Baryons

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

Field of study: Systematics (particle physics)

Baryons are one of the two subgroups of hadrons, which are particles that experience the strong force. The two best-known baryons are the nucleons, the proton and the neutron, which compose the bulk of all matter in the universe. Baryons are not fundamental but are composed of other particles.

Overview

Baryons and mesons are the two subgroups of hadrons, a type of particle that experiences the strong force. The two best-known baryons are the nucleons: the proton and the neutron. Baryons, which are composed of particles called quarks, include other, less stable particles of half-integer spin that are heavier than the nucleons, such as the hyperons, which are considered strange because they contain at least one strange quark, and the more massive charmed baryons, which are baryons containing at least one charm quark. Baryons participate in all the interactions: gravitational, electromagnetic, weak, and strong. The atomic nucleus consists of protons and neutrons, and thus, at least over some range of distance, the interaction between two nucleons must be attractive. The measured systematics of the nuclear charge radii show that they grow with the cube root of the number of nucleons. This is how a bag of marbles grows, which suggests that nucleons do not overlap and that they must repel each other at close distances. The fact that nuclei's binding energy per nucleon peaks and begins to decrease at isotopes of iron suggests a saturation of the nuclear force. This is an indication of the finite range of the nuclear force.

Experiments at Stanford University on high-energy electron scattering by nucleons in the late 1960s demonstrated that the central nucleon core contains three objects, now known to be quarks, that behave at high energies as if they were free and massless. Jerome I. Friedman, Henry W. Kendell, and Richard E. Taylor received the 1990 Nobel Prize in Physics for this work. The strong forces between constituent quarks result in the comparatively weak nuclear forces. Quarks that are close together feel almost no effects from the strong force, while quarks that are far apart feel an ever-increasing attraction and cannot be separated by a finite amount of energy. This is called quark confinement and is the reason that free quarks have never been observed.

In 1935, the first understanding of the size of the atomic nucleus came with Hideki Yukawa's meson theory of the nuclear force. He based his theory on an analogy to the Coulomb force between charged particles. The electric force is mediated by the exchange of virtual photons between charged particles and has infinite range because the photon has no mass.

It is believed that all forces arise from an exchange of virtual bosons. They are virtual, not real, just as an image in a mirror is not a real image that can be projected onto a screen. Virtual bosons can be observed only as forces affecting quantum fields, not directly as individual particles. Due to Heisenberg's uncertainty principle, they can be created without violating the conservation of energy if they exist for only a short time.

Yukawa postulated that a new meson field, the pion field, provides the finite-range force between the nucleons. The long-range part of the interaction is caused by the exchange of a virtual pion between the two nucleons, which creates an attractive force between them. At closer range, the force is still attractive, but this is caused by the exchange of heavier mesons and pairs of pions. At very close range, the interaction becomes very repulsive, as if there were a hard core inside each nucleon.

The quark model of the internal structure of hadrons was introduced by Murray Gell-Mann and George Zweig in 1964. Three quark flavors were enough to explain the observed baryons and mesons: up (u), down (d), and strange (s). Experimental evidence of new particles led to the addition of three new flavors: charmed (c), bottom (b), and top (t). The existence of the top quark was only hypothetical until 1995, when it was verified experimentally. A hadron can be built out of quarks in two ways. The combination of three quarks gives rise to a baryon (and three antiquarks form an antibaryon, such as the antiproton); a quark-antiquark pair bound together forms a meson. A baryon has a baryon number (B) of 1, while an antibaryon has a baryon number of -1. A baryon number is the approximate net quantum number of a system; because baryon numbers were defined before the establishment of the quark model, all quarks have a baryon number of 1/3, while antiquarks have a baryon number of -1/3. Mesons have a baryon number of 0, because the quark and antiquark cancel each other out.

In the theory of the strong force, the analogue of the electric charge found in the electromagnetic interaction is called color. This has nothing to do with the colors of the visible spectrum; it was chosen because of the simple way in which it can be used to express the required rules. All allowed combinations of quarks that form hadrons must be "white" or colorless. The quarks then have one of the additive primary colors: red, green, or blue. Antiquarks have complementary colors: cyan, magenta, or yellow. Colorless baryons are created from a combination of three quarks (or three antiquarks), each with one of the primary (or complementary) colors. Alternatively, one can derive colorless mesons from a quark-antiquark pair in a primary-complementary combination. The theory, which is modeled on the electromagnetic theory known as quantum electrodynamics (QED), is called quantum chromodynamics (QCD) and is the source of the alternative name for quark confinement: color confinement.

The model of the vacuum in modern field theories indicates that rather than being empty, it is filled with virtual particle-antiparticle pairs and exerts a pressure on "bubbles" or "bags." These bags are filled with three colored quarks and are surrounded by a cloud of virtual mesons, forming a baryon. The pressure of the vacuum keeps the bag from expanding. Inside the core region, the nearly massless quarks move almost freely, with only slight interactions. This is known as asymptotic freedom. The bag is surrounded by the larger external region in which pions and other mesons exist. In this model, a nearly perfect symmetry called chiral symmetry plays a crucial role. In QCD, if the masses of the u and d quarks are ignored, chiral invariance results from the fact that the equations of motion for the quark conserve its helicity, or handedness (left or right).

Applications

Most of the mass of an atom is in its nucleus. Nuclei are composed of protons and neutrons. The forces that hold the proton and neutron together, as well as the forces that bind them in a nucleus, are difficult to understand and explain. One way to study a physical system is to determine how it responds to stress or stimulation. For nucleons, this is accomplished by looking at unstable baryons, which can be formed in high-energy nuclear-scattering reactions.

Unstable baryons live for a relatively short period of time before they decay into protons, neutrons, and other particles. There are several baryons that are considered to be excited states of nucleons (N*) and are made up of the same quarks as the nucleons. Others, such as the δ (delta)-isobars, are quasi-bound states of the pion and nucleon. These are observed as resonances in the pion-nucleon cross section that are assigned to the list of baryons even though they exist for only 10^-23 seconds or so. From the spectrum of the excited states of the nucleons and delta-isobars, one can learn about the details of the interaction between quarks and aspects of the nuclear force.

The excited states of a nucleon made of three quarks result in a much simpler picture than those of conventional three-body systems. Because of quark confinement, there is no complicated continuum in this spectrum as there is in conventional systems. The lightest N* has a rest mass nearly 3/2 heavier than that of the proton (m_p), while the lightest delta-isobar is about 5/4 m_p. The nucleons are made of three 1/2-spin quarks, in states of angular momentum equal to zero, coupled to give a total nucleon spin of 1/2. The delta-isobar is made of three quarks coupled to give a total nucleon spin of 3/2. In models, one can attribute nearly all the mass difference to a one-gluon-exchange spin-spin interaction.

The size of the nucleon can be understood in this model. Since pions couple only to u and d quarks (and antiquarks), the pion cloud couples more strongly to the nucleons than to the strange baryons. The pion cloud exerts a pressure on the internal confinement region, and because this pressure is greater for nucleons than for other baryons, it tends to make the nucleons smaller than the other baryons.

In the model of coupling a pion cloud to a quark bag, it is straightforward to derive the force between baryons. The intermediate-range attraction, which is partially responsible for the stability of nuclei, comes from the exchange of a two-pion system, with relative angular momentum between them equal to zero. Vector mesons consist of two or three pions and give the strong repulsive force at short distances. Quark bags in nuclei do not move freely because the highly repulsive interaction arising from the vector-meson exchange keeps them apart. This repulsion between quark bags may be the reason that the quark substructure of the nucleon seems to have so little direct influence in nuclear-physics phenomena. Traditional explanations, which assume nucleons to be fundamental particles that exchange fundamental mesons, are able to explain most of nuclear structure and nuclear reactions over a large range of energies. Thus, finding quark effects in the nuclear properties of the simplest nucleus, the deuteron (the bound state of a neutron and proton), is extremely difficult.

It was expected that in proceeding to higher energies, the core regions of the two nucleons would push over the barriers and begin to overlap, a phenomenon known as nucleon-nucleon short-range correlation. In the early 2000s, experiments at two relatively new particle accelerators were conducted to test this theory. One experiment, at the Thomas Jefferson National Accelerator Facility in Virginia, showed that this correlation does occur for short periods of time, mainly between one proton and one neutron, though a small fraction of correlated pairs were composed of two protons. The density of these pairs is approximately five times that of ordinary nucleons, which may have implications for the study of neutron stars and other dense nuclear systems. The other experiment was performed at the Relativistic Heavy Ion Collider (RHIC), the world's first particle accelerator capable of colliding heavy ions, located at Brookhaven National Laboratory on Long Island, New York. By colliding two heavy gold nuclei, scientists at the RHIC hoped to separate the nucleons into the quark-gluon plasma that was present in the early stages of the universe. Rather than producing the gaseous plasma they expected, however, the experiment resulted in what the scientists described as a "perfect" liquid, so called because it exhibited virtually no viscosity or frictional resistance. While it took a different form than expected, this liquid was hot enough—approximately four trillion degrees Celsius—to be the sought-after quark-gluon plasma.

One of the major questions in physics is why the universe has more matter than antimatter. According to the CPT (charge conjugation, parity transformation, time reversal) theorem, matter and antimatter should be symmetrical, and indeed particles and their antiparticles are identical, the only difference being that they have opposite charges. As a result, the relative scarcity of antimatter presents a problem for physicists. One solution is baryogenesis, the hypothetical process by which the amount of antimatter present in the early universe was significantly reduced. While various theories of baryogenesis exist, the common feature to all is the assumption that at some point in the early universe, shortly after the big bang and prior to nucleosynthesis, some event took place that created an imbalance in the ratio of baryons to antibaryons. This imbalance may have initially been very small, as little as 10¹⁰ + 1 particles for every 10¹⁰ antiparticles; as long as there were more baryons than antibaryons, the two could have annihilated each other and still left sufficient baryons afterward to create the universe. If this imbalance did not exist, matter and antimatter would have canceled each other out and the universe as we know it would not have formed. In 1967, Andrei Sakharov proposed three necessary conditions, now known as the Sakharov conditions, for baryogenesis: baryon number violation, violation of C and CP symmetries, and the upset of thermal equilibrium.

Another application of baryons to cosmology is the phenomenon of baryon acoustic oscillations, in which acoustic waves that were present in the early universe continue to cause regular fluctuations in baryonic matter. These waves were initially caused by the interaction of gravity and pressure within the primordial quark-gluon plasma, in overdense areas consisting of baryons, photons, and dark matter. The baryons and photons moved away from the overdensities and then decoupled, allowing the photons to continue to disperse while the baryons remained in place, at a radius known as the sound horizon. The cosmic microwave background radiation—the same photons that decoupled from the baryons—allows cosmologists to determine the original size of this sound horizon; by comparing it to the sound horizon today, they can measure the acceleration of the expansion of the universe.

Context

In atomic physics, in order to calculate the electromagnetic molecular forces between two electrically neutral hydrogen atoms (H), it is necessary to know some of the properties of the atomic structure and the forces among its constituent particles—that is, the electron and the proton. Only then can one calculate the scattering of two hydrogen atoms, deduce an effective H-H force, and calculate the binding energy of the hydrogen molecule H₂. Similarly, in order to understand the nuclear force between two nucleons at short distances, one must have a good quark model that explains the properties of the nucleons and the excited baryon states.

In the atomic shell model of electron orbits and the nuclear physics shell model of nucleon orbits in the nucleus, one finds splitting of orbits from an interaction between the spin of the particle and its orbital angular momentum (spin-orbit interaction). For quarks, this interaction is very small, but the force of attraction between quarks becomes larger as they separate.

Any distribution of electric charges and currents produces electric and magnetic fields that vary with the distance from the location of the charges and currents in a characteristic fashion. For example, a current loop gives a magnetic dipole moment that is similar to a permanent bar magnet. One of the best achievements of theoretical physics is the explanation of the magnetic moment of the electron by the Dirac equation (formulated by Paul Adrien Maurice Dirac) and corrections found in QED. The fact that the anomalous magnetic moments of the proton and the neutron could not be explained in a similar way was an early indication that they were not fundamental. Early models presumed that this effect was caused by the meson cloud. With the advent of the quark model, the effect was then attributed to quarks. Looking at the effect for other baryons makes it clear that the situation is about halfway between these two pictures.

The electron and proton were known to exist early in the twentieth century. Ernest Rutherford showed in 1911 that most of the mass of atoms must be located in a small central region known as the nucleus. Neutrons were discovered by James Chadwick in 1932. The delta-isobars were discovered in the early 1950s, soon after the discovery of the pion by Cecil Frank Powell in cosmic-ray studies. The first strange baryon, the lambda baryon, was observed in 1947 by G. D. Rochester and C. C. Butler, also in cosmic-ray studies. Owen Chamberlain, Emilio Gino Segre, and others produced the first antiprotons in 1955. The first charmed baryons were observed in 1975 by E. Gazzoli and colleagues at the Brookhaven National Laboratory.

Principal terms

ASYMPTOTIC FREEDOM: a feature of quark theory in which interactions between quarks become weaker at shorter distances or higher momenta

BINDING ENERGY: a measure of the energy of attraction for constituents of a bound system; the sum of the rest mass energies (E = mc²) of the components of the system minus the mass energy of the system is positive for bound systems

CHIRAL SYMMETRY: a symmetry associated with massless fermions in which their helicity is conserved

COUPLING CONSTANT: a number that determines the strength of an interaction between two particles; the range over which the interaction takes place is given by the mass of the virtual boson that is exchanged between them

HADRON: any particle that participates in the strong interaction; comprises baryons, which obey the Pauli exclusion principle, and mesons, which do not

HELICITY: the handedness (left-handed or right-handed) of a particle, which is determined by how it spins with respect to the direction of its momentum

PAULI EXCLUSION PRINCIPLE: the principle that no two particles of the same type can occupy precisely the same quantum state; obeyed by baryons, leptons, and quarks, but not by photons, mesons, or gluons

QUANTUM CHROMODYNAMICS (QCD): the theory of the strong interaction that has colored gluons and quarks as fundamental components

SPIN: a fundamental property of particles that describes the state of rotation of the particle; particles whose spin is a whole number are called bosons, while those whose spin is half of a whole number are called fermions

STRANGE QUARK: a massive quark that is a constituent of hyperons

Bibliography

Brown, Gerald E., and Mannque Rho. "The Structure of the Nucleon." Physics Today 36.2 (1983): 24–32. Print. Although this review of the nuclear physicists' view of the nucleon is too advanced in some spots, it is well worth skimming through the details in order to find many well-written descriptions of the then-modern view of quarks in nuclear physics.

Carrigan, Richard A., Jr., and W. Peter Trower, eds. Particle Physics in the Cosmos. New York: Freeman, 1989. Print. These twelve articles from Scientific American show the connection between subatomic particles and the structure of the universe.

Carrigan, Richard A., Jr., and W. Peter Trower, eds. Particles and Forces: At the Heart of Matter. New York: Freeman, 1990. Print. These twelve Scientific American articles have excellent graphics, added postscripts, and notes. Several of the authors are Nobel Prize winners. This volume contains good explanations of the quark model, color, and chirality.

Chaichian, Masud, Hugo Perez Rojas, and Anca Tureanu. Basic Concepts in Physics: From the Cosmos to Quarks. Heidelberg: Springer, 2014. Print.

Close, Frank E. An Introduction to Quarks and Partons. London: Academic, 1979. Print. This is a good textbook with a fine explanation of the various symmetries in particle physics.

Gorbunov, Dmitry S., and Valery A. Rubakov. Introduction to the Theory of the Early Universe: Hot Big Bang Theory. Singapore: World Scientific, 2011. Print.

Krane, Kenneth S. Introductory Nuclear Physics. New York: Wiley, 1987. Print. This textbook for physics undergraduate students has a nice presentation of nuclear and particle physics. Although it is somewhat technical, the reader should follow the discussion and figures. Contains a good visual presentation of the symmetry of the quark model.

Riotto, Antonio. "Theories of Baryogenesis." CERN Document Server. CERN, 24 July 1998. Web. 8 Jan. 2014.

Subedi, R., et al. "Probing Cold Dense Nuclear Matter." Science 320.5882 (2008): 1476–77. Print.

Thomson, Mark. Modern Particle Physics. New York: Cambridge UP, 2013. Print.

Electrons and Atoms

Grand Unification Theories and Supersymmetry

Quarks and the Strong Interaction