particle’s short lifetime?
        3. Write the decay in terms of the constituent quarks.
        4. Verify that baryon number, lepton family numbers, and electric charge are conserved.
29. Another decay mode of the eta-zero meson is
    [latex]\eta^0\to\pi^0+\pi^0.[/latex]
    • • 1. Write the decay in terms of the quark constituents.
        2. How much energy is released?
        3. Each neutral pion subsequently decays according to
           [latex]\pi^0\to\gamma+\gamma.[/latex]

    What is the ultimate form and total amount of the released energy?

30. Is the decay
    [latex]n\to e^++e^-[/latex]

    possible under the relevant conservation laws? Explain why or why not.

31. Is the decay
    [latex]\mu^-\to e^-+\nu_e+\nu_\mu[/latex]

    possible under the relevant conservation laws? Explain why or why not.

32. (a) Is the decay
    [latex]\Lambda^0\to n+\pi^0[/latex]

    possible under the relevant conservation laws? Explain.

    (b) Write the decay in terms of the quark constituents of the particles.

33. (a) Is the decay
    [latex]\Sigma^-\to n+\pi^-[/latex]

    possible under the relevant conservation laws? Explain.

    (b) Write the decay in terms of the quark constituents.

34. The only combination of three quark colors that produces a color-neutral baryon is red, green, and blue. Identify all color–anticolor combinations that can produce a color-neutral meson.
35. (a) Three quarks form a baryon. How many ordered combinations can be formed from the six known quark flavors if repetition is allowed?(b) The number of observed baryons and baryon resonances is greater than this simple count. Explain why.
36. (a) Show that the proposed proton decay
    [latex]p\to\pi^0+e^+[/latex]

    violates conservation of baryon number and conservation of lepton number.

    (b) What is the analogous proposed decay process for an antiproton?

37. Verify the quantum numbers of the [latex]\Omega^+[/latex] by adding the quantum numbers of its three antiquark constituents. Determine its baryon number, electric charge, strangeness, and lepton family numbers.
38. Verify the quantum numbers of the proton and neutron by adding the quantum numbers of their constituent quarks.
39. (a) How much energy would be released if a proton decayed through the proposed reaction
    [latex]p\to\pi^0+e^+?[/latex]

    (b) The [latex]\pi^0[/latex] decays into two photons, and the positron eventually annihilates with an electron. What total energy is ultimately released?

    (c) Why is this total greater than the proton’s mass-energy alone?

40. (a) Determine the electric charge, baryon number, strangeness, charm, and bottomness of the [latex]J/\psi[/latex] meson from its quark composition.(b) Determine the same quantum numbers for the [latex]\Upsilon[/latex] meson.
41. The [latex]D^+[/latex] meson has electric charge [latex]+q_e[/latex], baryon number zero, charm [latex]+1[/latex], and zero strangeness, bottomness, and topness. What is its quark composition?
42. The [latex]B^-[/latex] meson has electric charge [latex]-q_e[/latex], baryon number zero, bottomness [latex]-1[/latex], and zero strangeness, charm, and topness. What is its quark composition?
43. (a) What particle has the antiquark composition
    [latex]\bar{u}\bar{u}\bar{d}?[/latex]

    (b) What decay process would be analogous to the proposed proton decay discussed earlier?

44. (a) Show that every possible combination of three quarks has an integer electric charge. Therefore, baryons must have integer charges.(b) Show that every possible combination of one quark and one antiquark has an integer electric charge. Therefore, mesons must have integer charges.