QUARKS

Quarks are subatomic particles that combine in various ways to form all of the known hadrons. In spite of their ubiquity, free quarks are not seen in nature. Besides this anomaly, they have fractional electric charge and a surprising number of nonclassical properties. They only form triplets, called baryons, such as the proton and neutron, or doublets, called mesons, such as the pi meson; they are bound together by a strong force field whose quanta are called gluons. However, this rather simple definition of the quarks does not convey the fascination and challenges of the fifty-year quest that led to their discovery and to the characterization of their properties. Table 1 provides a time line of important events in quark history.

Table 2 lists the quarks, their names (or flavor), and their quantum numbers. Their charge and spin are measured in units relative to those of the electron, and their approximate mass is given in MeV/c².

TABLE 1

This table shows some of the milestones in the discovery of the quark model. The first entry showed that there were two strongly interacting particles that had strikingly different characteristics. This work was done by one or two physicists looking at tracks left in photographic plates by cosmic ray particles. As the quark mass increased, it required increasingly more complicated experimental detectors. The last entry, the top quark, had over 200 experimenters on each of the two experiments and required the full energy of the Fermilab Tevatron Collider.

There are four forces that act between quarks: the strong force that binds together quarks; the electro-magnetic force whose quantum is the photon that couples to the quark charge; the weak force that causes beta decay and allows a quark of one type to change into another; and gravity that couples to their mass.

Early Discoveries

The first step in the discovery of quarks occurred in 1947 when a new particle, the K meson, with a mass of about 500 MeV/c², was discovered in cosmic rays. However, along with the discovery came a mystery. These particles were made in nuclear collisions by very-high-energy cosmic-ray particles via the strong force, with an interaction time of about 10^-24 s, which is approximated by dividing the radius of a nucleus by the speed of the cosmic-ray particle. The new particles were observed, though, to decay into pions with lifetimes of the order of 10^-9 s. If the strong force could make these particles so easily, why did it not cause them to decay just as fast? They were named strange particles. Later, in 1953, these particles were made in the Cosmotron at Brookhaven National Laboratory (BNL), and soon whole families of these particles were discovered. By 1964 two octets, one of baryons and one of mesons, and an additional decuplet of baryons had been discovered. Figure 1 lists their modern quark assignments.

In 1964 Murray Gell-Mann and George Zweig independently found the solution for explaining many of the observed properties of these particles. They proposed that all baryons were composed of triplets of quarks (selected from u , d , and s in Table2) and that mesons were doublets formed by qq , where the overbar indicates an antiquark.

Conservation Laws

To see how theory and experiment worked together to elucidate the quark model, it is important to understand conservation rules. Classical mechanics revealed the conservation of energy, momentum, and angular momentum. These conservation laws apply to collisions of particles: the total energy and momentum of the incoming particles are equal to those of the outgoing state. This is a powerful constraint on the reactions that can take place. In addition,

TABLE 2

electric charge conservation places constraints on reactions: the total charge of the initial state must be equal to that of the final one. How well is it known that charge is conserved? It has been determined that

FIGURE 1

the lifetime for the disappearance of an electron into an all-neutral final state (for instance, neutrinos and photons) must be greater than 4.2 × 10²⁴ years. Here, it will be assumed that this time is so long that charge is really conserved, but future experiments may discover otherwise. If the electron does not decay, does the proton? Charge conservation and energy conservation allow many final states, such as e⁺π⁰, into which the proton could decay, but measurements have shown that its lifetime is greater than 1.6 × 10²⁵ years!

Proton stability is incorporated into the quark model by positing the conservation of a new number N. Each quark is assigned an additive baryon quantum number of 1/3 or -1/3 for antiquarks. N is then equal to -1, 0, and 1 for antibaryons, mesons, and baryons. This law not only prohibits the decay of the proton into pions but also requires that any baryon made in a high-energy collision must be accompanied by an antibaryon.

Figure 2 shows a reaction between a 900-GeV/c² proton and an equal energy antiproton moving in the opposite direction for a total energy of 1,800 GeV/c². The incoming state has charge and baryon numbers zero. The conservation laws discussed assure that in this event the final state conserves energy and momentum, that there are as many positive particles as negative ones, and that an equal number of baryons and antibaryons exists.

We now return to the mystery mentioned above concerning the production of strange particles. It

FIGURE 2

was discovered that strange particles were made in pairs. The production and decay are given by The arrow indicates that the particles on the left turned into the particles on the right. The first reaction, which conserves Q and N, results from the strong force. The experiments on the production of strange particles indicated that there is a new additive quantum number called strangness that is conserved in strong interactions. It is zero for the u and d and (-1, 1) for the (s , s̄ ). Figure 1 shows that the Λ° has a strangeness of -1 and the Κ° is +1, so both sides of the equation balance to zero. In the two lower equations, which involve decay of the strange particles, S is not conserved and the weak force is responsible for the strangeness-changing decay of the s quark. Note that the decay of the neutron is also due to the weak force changing a d quark into a u quark. The general rule is that the strong force treats all the quarks equally and conserves the quantum numbers shown in Table 2, whereas the weak force allows quarks to change flavor or decay into leptons.

Particles Classified by Their Quark Content

Once the postulate was made that hadrons are composites of quarks, it became possible to explain the properties of the many different hadrons that had been discovered experimentally, in much the same way that the Periodic Table relates the chemical properties of different elements. Figure 1 shows three examples of hadrons and their quark compositions. Since quarks have spin 1/2, they can have spins parallel for a total spin of 1 or antiparallel for a spin of 0. The baryons, with three quarks, can have a total spin of either 3/2 or 1/2. The figure shows examples of spin-0 mesons, spin-1/2 baryons, and spin-3/2 baryons. Strangeness is plotted on the vertical axis.

Strangeness and spin are used to classify the particles in Figure 1, but there is still another connection between these particles. Isotopic spin I is the quantum number first observed in nuclear reactions, where isotopic states in nuclei with the same number of nucleons but different numbers of protons have very similar properties. Figure 1 shows similar behavior for the u and d quarks, and this feature is embedded in the quark model by assigning isotopic spin ½ to the u and d .

Unlike the additive quantum numbers Q and N, the total isospin for a qq̄ state combines the individual isospins in the same mathematical manner as spins are combined, that is, like vectors. Classically, if there are two forces on an object, one downward and an equal sideward force, the total force occurs at 45°. One does not just numerically add the forces, but one takes their vector sum. Since spin is a vector, the same rules apply for combining the spins of two particles. However, quantum mechanics quantizes the rules so that nature only allows integral or half-integral spin. Thus, for example, a neutron and proton, each with a spin of ½, can exist in a state with a total angular momentum of either 1 or 0. The rules for the vector addition of spin were first learned in studying the behavior of electrons around atoms and subsequently were found to be exactly the rules necessary for understanding a new quark quantum number. It was given the name isotopic spin and follows the same rules for addition as spin but has no relation to angular momentum,

Thus, a qq̄ state can have either I = 1 with I₃= (-1, 0, 1), I = 0 with I₃= 0 for the u plus d combinations, or I = ½ with I₃= +½ or -½ when only a single u or d is present. The π^-, π⁰, π⁺ in the middle row is an example with I = 1, I₃= -1, 0, +1, and the Κ⁺ and Κ^- doublets show I = ½, with I₃= -½ and +½. The isospin, which is plotted horizontally, is related to the actual charge of the hadron by the general formula Q =I₃ + N /2 + S /2 for the strange particles.

In 1962 Murray Gell-Mann and Yuval Ne'emann were the first to recognize the symmetries shown in Figure 1. At the time the Ω^- had not yet been discovered, and they predicted this state with S = -3 in the decuplet. There was great excitement in 1964 when experimenters discovered the Ω^- at Brookhaven's Cosmotron. The same year Gell-Mann, and independently Zweig, proposed the first elements of the quark model using u , d , and s quarks. This model naturally predicted the Ω^- but also raised a curious problem that led to an important extension of the theory.

Color

It has been known for a long time that particles come in two types: fermions, whose spins are odd multiples of ½, and bosons, which have zero or integral spin. Fermions obey the Pauli exclusion principle that states that two of them cannot occupy the same physical state simultaneously. On the other hand, one can collect as many bosons as desired into a given state. A simple example is the ground state of the helium atom with two electrons around the nucleus. The spatial state of the two electrons is the same, but because the electrons have spin ½, two electrons, one with spin up and the other with spin down, can occupy this state. The Ω was found to have a spin of 3/2, and the simplest configuration of the ground state to give this result would require all three quarks to have spin up. This violates the exclusion principle, as the quarks are supposed to be fermions.

This problem led to the surprising conclusion that there must be three different states for each quark. This is referred to as the color charge; each quark comes in one of three different states called red, blue, and green. These are just names for an additional quantum number and do not, of course, refer to an actual color. Thus, the three quarks in the Ω^- have their spins parallel and the same spatial wave function, but are of three different colors. Since all three colors are equally present, it is said that the state is color-neutral, and since this additional quantum number is not seen in real hadrons, one knows that these states must all be colorless. The baryons accomplish colorlessness by being composed of three different-colored quarks; the mesons are color-neutral as they are composed of quarks and antiquarks.

Finally, one comes to the force, carried by the gluons, that binds the quarks together. The development of the theory of quantum chromodynamics (QCD), which describes how these eight gluons interact among themselves and with the quarks, was started by the work of Yoichiro Nambu and by Oscar W. Greenberg in 1966. It was essentially completed by 1973 and remains the underlying theory of strong interactions.

Can the quark hypothesis be tested? The answer is yes. Direct experiments show that baryons are indeed composed of three quarks and that quarks have an additional three-valued quantum number, color. The first experiment that showed that the proton behaved dynamically, as if composed of subatomic particles, was done at the Stanford Linear Accelerator (SLAC) in 1969 using high-energy electrons to scatter off the constituent particles composing the proton. In 1990 a Nobel Prize in Physics was awarded to Henry W. Kendall, Jerome I. Friedman, and Richard E. Taylor for this discovery.

Charm, Bottom, and the Top

The next surprise occurred in 1974. As early as 1964 theorists had speculated on the existence of an additional quark. Ten years later the charm quark appeared simultaneously in experiments at SLAC and BNL, resulting in a Nobel Prizes in Physics for Burton Richter and Samuel C. Ting. They discovered a meson, called the J/ψ, consisting of a charm and anticharm quark. The new quark was more massive than the proton at 1,200 MeV/c² and had a charge of like the u . An additional beautiful feature of the J/ψ is that gluons bind the two quarks together in a fashion that leads to a spectrum of many excited states, called charmonium, that has played a role for QCD similar to that played by the hydrogen atom for quantum electrodynamics (QED). Soon experiments found new charmed mesons and baryons in which the charm quark formed states with the u and d ; even charmed-strange states with the s quark appeared.

In 1977 two more pieces of the puzzle were discovered. The tau, or τ, meson was discovered at SLAC by a collaboration led by Martin Perl, and the upsilon meson, or ψ, was discovered at Fermilab by a collaboration led by Leon Lederman. The upsilon had a mass of about 9.5 GeV/c² and, in a fashion analogous to the J/ψ , it is composed of a bb̄ pair. States have also been discovered in which the bottom quark, whose mass is about 4.5 GeV/c², binds via the strong force with the other quarks to form baryons and mesons that are several times as massive as the proton.

The discussion here has centered on the discovery of how quarks bind together to form the particles observed in nature and how they are produced by the strong force. At the same time, a parallel line of experiment and theory clarified how the quarks decay. Since the strong force treats quarks democratically, it is mainly the weak force that exposes their individual properties. It was discovered theoretically that the quarks should be grouped together into three doublets: (The t , or top quark, which was discovered later, is also included.) These doublets are related to the three lepton doublets by the weak force: This connection, called the electroweak theory, describes how the weak force mediates the decay of the various quarks. It represents a major triumph of theorists.

After the discovery of the τ lepton and b quark, there was much anticipation, based on the expectations mentioned above, that a sixth quark, the top, would exist. The surprise was that it took nearly twenty years before two groups at Fermilab announced the discovery. The reason for the long delay was that the top has a mass of 175 GeV/c². It was not until the Tevatron proton-antiproton collider came on-line that any machine had a high enough energy to make the top. It weighs about as much as a gold atom!

It took fifty years from the discovery of strangeness to the discovery of the top to complete what is called the Standard Model for quarks and leptons and their interactions. The first half of the quest was led by experiments making unexpected discoveries; the last half by theory making predictions of things to be discovered. A very accurate theory now exists for energies up to a few hundred GeV, but questions of why there are only three families of quarks and leptons, and an explanation of their masses, remain to be answered.

See also:Electroweak Symmetry Breaking; Experiment: Discovery of the Top Quark; J/ψ ; Lepton; Parity, Nonconservation of; Particle; Particle Physics, Elementary; Quantum Chromodynamics; Standard Model; Supersymmetry; Symmetry Principles

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Alvin V. Tollestrup