pions

(also pi-mesons, π-mesons), a group of three unstable elementary particles—two charged (π⁺ and π^–) and one neutral (π⁰). They belong to the class of strongly interacting particles, or hadrons, and are the lightest of the class. Pions are approximately one-seventh as heavy as protons and 270 times heavier than electrons. Since they have a mass intermediate between the masses of the proton and the electron, they were given the name “mesons,” a term that derives from a Greek word meaning “middle” or “intermediate.” Pions have zero spin and consequently are bosons—that is, they obey Bose-Einstein statistics. Pions are quanta of the field of nuclear forces that, in particular, bind nucleons in atomic nuclei.

Basic properties and quantum numbers. Pions take part in all known types of interactions between elementary particles: strong, electromagnetic, weak, and gravitational interactions. As with other elementary particles, the gravitational interaction of pions is extremely small and has not been studied. Weak interactions are responsible for the instability of charged pions, which decay primarily into a muon (μ) and a muon neutrino (v_μ) or antineutrino (v_μ):

π⁺ → μ⁺ + ν_μ π^–→μ^–+ν̄_μ

The neutral pion π° decays through the electromagnetic interaction preferentially into two photons: π⁰ → γ + γ.

The electric charge Q of pions in units of the elementary charge e is equal to +1 for π⁺, –1 for π^–, and 0 for π⁰. The intrinsic parity of pions is odd: P = – 1. Since they have spin J = 0 and P = – 1, they are pseudoscalar particles. The baryon charge B and the strangeness S of pions are equal to zero. The pions π⁺ and π^– form a particle-antiparticle pair; their lifetimes τ and masses m are therefore the same:

τ_π⁺ = τ_π^– = (2.6024 ± 0.0024) × 10^–8 sec

m_π⁺ = m_π^–

= (139.5688 ± 0.0064) megaelectron volts (MeV)/c²

≈ 264 m_e

where m_e is the mass of an electron and c is the speed of light. The neutral pion π⁰ is identical to its antiparticle—that is, it is an absolutely neutral particle—and has even charge parity: c = +1. The lifetime and mass of π⁰ are

τ_π⁰ = (0.84 ± 0.10) × 10^–16 sec

m_π⁰ = (134.9645 ± 0.0074)MeV/c² ≈ 273 m_e

Pions have an isotopic spin I = 1 and therefore form an isotopic triplet: the three charge states of pions (π⁺, π⁰, and π^-) correspond to the three possible projections of isotopic spin I₃ = -1-1,0, –1. In the classification scheme for hadrons, pions are united with the η-meson and kaons (K⁺, K^–, K⁰, K̄⁰) in the octet of pseudoscalar mesons. The generalized charge parity (G-parity) of pions is odd: G = –1.

The laws of conservation of quantum numbers impose certain prohibitions on various reactions involving pions. For example, the reaction π + π → π + π + π cannot occur through the strong interaction, in which C-parity is conserved. Another example is the impossibility for a neutral pion to decay into an odd number of photons, a situation due to the conservation of charge parity in the electromagnetic interactions: the photon has odd charge parity. The C-parity and the G-parity of a system of particles are equal to the product of the corresponding parities of the particles making up the system.

Pions interact strongly with atomic nuclei—causing, in particular, splitting of the nuclei. The mean free path of pions in a substance before a nuclear interaction occurs depends on the pions’ energy and is, for example, in graphite about 13 cm for π^–-mesons with an energy of 200 MeV and about 30 cm when the energy is 3 gigaelectron volts (GeV). At energies below 50 MeV the path length of charged pions in matter is determined primarily by the energy losses owing to ionization of the atoms, with the result that the pions lose speed and usually do not manage to interact with the nuclei before coming to a stop. Thus, for a π⁺- or π^–-meson with an energy of 15 MeV, the path length in a nuclear photographic emulsion is equal to approximately 4.7 mm. Here a π⁺-meson that has come to a stop decays into a positive muon and a neutrino (Figure 1); a π^–-meson, however, is captured by the closest atom, with which it forms a mesonic atom. The ensuing nuclear capture of the π^– -meson occurs from the mesonic atom orbits and results in the splitting of the nucleus.

Figure 1. Photograph of one of the first cases of the decay π⁺ → μ⁺ + γ_μ recorded in a nuclear photographic emulsion

Pions largely determine the composition of cosmic rays within the earth’s atmosphere. As the main products of the nuclear interactions of the particles of primary cosmic radiation (protons and heavier nuclei) with the nuclei of atoms of the atmosphere, pions are part of the nuclear-active component of cosmic rays. On decaying, π⁺ - and π^–-mesons create the penetrating component (high-energy muons and neutrinos) of cosmic radiation, and π⁰-mesons create the electron-photon component.

Discovery. The hypothesis of the existence of pions as the carriers of nuclear forces was advanced in 1935 by the Japanese physicist H. Yukawa to explain the short-range character and large magnitude of nuclear forces. It followed from the uncertainty principle for energy and time that if the forces acting between nucleons (protons and neutrons) in the nucleus are due to the exchange of quanta of the field of nuclear forces, then the mass of these quanta—later named π-mesons—should be about 200-300 electron masses. Particles of approximately this mass were detected in cosmic rays in 1936 and 1937, but they lacked the properties of the particles predicted by Yukawa. The search for charged π-mesons was crowned with success only in 1947, when the British sientists C. Lattes, H. Muirhead, G. Oc-chialini, and C. F. Powell found particle tracks indicating the decay π⁺ → μ⁺ + ν_μ (see Figure 1) in nuclear emulsions exposed to cosmic rays at an altitude high above the earth’s surface. Charged pions were first produced under laboratory conditions in 1948 in an accelerator in Berkeley in the USA.

The existence of neutral pions followed from the experimentally detected charge independence of the nuclear forces: the interaction between identical nucleons—two protons or two neutrons—can be accomplished only by the exchange of neutral pions. Neutral pions were first detected experimentally in 1950 on the basis of the γ-quanta from their decay; they were produced in collisions of high-energy (about 330 MeV) photons and protons with nuclei. Having a rest mass m_π, pions require energy expenditures no smaller than their rest energy m_πc² for their formation, or “production.” Thus, for the reaction p + p → p + p + π⁰ to occur, the kinetic energy of the incipient proton p must exceed the threshold energy, which in a laboratory coordinate system is about 282 MeV. The threshold energy of pion formation is smaller for heavy nuclei than for protons and is close to m_πc².

Sources. As indicated above, cosmic rays are one of the most important sources of pions in nature. Pions are produced in the upper layers of the atmosphere under the action of the primary component of cosmic rays, but because of nuclear absorption and decay only an insignificant fraction of them reach sea level. Important data on pions and pion interactions have been obtained through investigations of cosmic rays at high-altitude stations and by means of equipment sent into the upper layers of the atmosphere and into outer space.

Quantitative study of the properties of pions, however, is carried out primarily with beams of high-energy particles produced in proton and electron accelerators. Accelerators have been used to establish the quantum numbers of pions; to make accurate measurements of masses, lifetimes, and rare modes of decay; and to carry out a detailed study of the reactions induced by pions. Present-day accelerators create high-energy (tens of GeV) pion beams with fluxes of ~ 10⁷ pions/sec. Meson factories, or high-current accelerators with an energy of ~ 1 GeV, should produce fluxes of up to 10¹⁰ pions/sec. Beams of fast charged pions, which travel tens and hundreds of meters before decaying, are usually transported through special vacuum channels to the place where the properties and interactions of the particles are studied. A schematic of a unit for producing and investigating π^–-mesons is given in Figure 2.

Figure 2. Schematic of a typical unit for studying the interaction of π^– -mesons with protons. Protons accelerated to an energy of 600 MeV strike the beryllium target (1) located within the acceleration chamber. The π^–-mesons formed are removed from the acceleration chamber through the special aperture (2); after passing through the collimator (3), the deflecting magnetic field (magnet 4), and the pion flux counters (5), they move on to the liquid-hydrogen target (6). The products of the interaction of the π-mesons with the hydrogen nuclei are recorded by the scintillation-counter telescopes (7): (a) counters, (b) absorbers.

Accelerator-generated π^–-meson beams are coming into use in radio therapy. The decay products of pions—muons, neutrinos, photons, electrons, and positrons—are used to study weak and electromagnetic interactions.

Interactions. The interaction most specific to pions is the strong interaction, which is characterized by maximum symmetry (the largest number of laws of conservation is satisfied), a short range (≾ 10 “¹³ cm), and a large coupling constant g. Thus the dimensionless constant characterizing the binding of pions to nucleons, g²ℏc ≈ 14.6, is several thousand times greater than the dimensionless constant of the electromagnetic interaction,

α = e²/ℏc ≈ 1/137

where ℏ is Planck’s constant.

The processes of the strong interaction of pions include pion scattering by nucleons; pion production in collisions of hadrons; the annihilation of antinucleons and nucleons with the formation of pions; and the production by pions of strange particles, or kaons and hyperons. Inelastic interactions of hadrons at energies greater than 10⁹ electron volts (eV) are due primarily to processes of multiple pion production. In the low-energy region of 108-109eV, the formation of quasibound systems—excited states of mesons and baryons called resonances with a lifetime of 10^–22-10^–24 sec—is observed during the interaction of pions with other mesons and with baryons. These states can appear,

Figure 3. Dependence of the total cross sections σ̱ of the interaction of π⁺- and π^–-mesons with protons (p) on the total energy of the colliding particles in a center-of-mass system (E_c.m.)

for example, in the form of maxima in the energy dependence of total reaction cross sections (Figure 3).

Pions, like all hadrons, emit and absorb strongly interacting virtual particles or particle-antiparticle pairs. The radius of the cloud of virtual hadrons that is created in this manner and that surrounds the charged pions is approximately 0.7 × 10^–13 cm.

Among the electromagnetic interactions of pions, the processes of the production of π-mesons by photons and electrons have been studied most thoroughly. The decisive role of strong interactions is a specific feature of electromagnetic processes involving pions. Thus, the characteristic maximum in the energy dependence of the total cross section of the process e⁺ + e^– → π⁺ + π^– + π⁰ (Figure 4) is due to the resonance interaction in a system of three pions; the maximum corresponds to the rest energy of a ω-meson, which decays into three pions. The well-studied electromagnetic field serves as an effective tool for investigating the nature of π-mesons.

Figure 4. Dependence of the total cross section σ of the process e⁺ + e^– → π⁺ + π^– + π⁰ on the total energy (2E) of colliding beams of electrons (e^–) and positrons (e⁺)

The weak interaction plays an important role in the physics of π-mesons. It accounts for the instability of charged pions and for the decays of strange particles into pions. Study of the decays π → μ + ν, K → π + π, and K → π + π + π led to extremely important discoveries in physics. The neutrino formed as a result of the π-μ decay (ν_μ) was found to differ from the neutrino (ν_e) that arises during the beta decay of atomic nuclei. It was discovered that space parity (P) is not conserved in the weak interaction. In addition, the law of conservation of combined parity was found to be violated in the decays of long-lived neutral kaons (K⁰_L) into pions.

Role in nuclear and elementary-particle physics. The investigation of the processes of the interaction of pions with elementary particles and atomic nuclei has an important role in research on the nature of elementary particles and the structure of nuclei.

Since they have the smallest mass, pions occupy the most remote region in the cloud of virtual hadrons surrounding every strongly interacting particle. Pions therefore determine the peripheral part of strong interactions of elementary particles, in particular, the peripheral part of the nuclear forces, which is most important for nuclear theory. When the distances between hadrons are small, however, the nuclear forces are due primarily to the exchange of pion resonances.

The electromagnetic properties of hadrons—such as anomalous magnetic moment, polarizability, and the space distribution of electric charge—are determined primarily by the cloud of pions virtually emitted and absorbed by the hadrons. The resonance interactions of pions also play an important role here.

Finally, the effect of the strong interaction on the weak interaction is also determined largely by the π-meson field.

Scientists’ present conceptions of the nature of π-mesons are merely preliminary models. The mass of pions is generally assumed to be due to the strong interaction, and the difference in the masses of charged and neutral pions to the electromagnetic and weak interactions. The hypothesis of E. Fermi and Yang Chen Ning (1949) that the pion is a strongly coupled system with a binding energy of ~ 1,740 MeV and consisting of a nucleón and an antinucleon was of great heuristic importance. According to the quark model, pions are bound states of a quark and an antiquark. A consistent theory describing the π-meson field and its interactions with other fields, however, is lacking. Thus, the complicated problems of the nature and interactions of π-mesons are still not fully resolved.

The properties of pions and processes involving pions continue to be studied intensely in the principal laboratories of the world.