Quarks And The Strong Interaction

Type of physical science: Elementary particle (high-energy) physics

Field of study: Systematics (particle physics)

The strong interaction, or strong force, binds quarks into protons, neutrons, and other baryons and binds quarks and antiquarks into mesons. Its remnants at longer distances and low energies form the nuclear forces that hold protons and neutrons together in nuclei.

Overview

The proton, once thought to be an elementary and pointlike particle in the atomic nucleus, is composed of other elementary particles, which are called quarks. Quarks are held together by a force that is much stronger than the electromagnetic interaction, called the strong interaction, that holds electrons in atoms. The strong interaction has the peculiar property of asymptotic freedom, in which it becomes weak at short interquark distances and grows stronger when quarks move apart, thereby confining them inside strongly interacting particles. Protons and neutrons are bound in nuclei at the center of an atom by the nuclear forces, which are another aspect of the strong interaction. The proton is the lightest member of a family of strongly interacting particles called baryons, which are mainly made up of three quarks. Each quark has a twin of opposite electric charge, called an antiquark, just as the positron is the antiparticle of the electron. Quarks and antiquarks are also held together by the strong interaction, forming another family of strongly interacting particles called mesons. The π-meson, or pion, is the lightest quark-antiquark system. It was first discovered in the late 1940s in cosmic rays, which are energetic particles from outer space that sometimes reach the earth's atmosphere. Pions are produced in the laboratory by violent collisions of protons and can be driven to high velocity by means of electric and magnetic forces in machines called particle accelerators.

The size of the proton began to be measured in the 1950s in a series of electron-scattering experiments. These experiments showed that the proton has its charge distributed smoothly over a radius slightly less than one fermi (10^-13 centimeter), which is one hundred thousand times smaller than the hydrogen atom but clearly is not pointlike. The finite size of the proton was an early indication that the proton has an internal structure and is not elementary. Another indication of the composite nature of the proton was the numerous peaks in the observed numbers of scattered pions in pion-proton collisions. Such peaks are called resonances. Two particles in a resonance act like dancers who embrace and turn together a few times and then part. Resonances are interpreted as excited states of the proton. Usually, such excited states come from rearranging the quarks in the system. Once such a resonance is excited, it decays extremely quickly, emitting one or more pions, a characteristic feature of the strong force.

By the 1960s, numerous different resonances had been produced by particle accelerators, creating a virtual particle zoo. To bring some order, physicists characterized the resonances by means of quantum numbers, such as spin, parity, electric charge, baryon number, isospin, strangeness, charm, and beauty or bottom, which stay unchanged or conserved in these reactions. Two of these characteristics, isospin and strangeness, are the key to the underlying special unitary group (SU) symmetry, which contains quarks as its most fundamental building blocks.

It has long been known that each conserved quantum number originates from some symmetry, and symmetries can be represented in terms of groups of transformations such as rotations. Such transformations naturally order particles into families called multiplets, which have the same mass, spin, and parity but may differ in other quantum numbers, such as isospin (which relates to electric charge) and strangeness. For example, the neutron is the electrically neutral companion of protons in nuclei. Its mass differs from that of the proton by only 1.6 percent. If this tiny mass difference is ignored, the neutron and proton may be considered as two charge (or isospin) states of a doublet, called the nucleon. Similarly, the three charge states of the pion—π+, π-, and π0—form a triplet. The strong interaction treats alike members of these particle families, or multiplets, and conserves isospin.

American physicist Murray Gell-Mann paved the way from isospin invariance toward the larger SU symmetry that provides the analogue of a periodic table for hadrons. As often happens in science when the time is right, several of his discoveries were also made independently by others, but Gell-Mann alone was involved in practically every important aspect. The proton, neutron, and six other baryons of the same 1/2 spin and parity as the nucleon sit in an octet, a type of multiplet, in which six particles are at the corners of a hexagon and the other two particles are at the center. Each particle is labeled by its strangeness (which is 0 for the top row, -1 for the next, and -2 for the last row) and electric charge (or isospin). The mesons are also arranged in similar octet patterns, one octet for each meson spin and parity. The δ (delta resonance), the first excited state of the nucleon, is part of a collection of ten particles called a decuplet or decimet that can be arranged in a triangular pattern, of which only the four δ-charge states in its top row were known in 1961. The Ω-, an omega baryon, sits at its bottom tip, and its decay, mass, and spin were correctly predicted by Gell-Mann even before its discovery in 1964. Since the completion of the decuplet, the SU symmetry has become generally accepted. The particles in the octets have only roughly the same mass, so the symmetry is only approximate, or broken. Gell-Mann dubbed the organization of baryons and mesons into octets "the eightfold way," after the prominent role of its octet.

The simplest multiplet of SU is a triangle containing three particles called quarks, one at each corner, from which the octet and all others can be obtained by a generalized multiplication rule. The product of three quarks generates the octet and decuplet, while a quark and antiquark give the octet for mesons; by extension, baryons consist of three quarks, and mesons consist of a quark-antiquark pair. Due to a phenomenon called color confinement, quarks cannot be isolated from hadrons; when a quark is knocked free from a hadron in an experimental setting, it breaks into fragments, which then group together to form new hadrons. Nevertheless, the quark model of the hadron, developed in the mid-1960s, rather successfully describes mesons, baryons, and their excited states as composed of quarks. It explains their magnetism and other properties in terms of a few adjusted parameters, such as the quark masses.

There are six different types, or flavors, of quark, based on their quantum numbers: up, down, strange, charm, bottom, and top. They are usually discussed as pairs: up and down (part of the first generation of fermions), strange and charm (second generation), and bottom and top (third generation). Only up and down quarks occur naturally in a stable state; the rest are only produced by high-energy collisions. Protons consist of two up quarks and one down quark, while neutrons are made of two down quarks and one up quark. The existence of up, down, and strange quarks was confirmed by experiments performed at Stanford University in 1968; the existence and properties of the charm, bottom, and top quarks were predicted prior to their discovery, in 1974, 1977, and 1995, respectively. Each flavor of quark has a corresponding antiparticle, or antiquark, defined as having the same properties as the quark but with the opposite electrical charge.

Isospin invariance requires equal up and down quark masses, while the strange quark is much heavier, thus breaking the SU flavor symmetry. When the 1/2 spin of quarks is incorporated into the SU flavor symmetry, the static SU symmetry results, which has led to a number of successful predictions in strong, electromagnetic, and weak interactions, such as predicting the magnetism of the neutron from that of the proton.

A profound problem in the quark model showed up early and was solved in the 1960s, but the solution was not generally accepted then. Wolfgang Pauli's exclusion principle forbids the presence of two electrons of the same spin orientation at the same place and time. This principle was discovered in atomic physics in the 1920s and is vital for understanding the periodic table of chemical elements. It also applies to quarks. Yet the doubly charged Δ ++ is composed of three up quarks in the same place, in violation of the exclusion principle. Such a phenomenon would be impossible unless quarks had another property to distinguish them. This new property is called color charge, or simply color, and there are three colors for each flavor of quark. The concept of color charge also explains the decay of the neutral pion into two photons; the quark that emits the photons had to be counted three times to achieve agreement with the observed pion decay rate, as if each quark came in three colors. More evidence for three colors came when the electroweak gauge theory was shown to unify quantum electrodynamics (QED) and the weak interaction.

The concept of a gauge theory is closely connected with symmetry. Consider isospin invariance. It is a global symmetry. If the convention regarding which of the nucleon states is a proton were to change, it would change everywhere in space and time, as if a measuring device or gauge were changed. Global gauge invariance says that the size of the standard can be changed at will, but the results of measurements stay the same. In electrodynamics, local gauge invariance means that different changes are allowed at each location and time, but in such a way that the charge of particles stays conserved. Similarly, changes in local gauge symmetry can occur only if they are compensated by the electromagnetic force, so that the charge remains conserved everywhere. In this sense, the gauge principle requires and generates the electromagnetic forces; it drives the dynamics. For isospin, the analogous gauge invariance, introduced in 1954 by Chen Ning Yang and Robert L. Mills, is called Yang-Mills gauge theory.

It was also natural, then, to describe the strong force as a Yang-Mills gauge theory based on the SU color symmetry and carried by an octet of massless spin 1 particles called gluons, strong interaction analogues of the photon of QED. This theory is called quantum chromodynamics (QCD) because of the role color plays in it, chromo- being derived from the Greek word for color.

QCD sheds more light on the quark confinement puzzle. Between 1967 and 1973 at Stanford University, high-energy electron-scattering experiments were performed on protons. A surprisingly large number of backward-scattered electrons were observed, recalling Ernest Rutherford's helium-scattering experiment in 1911, in which the unexpected backward scattering of helium ions revealed the nucleus as the tiny but massive center of atoms. Similarly, deeply probing electron scattering reveals quarks as hard nuggets inside protons that behave as if they were free at high energy. This puzzling behavior was cleared up in 1973, when several theorists pointed out that in Yang-Mills gauge theories such as QCD, the interaction at high energy becomes weak when the distances between particles become small. This unusual property, called asymptotic freedom, means that a quark feels almost no interaction at high energy; that is, it is isolated when it is close to others. In this sense, quarks of QCD have been seen almost as clearly as electrons have been seen at large distances, at which their electromagnetic interactions are weak. On the other hand, the strong interaction grows with the distance between quarks, binding them to each other ever more tightly, so that they stay permanently confined inside color-neutral hadrons at low energy.

Nevertheless, quarks were still considered merely mnemonic mathematical entities until 1974. At that time, the same unexpectedly sharp peak was found in electron experiments in Stanford University and in electron-positron production in hadronic collisions at Brookhaven National Laboratory. This discovery electrified the high-energy physics community. The peak, called charmonium, was quickly recognized as a new vector meson of spin 1, similar to the photon with a preferred direction in space, made up of a charmed quark-antiquark pair. The existence of the charmed quark was postulated earlier by theorists to explain the otherwise inexplicable suppression of certain reactions involving the weak interactions. This put quarks on the map as real particles, despite their fractional charges and confinement problem, as strong force partners of the leptons. Quarks came to be grouped with leptons such as the electron in one of the two main classes of elementary particles, fermions (the other class being bosons).

Several predictions from QCD at high energies and short distances have been verified by experiments, but QCD is a nonlinear theory. Just as linear equations are easy to solve, while quadratic, cubic, and higher powers are more difficult to handle, QCD is so complicated at long distances that it remains unsolved there. Nevertheless, many approximation methods and models have been developed that shed light on its low-energy regime. One is the large color limit, in which SU(NC) gauge theory is studied with NC colors. When NC becomes very large, such a theory has been shown to lead to meson dynamics and to baryons made up of a cloud of mesons. This provides a bridge to the conventional explanation of nuclear forces in terms of pion exchanges. Another approximation consists of formulating QCD on a four-dimensional lattice of points (for the three spatial dimensions plus time) and solving it numerically. Such lattice-gauge calculations have been carried out with increasing numbers of points and accuracy.

Applications

Albert Einstein spent half of his life in vain attempts to develop a single theory that would relate gravity and electrodynamics, just as electricity, magnetism, and light are related in electrodynamics. Although he did not succeed, the drive for such a "grand unification theory" has remained strong. When, between 1967 and 1971, the electromagnetic and weak forces were united in a gauge field theory, the excitement quickly led to a similar gauge theory for the strong force based on the SU color group. In the electroweak theory, there are still independent electric and weak charges; in this sense, both forces are not fully united. Quarks and leptons, however, are grouped together as fermions, which suggests a deeper unity among them.

In 1974, a gauge theory was proposed whose SU symmetry is big enough to contain the SU color gauge symmetry of the strong force, along with SU and U of the electroweak theory. Here, all charges are related to one another, and all forces except gravity are truly united; however, quarks and leptons are necessarily grouped together in multiplets, where gauge transformations change them into each other. This implies that when a down quark inside a proton changes into a positron, the proton decays. Hence, ordinary matter is no longer stable. Fortunately, the lifetime of protons is predicted to be much longer than the age of the universe. Unfortunately for the theory, SU grand unification predicts a proton lifetime one order of magnitude below the lower limit established by several experiments. Although this particular SU model is ruled out, the general idea of a grand unified gauge theory of the strong and electroweak forces is still thought to be correct and continues to play a role in big-bang cosmology.

High-energy physics and astrophysics become closely linked in cosmology in the twentieth century. Everyone knows from experience that the siren of an ambulance changes its pitch as it drives by. This change of pitch, called the Doppler effect, applies to all waves. Similarly, light from distant galaxies, systems of billions of stars like the Milky Way, shows this Doppler effect; when those galaxies move away from observers on Earth, its color is redshifted, meaning that the light waves reach the observers with lower frequency. This is precisely what Edwin Powell Hubble discovered in the 1920s. It appears that all galaxies are flying away from this one at high speeds that increase with distance, like fragments from a huge explosion (the big bang) at the beginning of the universe. According to big-bang cosmology, the universe began around fourteen billion years ago, caused by a primordial fireball that kept expanding and cooling down. More evidence for the big-bang cosmology came in 1965, when Arno A. Penzias and Robert W. Wilson discovered background radiation in the sky with a wavelength in the centimeter range (called microwave, similar to that generated in a microwave oven for cooking, but much less intense) that looks the same in all directions. It is interpreted as being left over from the big bang at a temperature of only 2.7 kelvins above absolute zero.

Gravity is thought to have become distinct from the other forces well within the first second after the birth of the universe. Shortly afterward and still within this fraction of a second, it became cool enough for the strong force to separate from the grand unified force. A little later, when the whole universe was about the size of a bowling ball, the electromagnetic and weak forces split apart, and leptons and quarks emerged as separate particles. At this stage in the early universe, it was still so hot that quarks and gluons formed a quark-gluon plasma, in which quarks roamed freely and had not yet condensed to form hadrons. (One of the main goals of scientists using heavy-ion accelerators at high energy is to generate such a quark-gluon plasma under controlled conditions in the laboratory, in order to study its properties and implications for the early universe.) As the universe continued to cool, protons and neutrons formed, along with the light nuclei up to helium—the beginning of nucleosynthesis. Heavier nuclei were produced in stars.

The remnant of a supernova explosion of a giant star of four or more solar masses is often a rotating neutron star or pulsar. Such stars have a radius of about ten kilometers, a crust of iron nuclei, and nuclear density in the main interior. The density in their core can be even higher than that inside a proton and may consist of unconfined quarks and strange matter. The minimal rotation period of neutron stars depends on the composition of the core, which is not yet well understood.

Cosmic rays no longer play an important role in the discovery of new particles, as they did in the early development of particle physics, when the positron, pion, and muon were discovered.

Context

For fifty years after Rutherford's discovery of the nucleus in 1911, protons and neutrons were believed to be pointlike elementary particles. The strong forces that hold atomic nuclei together were studied in terms of meson exchange dynamics, starting with Hideki Yukawa's pion exchange in 1935.

Particle physics branched out from nuclear physics in the 1950s, when the first mesons were discovered in cosmic rays. When numerous resonances were produced in nucleon-nucleon and pion-nucleon collisions, accelerators started to dominate: They have been the principal tool of experimental high-energy physics ever since, along with sophisticated particle-detector systems.

The successful QCD description of charmonium's hydrogen-like spectrum in the mid-1970s reinforced belief in QCD and in the electroweak gauge theory, which together form the standard model of particle physics. Nuclear and particle physics joined forces again in the 1980s in efforts to understand, solve, and test QCD at low energy and long distances.

Principal terms

ANTIQUARK: the antiparticle of a quark, which has the same properties as a quark except for its opposite electrical charge

ASYMPTOTIC FREEDOM: the phenomenon in which the strong interaction diminishes at short distances and high energies, in contrast to electrodynamics, in which the forces disappear at large distances between charges

BARYON: a strongly interacting particle, such as a proton, that is made up of three quarks

COLOR: the analogue of electric charge for the strong interaction; it has nothing to do with ordinary colors

FLAVOR: denotes the different kinds of quarks: up (u) and down (d), with fractional electric charges of 2/3 and -1/3 in units of the proton charge; charmed (c), with a charge of 2/3; strange (s), with a charge of -1/3; top (t), with a charge of 2/3; and bottom (b), with a charge of -1/3

GAUGE TRANSFORMATION: changes the gluon and quark fields consistently at each point in space and time so that their motion stays unchanged

GLUON: an analogue of the photon, the quantum of light, for the strong interaction; is the carrier of the strong force over short distances and at high energies, has a spin of 1, comes in eight colors, and is massless

HADRON: any strongly interacting particle

MESON: a strongly interacting particle made up of a quark and an antiquark

PI-MESON: the lightest of all strongly interacting particles, also called the pion, which comes in three charge states (π+, π0, π-) and is a carrier of nuclear forces

QUARKS: elementary constituents of protons, neutrons, and other hadrons that come in three colors and have a fractional charge of 2/3 or -1/3 and a spin of 1/2

Bibliography

Cheng, Ta-Pei, and Li, Ling-Fong, eds. Gauge Invariance. College Park: Amer. Assn. of Physics Teachers, 1990. Print. A collection of articles on the strong interaction, asymptotic freedom, and unified gauge theories by leaders of the field.

Crease, Robert P., and Charles C. Mann. The Second Creation. New York: Macmillan, 1982. Print. The development of particle and nuclear physics is described by many of the main participants in interviews with authors, making a lively story.

Fujikage, Haruki, and Kyou Hyobanshi, eds. Recent Advances in Quarks Research. New York: Nova, 2013. Print.

Greenberg, O. Wallace, ed. Quarks. College Park: Amer. Assn. of Physics Teachers, 1986. Print. Contains articles relating to the development of quark model ideas, quarks as constituents of hadrons, quarks as partons, permanent quark and color confinement, possible quark compositeness, and astrophysical and cosmological implications of quarks.

Liss, Tony M., and Paul L. Tipton. "The Discovery of the Top Quark." Scientific American Sept. 1997: 54–59. Print.

Pagels, Heinz. The Cosmic Code. Toronto: Bantam, 1982. Print. This book for the general public describes the environment of particle physics and some of its history.

Pais, Abraham. Inward Bound. Oxford: Clarendon, 1986. Print. A fascinating historical account of the development of nuclear and particle physics in the twentieth century. This in-depth description, which includes quarks, the strong interaction, and nuclear forces, is often but not always nontechnical.

Quigg, Chris. Gauge Theories of the Strong, Weak, and Electromagnetic Interactions. 2nd ed. Princeton: Princeton UP, 2013. Print.

Riordan, Michael. The Hunting of the Quark. New York: Simon, 1987. Print. A lively and accessible story of the development of the strong force and the discovery of quarks and their properties.

Satz, Helmut. "Quark Matter and Nuclear Collisions: A Brief History of Strong Interaction Thermodynamics." International Journal of Modern Physics E 21.8 (2012): n. pag. Web. 10 Dec. 2013.

Segre, Emilio. From X-Rays to Quarks. San Francisco: Freeman, 1976. Print. Covers roughly the same period and material as Pais's book (cited above), but is easier to read and much less detailed.

Weinberg, Steven. The First Three Minutes. New York: Basic, 1977. Print. A nontechnical description of big bang cosmology.

Elementary particles: fermions

Quark composition of protons and neutrons

Examples of radiation penetration of matter

Grand Unification Theories and Supersymmetry

Group Theory and Elementary Particles

Leptons and the Weak Interaction

Thermonuclear Reactions in Stars

The Unification of the Weak and Electromagnetic Interactions