Pion

Pion

Discussion
Ask a question about 'Pion'
Start a new discussion about 'Pion'
Answer questions from other users
Full Discussion Forum
 
Encyclopedia
In particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

, a pion (short for pi meson, denoted with ) is any of three subatomic particle
Subatomic particle
In physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...

s: , , and . Pions are the lightest meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...

s and they play an important role in explaining the low-energy properties of the strong nuclear force.

Basic properties


Pions are meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...

s with zero spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

, and they are composed of first-generation
Generation (particle physics)
In particle physics, a generation is a division of the elementary particles. Between generations, particles differ by their quantum number and mass, but their interactions are identical....

 quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...

s. In the quark model
Quark model
In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons....

, an up quark
Up quark
The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...

 and an anti-down quark make up a , whereas a down quark
Down quark
The down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...

 and an anti-up quark make up the , and these are the antiparticle
Antiparticle
Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...

s of one another. The uncharged pions are combinations of an up quark with an anti-up quark or a down quark with an anti-down quark, have identical quantum number
Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...

s, and hence they are only found in superposition
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...

s. The lowest-energy superposition of these is the , which is its own antiparticle. Together, the pions form a triplet of isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...

. Each pion has isospin (I = 1) and third-component isospin equal to its charge
Gell-Mann–Nishijima formula
The Gell-Mann–Nishijima formula relates the baryon number B, the strangeness S, the isospin I3 of hadrons to the charge Q. It was originally given by Kazuhiko Nishijima and Tadao Nakano in 1953, and lead to the proposal of strangeness as a concept, which Nishijima originally called "eta-charge"...

 (Iz = +1, 0 or −1).

Charged pion decays



The mesons have a mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 of and a mean lifetime of . They decay due to the weak interaction. The primary decay mode of a pion, with probability 0.999877, is a purely lepton
Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...

ic decay into a anti-muon and a muon neutrino
Muon neutrino
The muon neutrino is a subatomic lepton elementary particle which has the symbol and no net electric charge. Together with the muon it forms the second generation of leptons, hence its name muon neutrino. It was first hypothesized in the early 1940s by several people, and was discovered in 1962 by...

:
+
+


The second most common decay mode of a pion, with probability 0.000123, is also a leptonic decay into an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

 and the corresponding electron neutrino
Electron neutrino
The electron neutrino is a subatomic lepton elementary particle which has no net electric charge. Together with the electron it forms the first generation of leptons, hence its name electron neutrino...

. This mode was discovered at CERN
CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...

 in 1958:
+
+


The suppression of the electronic mode, with respect to the muonic one, is given approximately (to within radiative corrections) by the ratio of the half-widths of the pion–electron and the pion–muon decay reactions:


and is a spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

 effect known as the helicity suppression. Measurements of the above ratio have been considered for decades to be tests of the V − A structure (vector minus axial vector or left-handed lagrangian
Lagrangian
The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...

) of the charged weak current
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

 and of lepton universality. Experimentally this ratio is .

Besides the purely leptonic decays of pions, also observed have been some structure-dependent radiative leptonic decays, and also the very rare beta decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

 of pions (with probability of about 10−8) with a neutral pion as the final state.

Neutral pion decays


The meson has a slightly smaller mass of and a much shorter mean lifetime of . This pion decays in an electromagnetic force process. The main decay mode, with probability 0.98798, is into two photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s (two gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...

 photons in this case):
2


Its second most common decay mode, with probability 0.01198, is the Dalitz
Richard Dalitz
Richard Henry Dalitz was an Australian physicist known for his work in particle physics.Born Dimboola, Victoria near Melbourne, Dalitz studied physics and mathematics at Melbourne University before moving to the United Kingdom in 1946, starting his PhD research at the University of Cambridge...

 decay into a photon and an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

 pair:
+ +


The rate at which pions decay is a prominent quantity in many sub-fields of particle physics, such as chiral perturbation theory
Chiral perturbation theory
Chiral perturbation theory is an effective field theory constructed with a Lagrangian consistent with the chiral symmetry of quantum chromodynamics , as well as the other symmetries of parity and charge conjugation. ChPT is a theory which allows one to study the low-energy dynamics of QCD...

. This rate is parametrized by the pion decay constant
Pion decay constant
In particle physics, the pion decay constant is the square root of the coefficient in front of the kinetic term for the pion in the low-energy effective action. It is dimensionally an energy scale and it determines the strength of the chiral symmetry breaking...

 (ƒπ), which is about .
Pions
Particle name Particle
symbol
Antiparticle
symbol
Quark
content
Rest mass (MeV/c
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

2)
I
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...

G
JP
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...

C
C parity
In physics, C parity or charge parity is a multiplicative quantum number of some particles that describes its behavior under a symmetry operation of charge conjugation ....

S
Strangeness
In particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...

C B'
Bottomness
In physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a...

Mean lifetime (s
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

)
Commonly decays to

(>5% of decays)
Pion 139.570 18(35) 1 0 0 0 0
Pion Self 134.976 6 ± 0.000 6 1 0−+ 0 0 0

[a] Make-up inexact due to non-zero quark masses.

History


Theoretical work by Hideki Yukawa
Hideki Yukawa
né , was a Japanese theoretical physicist and the first Japanese Nobel laureate.-Biography:Yukawa was born in Tokyo and grew up in Kyoto. In 1929, after receiving his degree from Kyoto Imperial University, he stayed on as a lecturer for four years. After graduation, he was interested in...

 in 1935 had predicted the existence of meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...

s as the carrier particles of the strong nuclear force. From the range of the strong nuclear force (inferred from the radius of the atomic nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

), Yukawa predicted the existence of a particle having a mass of about 100 MeV. Initially after its discovery in 1936, the muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...

 (initially called the "mu meson") was thought to be this particle, since it has a mass of 106 MeV. However, later particle physics experiments showed that the muon did not participate in the strong nuclear interaction. In modern terminology, this makes the muon a lepton
Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...

, and not a true meson.

In 1947, the first true mesons, the charged pions, were found by the collaboration of Cecil Powell, César Lattes
César Lattes
Cesare Mansueto Giulio Lattes , also known as Cesar Lattes, was a Brazilian experimental physicist, one of the discoverers of the pion, a composite subatomic particle made of a quark and an antiquark.-Life:Lattes was born to a family of Italian Jewish immigrants in Curitiba, Southern Brazil...

, Giuseppe Occhialini
Giuseppe Occhialini
Giuseppe Paolo Stanislao "Beppo" Occhialini ForMemRS was an Italian physicist, who contributed to the discovery of the pion or pi-meson decay in 1947, with César Lattes and Cecil Frank Powell . At the time of this discovery, they were all working at the H. H...

, et. al., at the University of Bristol
University of Bristol
The University of Bristol is a public research university located in Bristol, United Kingdom. One of the so-called "red brick" universities, it received its Royal Charter in 1909, although its predecessor institution, University College, Bristol, had been in existence since 1876.The University is...

, in England. Since the advent of particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s had not yet come, high-energy subatomic particles were only obtainable from atmospheric cosmic ray
Cosmic ray
Cosmic rays are energetic charged subatomic particles, originating from outer space. They may produce secondary particles that penetrate the Earth's atmosphere and surface. The term ray is historical as cosmic rays were thought to be electromagnetic radiation...

s. Photographic emulsion
Photographic emulsion
Photographic emulsion is a light-sensitive colloid, such as gelatin, coated onto a substrate. In silver-gelatin photography, the emulsion consists of silver halide crystals suspended in gelatin, and the substrate may be glass, plastic film, paper or fabric....

s, which used the gelatin-silver process
Gelatin-silver process
The gelatin silver process is the photographic process used with currently available black-and-white films and printing papers. A suspension of silver salts in gelatin is coated onto a support such as glass, flexible plastic or film, baryta paper, or resin-coated paper...

, were placed for long periods of time in sites located at high altitude mountains, first at Pic du Midi de Bigorre
Pic du Midi de Bigorre
The Pic du Midi de Bigorre or simply Pic du Midi is a mountain in the French Pyrenees famous for its astronomical observatory, the Observatoire du Pic du Midi de Bigorre , part of the Observatoire Midi-Pyrénées .-Pic du Midi Observatory:Construction of the observatory began in 1878 under the...

 in the Pyrenees
Pyrenees
The Pyrenees is a range of mountains in southwest Europe that forms a natural border between France and Spain...

, and later at Chacaltaya
Chacaltaya
Chacaltaya is a mountain in the Cordillera Real, one of the mountain ranges of the Cordillera Oriental, itself a range of the Bolivian Andes. Its elevation is . Chacaltaya's glacier - which was as old as 18,000 years – had in 1940 an area of , reduced to in 2007 and was completely gone by 2009....

 in the Andes Mountains, where they were impacted by cosmic rays.

After the development of the photographic plate
Photographic plate
Photographic plates preceded photographic film as a means of photography. A light-sensitive emulsion of silver salts was applied to a glass plate. This form of photographic material largely faded from the consumer market in the early years of the 20th century, as more convenient and less fragile...

s, microscopic
Microscope
A microscope is an instrument used to see objects that are too small for the naked eye. The science of investigating small objects using such an instrument is called microscopy...

 inspection of the emulsions revealed the tracks of charged subatomic particles. Pions were first identified by their unusual "double meson" tracks, which were left by their decay into another "meson". (It was actually the muon, which is not classified as a meson in modern particle physics.) In 1948, Lattes, Eugene Gardner, and their team first artificially produced pions at the University of California's cyclotron
Cyclotron
In technology, a cyclotron is a type of particle accelerator. In physics, the cyclotron frequency or gyrofrequency is the frequency of a charged particle moving perpendicularly to the direction of a uniform magnetic field, i.e. a magnetic field of constant magnitude and direction...

 in Berkeley, California
Berkeley, California
Berkeley is a city on the east shore of the San Francisco Bay in Northern California, United States. Its neighbors to the south are the cities of Oakland and Emeryville. To the north is the city of Albany and the unincorporated community of Kensington...

, by bombarding carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 atoms with high-speed alpha particle
Alpha particle
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus, which is classically produced in the process of alpha decay, but may be produced also in other ways and given the same name...

s. Further advanced theoretical work was carried out by Riazuddin, who in 1959, used the dispersion relation
Dispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....

 for Compton scattering
Compton scattering
In physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an X-ray or gamma ray photon, called the Compton effect...

 of virtual photons on pions to analyze their charge radius.

Nobel Prizes in Physics
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...

 were awarded to Yukawa in 1949 for his theoretical prediction of the existence of mesons, and to Cecil Powell in 1950 for developing and applying the technique of particle detection using photographic emulsion
Photographic emulsion
Photographic emulsion is a light-sensitive colloid, such as gelatin, coated onto a substrate. In silver-gelatin photography, the emulsion consists of silver halide crystals suspended in gelatin, and the substrate may be glass, plastic film, paper or fabric....

s.

Since the neutral pion is not electrically charged
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

, it is more difficult to detect and observe than the charged pions are. Neutral pions do not leave tracks in photographic emulsions, and neither do they in Wilson cloud chamber
Cloud chamber
The cloud chamber, also known as the Wilson chamber, is a particle detector used for detecting ionizing radiation. In its most basic form, a cloud chamber is a sealed environment containing a supersaturated vapor of water or alcohol. When a charged particle interacts with the mixture, it ionizes it...

s. The existence of the neutral pion was inferred from observing its decay products from cosmic ray
Cosmic ray
Cosmic rays are energetic charged subatomic particles, originating from outer space. They may produce secondary particles that penetrate the Earth's atmosphere and surface. The term ray is historical as cosmic rays were thought to be electromagnetic radiation...

s, a so-called "soft component" of slow electrons with photons. The was identified definitively at the University of California's cyclotron in 1950 by observing its decay into two photons . Later in the same year, they were also observed in cosmic-ray balloon experiments at Bristol University.

The pion also plays a role in cosmology by imposing an upper limit on the energies of cosmic rays through the Greisen–Zatsepin–Kuzmin limit
Greisen–Zatsepin–Kuzmin limit
The Greisen–Zatsepin–Kuzmin limit is a theoretical upper limit on the energy of cosmic rays coming from "distant" sources. The limit is 5×1019 eV, or about 8 joules. The limit is set by slowing-interactions of cosmic ray protons with the microwave background radiation over long distances...

.

In the modern understanding of the strong force interaction, called "quantum chromodynamics
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...

", pions are considered to be the pseudo Nambu-Goldstone boson
Goldstone boson
In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries...

s of spontaneously broken
Spontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....

 chiral symmetry
Chiral symmetry
In quantum field theory, chiral symmetry is a possible symmetry of the Lagrangian under which the left-handed and right-handed parts of Dirac fields transform independently...

. This explains why the three kinds of pion's masses are considerably less than the masses of the other true mesons, such as the meson (958 MeV). If their constituent quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...

s were massless particles, hypothetically, making the chiral symmetry exact, then calculations with the Goldstone theorem would give all pions zero masses. In reality, since all quarks actually have nonzero masses, the pions also have nonzero rest masses.

The use of pions in medical radiation therapy, such as for cancer, was explored at a number of research institutions, including the Los Alamos National Laboratory
Los Alamos National Laboratory
Los Alamos National Laboratory is a United States Department of Energy national laboratory, managed and operated by Los Alamos National Security , located in Los Alamos, New Mexico...

's Meson Physics Facility, which treated 228 patients between 1974 and 1981 in New Mexico
New Mexico
New Mexico is a state located in the southwest and western regions of the United States. New Mexico is also usually considered one of the Mountain States. With a population density of 16 per square mile, New Mexico is the sixth-most sparsely inhabited U.S...

, and the TRIUMF
TRIUMF
TRIUMF is Canada’s national laboratory for particle and nuclear physics. Its headquarters are located on the south campus of the University of British Columbia in Vancouver, British Columbia. TRIUMF houses the world's largest cyclotron, source of 500 MeV protons, which was named an IEEE Milestone...

 laboratory in Vancouver, British Columbia.

Theoretical overview


The pion can be thought of as one of the particles that mediate the interaction between a pair of nucleons. This interaction is attractive: it pulls the nucleons together. Written in a non-relativistic form, it is called the Yukawa potential. The pion, being spinless, has kinematics
Kinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....

 described by the Klein–Gordon equation. In the terms of quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

, the effective field theory
Effective field theory
In physics, an effective field theory is, as any effective theory, an approximate theory, that includes appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, while ignoring substructure and degrees of freedom at shorter distances .-The renormalization...

 Lagrangian
Lagrangian
The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...

 describing the pion-nucleon interaction is called the Yukawa interaction
Yukawa interaction
In particle physics, Yukawa's interaction, named after Hideki Yukawa, is an interaction between a scalar field \phi and a Dirac field \Psi of the typeV \approx g\bar\Psi \phi \Psi or g \bar \Psi \gamma^5 \phi \Psi ....

.

The nearly identical masses of and imply that there must be a symmetry at play; this symmetry is called the SU(2) flavour symmetry or isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...

. The reason that there are three pions, , and , is that these are understood to belong to the triplet representation or the adjoint representation 3 of SU(2). By contrast, the up and down quarks transform according to the fundamental representation
Fundamental representation
In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group...

 2 of SU(2), whereas the anti-quarks transform according to the conjugate representation 2*.

With the addition of the strange quark
Strange quark
The strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...

, one can say that the pions participate in an SU(3) flavour symmetry, belonging to the adjoint representation 8 of SU(3). The other members of this octet
Octet
-Music:* Octet , ensemble consisting of eight instruments or voices, or composition written for such an ensemble* Octet , 1793 composition by Ludwig van Beethoven* Octet , 1825 composition by Felix Mendelssohn...

 are the four kaon
Kaon
In particle physics, a kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness...

s and the eta meson.

Pions are pseudoscalars under a parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...

 transformation. Pion currents thus couple to the axial vector current and pions participate in the chiral anomaly
Chiral anomaly
A chiral anomaly is the anomalous nonconservation of a chiral current. In some theories of fermions with chiral symmetry, the quantization may lead to the breaking of this chiral symmetry. In that case, the charge associated with the chiral symmetry is not conserved.The non-conservation happens...

.

See also

  • Pionium
    Pionium
    Pionium is an exotic atom consisting of one and one mesons. It can be created, for instance, by interaction of a proton beam accelerated by a particle accelerator and a target nucleus....

  • List of particles
  • Quark model
    Quark model
    In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons....

  • Static forces and virtual-particle exchange
    Static forces and virtual-particle exchange
    Static force fields are fields, such as a simple electric, magnetic or gravitational fields, that exist without excitations. The most common approximation method that physicists use for scattering calculations can be interpreted as static forces arising from the interactions between two bodies...


Further reading

  • Gerald Edward Brown and A. D. Jackson, The Nucleon-Nucleon Interaction, (1976) North-Holland Publishing, Amsterdam ISBN 0-7204-0335-9

External links