In
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, a pion (or a pi meson, denoted with the
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
letter
pi: ) is any of three
subatomic particle
In physical sciences, a subatomic particle is a particle that composes an atom. According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a pr ...
s: , , and . Each pion consists of a
quark
A quark () is a type of 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. All commonly o ...
and an
antiquark
A quark () is a type of 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. All commonly o ...
and is therefore a
meson
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles ...
. Pions are the lightest mesons and, more generally, the lightest
hadron
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ele ...
s. They are unstable, with the charged pions and decaying after a
mean lifetime
A quantity is subject to exponential decay if it decreases at a rate Proportionality (mathematics), proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and ...
of 26.033
nanosecond
A nanosecond (ns) is a unit of time in the International System of Units (SI) equal to one billionth of a second, that is, of a second, or 10 seconds.
The term combines the SI prefix ''nano-'' indicating a 1 billionth submultiple of an SI unit ( ...
s ( seconds), and the neutral pion decaying after a much shorter lifetime of 85
attoseconds ( seconds).
Charged pions most often
decay
Decay may refer to:
Science and technology
* Bit decay, in computing
* Software decay, in computing
* Distance decay, in geography
* Decay time (fall time), in electronics
Biology
* Decomposition of organic matter
* Tooth decay (dental caries ...
into
muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As wi ...
s and
muon neutrino
The muon neutrino is an elementary particle which has the symbol () and zero electric charge. Together with the muon it forms the second generation of leptons, hence the name muon neutrino. It was discovered in 1962 by Leon Lederman, Melvin Schwar ...
s, while neutral pions generally decay into
gamma ray
A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically ...
s.
The exchange of
virtual pions, along with
vector
Vector most often refers to:
*Euclidean vector, a quantity with a magnitude and a direction
*Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematic ...
,
rho
Rho (uppercase Ρ, lowercase ρ or ; el, ρο or el, ρω, label=none) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the sa ...
and
omega meson
The omega meson () is a flavourless meson formed from a superposition of an up quark–antiquark and a down quark–antiquark pair. It is part of the vector meson nonet and mediates the nuclear force along with pions and rho mesons.
Properti ...
s, provides an explanation for the
residual strong force between
nucleon
In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number).
Until the 1960s, nucleons were ...
s. Pions are not produced in
radioactive decay
Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...
, but commonly are in high-energy collisions between
hadron
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ele ...
s. Pions also result from some matter–antimatter
annihilation
In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons. The total energy a ...
events. All types of pions are also produced in natural processes when high-energy
cosmic-ray
Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our own ...
protons and other hadronic cosmic-ray components interact with matter in Earth's atmosphere. In 2013, the detection of characteristic gamma rays originating from the decay of neutral pions in two
supernova remnants has shown that pions are produced copiously after supernovas, most probably in conjunction with production of high-energy protons that are detected on Earth as cosmic rays.
[
]
The pion also plays a crucial role in cosmology, by imposing an upper limit on the energies of cosmic rays surviving collisions with the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
, through the
Greisen–Zatsepin–Kuzmin limit
The Greisen–Zatsepin–Kuzmin limit (GZK limit or GZK cutoff) is a theoretical upper limit on the energy of cosmic ray protons traveling from other galaxies through the intergalactic medium to our galaxy. The limit is (50 EeV), or about 8 j ...
.
History
![Pn Scatter Quarks](https://upload.wikimedia.org/wikipedia/commons/2/2e/Pn_Scatter_Quarks.svg)
Theoretical work by
Hideki Yukawa
was a Japanese theoretical physicist and the first Japanese Nobel laureate for his prediction of the pi meson, or pion.
Biography
He was born as Hideki Ogawa in Tokyo and grew up in Kyoto with two older brothers, two older sisters, and two yo ...
in 1935 had predicted the existence of
meson
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles ...
s as the carrier particles of the
strong nuclear force
The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the n ...
. From the range of the strong nuclear force (inferred from the radius of the
atomic nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron i ...
), Yukawa predicted the existence of a particle having a mass of about 100 MeV/c. Initially after its discovery in 1936, the
muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As wi ...
(initially called the "mu meson") was thought to be this particle, since it has a mass of 106 MeV/c. However, later experiments showed that the muon did not participate in the strong nuclear interaction. In modern terminology, this makes the muon a
lepton
In particle physics, a lepton is an elementary particle of half-integer spin ( spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
, and not a meson. However, some communities of astrophysicists continue to call the muon a "mu-meson". The pions, which turned out to be examples of Yukawa's proposed mesons, were discovered later: the charged pions in 1947, and the neutral pion in 1950.
During 1939–1942,
Debendra Mohan Bose
Debendra Mohan Bose (26 November 1885 – 2 June 1975) was an Indian physicist who made contributions in the field of cosmic rays, artificial radioactivity and neutron physics. He was the longest serving Director (1938–1967) of Bose Institut ...
and
Bibha Chowdhuri
Bibha Chowdhuri (3 July 1913 – 2 June 1991) was an Indian physicist. She worked on particle physics and cosmic rays. The IAU has re-christened the star HD 86081 as Bibha (a yellow-white dwarf star in the constellation Sextans south of the cele ...
exposed
Ilford half-tone
Halftone is the reprographic technique that simulates continuous-tone imagery through the use of dots, varying either in size or in spacing, thus generating a gradient-like effect.Campbell, Alastair. The Designer's Lexicon. ©2000 Chronicle, S ...
photographic plates in the high altitude mountainous regions of
Darjeeling
Darjeeling (, , ) is a town and municipality in the northernmost region of the Indian state of West Bengal. Located in the Eastern Himalayas, it has an average elevation of . To the west of Darjeeling lies the easternmost province of Nepal, ...
,
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
and observed long curved ionizing tracks that appeared to be different from the tracks of alpha particles or protons. In a series of articles published in ''
Nature
Nature, in the broadest sense, is the physics, physical world or universe. "Nature" can refer to the phenomenon, phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. ...
'', they identified a cosmic particle having an average mass close to 200 times the mass of electron, today known as pions. In 1947, the charged pions were again found independently by the collaboration led by
Cecil Powell at the
University of Bristol
, mottoeng = earningpromotes one's innate power (from Horace, ''Ode 4.4'')
, established = 1595 – Merchant Venturers School1876 – University College, Bristol1909 – received royal charter
, type ...
, in England. The discovery article had four authors:
César Lattes
Cesare Mansueto Giulio Lattes (11 July 1924 – 8 March 2005), also known as César 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
Latte ...
,
Giuseppe Occhialini
Giuseppe Paolo Stanislao "Beppo" Occhialini ForMemRS (; 5 December 1907 – 30 December 1993) 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, the latter ...
,
Hugh Muirhead
Hugh Muirhead (1925 – 19 January 2007) was a British nuclear physicist and the last surviving author of the scientific paper announcing the discovery of the pion, a particle predicted by Hideki Yukawa.
Muirhead did his PhD studies at the Unive ...
and Powell. Since the advent of
particle accelerator
A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams.
Large accelerators are used for fundamental research in particle ...
s had not yet come, high-energy subatomic particles were only obtainable from atmospheric
cosmic ray
Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our own ...
s.
Photographic emulsion
Photographic emulsion is a light-sensitive colloid used in film-based photography. Most commonly, in silver-gelatin photography, it consists of silver halide crystals dispersed in gelatin. The emulsion is usually coated onto a substrate of g ...
s based on the
gelatin-silver process
The gelatin silver process is the most commonly used chemical process in black-and-white photography, and is the fundamental chemical process for modern analog color photography. As such, films and printing papers available for analog photography ...
were placed for long periods of time in sites located at high-altitude mountains, first at
Pic du Midi de Bigorre
The Pic du Midi de Bigorre or simply the Pic du Midi (elevation ) is a mountain in the French Pyrenees. It is the site of the Pic du Midi Observatory.
Pic du Midi Observatory
The Pic du Midi Observatory (french: Observatoire du Pic du Mid ...
in the
Pyrenees
The Pyrenees (; es, Pirineos ; french: Pyrénées ; ca, Pirineu ; eu, Pirinioak ; oc, Pirenèus ; an, Pirineus) is a mountain range straddling the border of France and Spain. It extends nearly from its union with the Cantabrian Mountains to C ...
, and later at
Chacaltaya
Chacaltaya ( Mollo language for "''bridge of winds''" or "''winds meeting point''", Aymara for "cold road") is a mountain in the Cordillera Real, one of the mountain ranges of the Cordillera Oriental, itself a range of the Bolivian Andes. Its ...
in the
Andes Mountains
The Andes, Andes Mountains or Andean Mountains (; ) are the List of mountain ranges#Mountain ranges by length, longest continental mountain range in the world, forming a continuous highland along the western edge of South America. The range i ...
, where the plates were struck by cosmic rays.
After development, the
photographic plate
Photographic plates preceded photographic film as a capture medium in photography, and were still used in some communities up until the late 20th century. The light-sensitive emulsion of silver salts was coated on a glass plate, typically thinn ...
s were inspected under a
microscope
A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisibl ...
by a team of about a dozen women.
Marietta Kurz was the first person to detect the unusual "double meson" tracks, characteristic for a pion decaying into a
muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As wi ...
, but they were too close to the edge of the photographic emulsion and deemed incomplete. A few days later, Irene Roberts observed the tracks left by pion decay that appeared in the discovery paper. Both women are credited in the figure captions in the article.
In 1948,
Lattes,
Eugene Gardner, and their team first artificially produced pions at the
University of California
The University of California (UC) is a public land-grant research university system in the U.S. state of California. The system is composed of the campuses at Berkeley, Davis, Irvine, Los Angeles, Merced, Riverside, San Diego, San Francisco, ...
's
cyclotron
A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929–1930 at the University of California, Berkeley, and patented in 1932. Lawrence, Ernest O. ''Method and apparatus for the acceleration of ions'', filed: Janu ...
in
Berkeley, California
Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Irish bishop and philosopher George Berkeley. It borders the cities of Oakland and Emer ...
, by bombarding
carbon
Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent
In chemistry, the valence (US spelling) or valency (British spelling) of an element is the measure of its combining capacity with o ...
atoms with high-speed
alpha particle
Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produce ...
s. Further advanced theoretical work was carried out by
Riazuddin, who in 1959 used the
dispersion relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...
for
Compton scattering
Compton scattering, discovered by Arthur Holly Compton, is the scattering of a high frequency photon after an interaction with a charged particle, usually an electron. If it results in a decrease in energy (increase in wavelength) of the photon ...
of
virtual photon
A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbat ...
s on pions to analyze their charge radius.
Since the neutral pion is not
electrically charged
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
, it is more difficult to detect and observe than the charged pions are. Neutral pions do not leave tracks in photographic emulsions or Wilson
cloud chamber
A cloud chamber, also known as a Wilson cloud chamber, is a particle detector used for visualizing the passage of ionizing radiation.
A cloud chamber consists of a sealed environment containing a supersaturated vapour of water or alcohol. An ...
s. The existence of the neutral pion was inferred from observing its decay products from
cosmic ray
Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our own ...
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.
Possible applications
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 (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, ...
's Meson Physics Facility, which treated 228 patients between 1974 and 1981 in
New Mexico
)
, population_demonym = New Mexican ( es, Neomexicano, Neomejicano, Nuevo Mexicano)
, seat = Santa Fe
, LargestCity = Albuquerque
, LargestMetro = Tiguex
, OfficialLang = None
, Languages = English, Spanish ( New Mexican), Navajo, Ker ...
, and the
TRIUMF
TRIUMF is Canada's national particle accelerator centre. It is considered Canada's premier physics laboratory, and consistently regarded as one of the world's leading subatomic physics research centers. Owned and operated by a consortium of u ...
laboratory in
Vancouver, British Columbia
Vancouver ( ) is a major city in western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the ...
.
Theoretical overview
In the standard understanding of the
strong force
The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the n ...
interaction as defined by
quantum chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type ...
, pions are loosely portrayed as
Goldstone boson
In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu in par ...
s of spontaneously
broken chiral symmetry. That explains why the masses of the three kinds of pions are considerably less than that of the other mesons, such as the scalar or vector mesons. If their current
quark
A quark () is a type of 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. All commonly o ...
s were massless particles, it could make the chiral symmetry exact and thus the Goldstone theorem would dictate that all pions have a zero mass.
In fact, it was shown by Gell-Mann, Oakes and Renner (GMOR)
that the square of the pion mass is proportional to the sum of the quark masses times the
quark condensate
A fermionic condensate or Fermi–Dirac condensate is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic atoms under similar cond ...
: , with the quark condensate. This is often known as the GMOR relation and it explicitly shows that in the massless quark limit. The same result also follows from
Light-front holography.
[S. J. Brodsky, G. F. de Teramond, H. G. Dosch and J. Erlich (2015) “Light-Front Holographic QCD and Emerging Confinement”](_blank)
Phys. Rep. 584, 1-105
Empirically, since the light quarks actually have minuscule nonzero masses, the pions also have nonzero
rest mass
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, i ...
es. However, those masses are ''almost an order of magnitude smaller'' than that of the nucleons, roughly
≈ ≈ 45 MeV, where are the relevant current-quark masses in MeV, around 5−10 MeV.
The pion can be thought of as one of the particles that mediate the residual strong interaction between a pair of
nucleons
In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number).
Until the 1960s, nucleons we ...
. This interaction is attractive: it pulls the nucleons together. Written in a non-relativistic form, it is called the
Yukawa potential
In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa. The potential is of the form:
:V_\text(r)= -g^2\frac,
where is a m ...
. The pion, being spinless, has
kinematics
Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...
described by the
Klein–Gordon equation
The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and time and manifestly Lorentz-covariant. ...
. In the terms of
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
, the
effective field theory
In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees ...
Lagrangian
Lagrangian may refer to:
Mathematics
* Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier
** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...
describing the pion-nucleon interaction is called the
Yukawa interaction
In particle physics, Yukawa's interaction or Yukawa coupling, named after Hideki Yukawa, is an interaction between particles according to the Yukawa potential. Specifically, it is a scalar field (or pseudoscalar field) and a Dirac field of the ...
.
The nearly identical masses of and indicate that there must be a symmetry at play: this symmetry is called the
SU(2)
In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1.
The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special ...
flavour symmetry
In particle physics, flavour or flavor refers to the ''species'' of an elementary particle. The Standard Model counts six flavours of quarks and six flavours of leptons. They are conventionally parameterized with ''flavour quantum numbers'' th ...
or
isospin
In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions ...
. The reason that there are three pions, , and , is that these are understood to belong to the triplet representation or the
adjoint representation
In mathematics, the adjoint representation (or adjoint action) of a Lie group ''G'' is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if ''G'' is G ...
3 of SU(2). By contrast, the up and down quarks transform according to the
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
or Lie algebra whose highest weight is a fundamental weight. For example, the defini ...
2 of SU(2), whereas the anti-quarks transform according to the conjugate representation 2*.
With the addition of the
strange quark, the pions participate in a larger, SU(3), flavour symmetry, in the adjoint representation, 8, of SU(3). The other members of this
octet
Octet may refer to:
Music
* Octet (music), ensemble consisting of eight instruments or voices, or composition written for such an ensemble
** String octet, a piece of music written for eight string instruments
*** Octet (Mendelssohn), 1825 compos ...
are the four
kaon
KAON (Karlsruhe ontology) is an ontology infrastructure developed by the University of Karlsruhe and the Research Center for Information Technologies in Karlsruhe.
Its first incarnation was developed in 2002 and supported an enhanced version of ...
s and the
eta meson
The eta () and eta prime meson () are isosinglet mesons made of a mixture of up, down and strange quarks and their antiquarks. The charmed eta meson () and bottom eta meson () are similar forms of quarkonium; they have the same spin and parity ...
.
Pions are
pseudoscalar
In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does not.
Any scalar product between a pseudovector and an ordinary vector is a pseudoscalar. The ...
s under a
parity transformation. Pion currents thus couple to the axial vector current and so participate in the
chiral anomaly
In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have mor ...
.
Basic properties
Pions, which are
meson
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles ...
s with zero
spin, are composed of first-
generation
A generation refers to all of the people born and living at about the same time, regarded collectively. It can also be described as, "the average period, generally considered to be about 20–30 years, during which children are born and gr ...
quark
A quark () is a type of 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. All commonly o ...
s. In the
quark model
In particle 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. The quark model underlies "flavor SU(3)", or the E ...
, an
up quark
The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a significant constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up quark ...
and an anti-
down quark
The down quark or d quark (symbol: d) is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. Together with the up quark, it forms the neutrons (one up quark, two down quarks) and protons (two up q ...
make up a , whereas a
down quark
The down quark or d quark (symbol: d) is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. Together with the up quark, it forms the neutrons (one up quark, two down quarks) and protons (two up q ...
and an anti-
up quark
The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a significant constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up quark ...
make up the , and these are the
antiparticle
In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
s of one another. The neutral pion is a combination of an up quark with an anti-up quark or a down quark with an anti-down quark. The two combinations have identical
quantum number
In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be kno ...
s, and hence they are only found in
superpositions. The lowest-energy superposition of these is the , which is its own antiparticle. Together, the pions form a triplet of
isospin
In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions ...
. Each pion has isospin (''I'' = 1) and third-component
isospin equal to its charge (''I''
z = +1, 0 or −1).
Charged pion decays
The mesons have a
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
of and a
mean lifetime of . They decay due to the
weak interaction
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, ...
. The primary decay mode of a pion, with a
branching fraction
In particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to eithe ...
of 0.999877, is a
lepton
In particle physics, a lepton is an elementary particle of half-integer spin ( spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
ic decay into a
muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As wi ...
and a
muon neutrino
The muon neutrino is an elementary particle which has the symbol () and zero electric charge. Together with the muon it forms the second generation of leptons, hence the name muon neutrino. It was discovered in 1962 by Leon Lederman, Melvin Schwar ...
:
:
The second most common decay mode of a pion, with a branching fraction of 0.000123, is also a leptonic decay into an
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
and the corresponding
electron antineutrino
The electron neutrino () is an elementary particle which has zero electric charge and a spin of . Together with the electron, it forms the first generation of leptons, hence the name electron neutrino. It was first hypothesized by Wolfgang Pauli ...
. This "electronic mode" was discovered at
CERN
The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in a northwestern suburb of Gene ...
in 1958:
:
The suppression of the electronic decay mode with respect to the muonic one is given approximately (up to a few percent effect of the radiative corrections) by the ratio of the half-widths of the pion–electron and the pion–muon decay reactions,
:
and is a
spin effect known as
helicity suppression.
Its mechanism is as follows: The negative pion has spin zero; therefore the lepton and the antineutrino must be emitted with opposite spins (and opposite linear momenta) to preserve net zero spin (and conserve linear momentum). However, because the weak interaction is sensitive only to the left
chirality
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...
component of fields, the antineutrino has always left
chirality
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...
, which means it is right-handed, since for massless anti-particles the helicity is opposite to the chirality. This implies that the lepton must be emitted with spin in the direction of its linear momentum (i.e., also right-handed). If, however, leptons were massless, they would only interact with the pion in the left-handed form (because for massless particles helicity is the same as chirality) and this decay mode would be prohibited. Therefore, suppression of the electron decay channel comes from the fact that the electron's mass is much smaller than the muon's. The electron is relatively massless compared with the muon, and thus the electronic mode is greatly suppressed relative to the muonic one, virtually prohibited.
Although this explanation suggests that parity violation is causing the helicity suppression, the fundamental reason lies in the vector-nature of the interaction which dictates a different handedness for the neutrino and the charged lepton. Thus, even a parity conserving interaction would yield the same suppression.
Measurements of the above ratio have been considered for decades to be a test of
lepton universality. Experimentally, this ratio is .
Beyond the purely leptonic decays of pions, some structure-dependent radiative leptonic decays (that is, decay to the usual leptons plus a gamma ray) have also been observed.
Also observed, for charged pions only, is the very rare "pion
beta decay
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
" (with branching fraction of about 10
−8) into a neutral pion, an electron and an electron antineutrino (or for positive pions, a neutral pion, a positron, and electron neutrino).
:
The rate at which pions decay is a prominent quantity in many sub-fields of particle physics, such as
chiral perturbation theory. This rate is parametrized by the
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 symm ...
(ƒ
''π''), related to the
wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
overlap of the quark and antiquark, which is about .
Neutral pion decays
The meson has a mass of and a mean lifetime of .
It decays via the
electromagnetic force
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
, which explains why its mean lifetime is much smaller than that of the charged pion (which can only decay via the
weak force
Weak may refer to:
Songs
* Weak (AJR song), "Weak" (AJR song), 2016
* Weak (Melanie C song), "Weak" (Melanie C song), 2011
* Weak (SWV song), "Weak" (SWV song), 1993
* Weak (Skunk Anansie song), "Weak" (Skunk Anansie song), 1995
* "Weak", a song ...
).
The dominant decay mode, with a
branching ratio
In particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to eithe ...
of is into two
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s:
:
The decay → 3 (as well as decays into any odd number of photons) is forbidden by the
C-symmetry
In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symm ...
of the electromagnetic interaction: The intrinsic C-parity of the is +1, while the C-parity of a system of photons is (−1).
The second largest decay mode () is the Dalitz decay (named after
Richard Dalitz
Richard Henry Dalitz, FRS (28 February 1925 – 13 January 2006) was an Australian physicist known for his work in particle physics.
Education and early life
Born in the town of Dimboola, Victoria, Dalitz studied physics and mathematics at Me ...
), which is a two-photon decay with an internal photon conversion resulting a photon and an
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
-
positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collides ...
pair in the final state:
:
The third largest established decay mode () is the double-Dalitz decay, with both photons undergoing internal conversion which leads to further suppression of the rate:
:
The fourth largest established decay mode is the
loop-induced and therefore suppressed (and additionally
helicity-suppressed) leptonic decay mode ():
:
The neutral pion has also been observed to decay into
positronium
Positronium (Ps) is a system consisting of an electron and its antimatter, anti-particle, a positron, bound together into an exotic atom, specifically an onium. Unlike hydrogen, the system has no protons. The system is unstable: the two parti ...
with a branching fraction on the order of . No other decay modes have been established experimentally. The branching fractions above are the
PDG central values, and their uncertainties are omitted, but available in the cited publication.
/sup> Make-up inexact due to non-zero quark masses.
See also
*Pionium
Pionium is a composite particle consisting of one and one meson. It can be created, for instance, by interaction of a proton beam accelerated by a particle accelerator and a target nucleus. Pionium has a short lifetime, predicted by chiral pertur ...
*Quark model
In particle 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. The quark model underlies "flavor SU(3)", or the E ...
*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 ...
* Sanford-Wang parameterisation
References
Further reading
* Gerald Edward Brown and A. D. Jackson, ''The Nucleon-Nucleon Interaction'' (1976), North-Holland Publishing, Amsterdam
External links
*
Mesons
at the Particle Data Group
{{Authority control
Mesons