Meson
Encyclopedia
In particle physics
, mesons (ˈmiːzɒnz, ˈmɛzɒnz) are subatomic particle
s 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 or neutron. All mesons are unstable, with the longest-lived lasting for only a few 100-millionths (10−8) of a second. Charged mesons decay (sometimes through intermediate particles) to form electrons and neutrinos. Uncharged mesons may decay to photons.
Mesons are not produced by radioactive decay, but appear in nature only as short-lived products of very high-energy interactions in matter, between particles made of quarks. In cosmic ray
interactions, for example, such particles are ordinary protons and neutrons. Mesons are also frequently produced artificially in high-energy particle accelerators that collide protons, anti-protons, or other particles containing quarks.
In nature, the importance of lighter mesons is that they are the associated quantum-field particles that transmit the nuclear force
, in the same way that photons are the particles that transmit the electromagnetic force. The higher energy (more massive) mesons were created momentarily in the Big Bang
but are not thought to play a role in nature today. However, such particles are regularly created in experiments, in order to understand the nature of the heavier types of quark which compose the heavier mesons.
Mesons are part of the hadron
particle family, defined simply as particles composed of quarks. The other members of the hadron family are the baryon
s: subatomic particles composed of three quarks rather than two. Some experiments show evidence of tetraquark
s—"exotic" mesons made of two quarks and two antiquarks; the particle physics community regards their existence as unlikely, although possible. Since quarks have a spin of , the difference in quark-number between mesons and baryons results in mesons being boson
s while baryons are fermion
s.
Each type of meson has a corresponding antiparticle
(antimeson) in which quarks are replaced by their corresponding antiquarks and vice-versa. For example, a positive pion
is made of one up quark and one down antiquark; and its corresponding antiparticle, the negative pion , is made of one up antiquark and one down quark.
Since mesons are composed of quarks, they participate in both the weak
and strong interaction
s. Mesons with net electric charge
also participate in the electromagnetic interaction. They are classified according to their quark content, total angular momentum, parity
, and various other properties such as C-parity and G-parity
. While no meson is stable, those of lower mass
are nonetheless more stable than the most massive mesons, and are easier to observe and study in particle accelerator
s or in cosmic ray
experiments. They are also typically less massive than baryons, meaning that they are more easily produced in experiments, and thus exhibit certain higher energy phenomena more readily than baryons composed of the same quarks would. For example, the charm quark was first seen in the J/Psi meson in 1974, and the bottom quark in the upsilon meson in 1977.
in 1934 predicted the existence and the approximate mass of the "meson" as the carrier of the nuclear force
that holds atomic nuclei
together. If there was no nuclear force, all nuclei with two or more proton
s would fly apart because of the electromagnetic
repulsion. Yukawa called his carrier particle the meson, from mesos, the Greek word for intermediate, because its predicted mass was between that of the electron and that of the proton, which has about 1,836 times the mass of the electron. Yukawa had originally named his particle the "mesotron", but he was corrected by the physicist Werner Heisenberg
(whose father was a professor of Greek at the University of Munich). Heisenberg pointed out that there is no "tr" in the Greek word "mesos".
The first candidate for Yukawa's meson, then dubbed the "mu meson
" (or muon) was discovered 1936 by Carl David Anderson
and others in the decay product
s of cosmic ray interactions. The mu meson had about the right mass to be Yukawa's carrier of the strong nuclear force, but over the course of the next decade, it became evident that it was not the right particle. It was eventually found that the mu meson did not participate in the strong nuclear interaction at all, but rather behaved like a heavy version of the electron
, and is in fact a lepton
rather than a meson.
There were years of delays in subatomic particle research during World War II
in 1939−45, with most physicists working in applied projects for wartime necessities. When the war ended in August 1945, many physicists gradually returned to peacetime research. The first true meson to be discovered was the "pi meson
" (or pion) in 1947, by Cecil Powell, César Lattes
, and Giuseppe Occhialini
, who were
investigating cosmic ray products at the University of Bristol
in England
. It also had about the right mass, and over the next few years, more experiments showed that the pion was indeed involved in strong interactions. The pion (as a virtual particle
) is the primary force carrier for the nuclear force
in atomic nuclei
. Other mesons, such as the rho meson
s are involved in mediating this force as well, but to lesser extents. Following the discovery of the pion, Yukawa was awarded the 1949 Nobel Prize in Physics
for his predictions.
The word meson has at times been used to mean any force carrier, such as "Z0 meson
" which is involved in mediating the weak interaction
. However, this spurious usage has fallen out of favor. Mesons are now defined as particles composed of pairs of quarks and antiquarks.
(quantum number S) is a vector quantity that represents the "intrinsic" angular momentum
of a particle. It comes in increments of ħ . The ħ is often dropped because it is the "fundamental" unit of spin, and it is implied that "spin 1" means "spin 1 ħ". (In some systems of natural units
, ħ is chosen to be 1, and therefore does not appear in equations).
Quark
s are fermion
s—specifically in this case, particles having spin (S = ). Because spin projections vary in increments of 1 (that is 1 ħ), a single quark has a spin vector of length , and has two spin projections (Sz = + and Sz = −). Two quarks can have their spins aligned, in which case the two spin vectors add to make a vector of length S = 1 and three spin projections (Sz = +1, Sz = 0, and Sz = −1), called the spin-1 triplet. If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and only one spin projection (Sz = 0), called the spin-0 singlet. Since mesons are made of one quark and one antiquark, they can be found in triplet and singlet spin states.
There is another quantity of quantized angular momentum, called the orbital angular momentum (quantum number L), that comes in increments of 1 ħ, which represent the angular moment due to quarks orbiting around each other. The total angular momentum (quantum number J) of a particle is therefore the combination of intrinsic angular momentum (spin) and orbital angular momentum. It can take any value from to , in increments of 1.
Particle physicists are most interested in mesons with no orbital angular momentum (L = 0), therefore the two groups of mesons most studied are the S = 1; L = 0 and S = 0; L = 0, which corresponds to J = 1 and J = 0, although they are not the only ones. It is also possible to obtain J = 1 particles from S = 0 and L = 1. How to distinguish between the S = 1, L = 0 and S = 0, L = 1 mesons is an active area of research in meson spectroscopy.
(P). Gravity, the electromagnetic force, and the strong interaction
all behave in the same way regardless of whether or not the universe is reflected in a mirror, and thus are said to conserve parity (P-symmetry). However, the weak interaction
does distinguish "left" from "right", a phenomenon called parity violation (P-violation).
Based on this, one might think that if the wavefunction
for each particle (more precisely, the quantum field for each particle type) were simultaneously mirror-reversed, then the new set of wavefunctions would perfectly satisfy the laws of physics (apart from the weak interaction). It turns out that this is not quite true: In order for the equations to be satisfied, the wavefunctions of certain types of particles have to be multiplied by −1, in addition to being mirror-reversed. Such particle types are said to have negative or odd parity (P = −1, or alternatively P = –), while the other particles are said to have positive or even parity (P = +1, or alternatively P = +).
For mesons, the parity is related to the orbital angular momentum by the relation:
where the L is a result of the parity of the corresponding spherical harmonic
of the wavefunction
. The '+1' in the exponent comes from the fact that, according to the Dirac equation
, a quark and an antiquark have opposite intrinsic parities. Therefore the intrinsic parity of a meson is the product of the intrinsic parities of the quark (+1) and antiquark (−1). As these are different, their product is −1, and so it contributes a +1 in the exponent.
As a consequence, mesons with no orbital angular momentum (L = 0) all have odd parity (P = −1).
then, the meson is "C even" (C = +1). On the other hand, if
then the meson is "C odd" (C = −1).
C-parity rarely is studied on its own, but the combination of C- and P-parity into CP-parity. CP-parity was thought to be conserved, but was later found to be violated in weak interaction
s.
If
then, the meson is "G even" (G = +1). On the other hand, if
then the meson is "G odd" (G = −1).
The concept of isospin was first proposed by Werner Heisenberg
in 1932 to explain the similarities between protons and neutrons under the strong interaction
. Although they had different electric charges, their masses were so similar that physicists believed they were actually the same particle. The different electric charges were explained as being the result of some unknown excitation similar to spin. This unknown excitation was later dubbed isospin by Eugene Wigner in 1937. When the first mesons were discovered, they too were seen through the eyes of isospin. The three pions were believed to be the same particle, but in different isospin states.
This belief lasted until Murray Gell-Mann
proposed the quark model
in 1964 (containing originally only the u, d, and s quarks). The success of the isospin model is now understood to be the result of the similar masses of the u and d quarks. Since the u and d quarks have similar masses, particles made of the same number of them also have similar masses. The exact specific u and d quark composition determines the charge, as u quarks carry charge + while d quarks carry charge −. For example the three pions all have different charges ( , (a quantum superposition
of and states), ), but have similar masses (~) as they are each made of a same number of total of up and down quarks and antiquarks. Under the isospin model, they were considered to be a single particle in different charged states.
The mathematics of isospin was modeled after that of spin. Isospin projections varied in increments of 1 just like those of spin, and to each projection was associated a "charged state". Since the "pion particle" had three "charged states", it was said to be of isospin I = 1. Its "charged states" , , and , corresponded to the isospin projections I3 = +1, I3 = 0, and I3 = −1 respectively. Another example is the "rho particle
", also with three charged states. Its "charged states" , , and , corresponded to the isospin projections I3 = +1, I3 = 0, and I3 = −1 respectively. It was later noted that the isospin projections were related to the up and down quark content of particles by the relation
where the ns are the number of up and down quarks and antiquarks.
In the "isospin picture", the three pions and three rhos were thought to be the different states of two particles. However in the quark model, the rhos are excited states of pions. Isospin, although conveying an inaccurate picture of things, is still used to classify hadrons, leading to unnatural and often confusing nomenclature. Since mesons are hadrons, the isospin classification is also used, with I3 = + for up quarks and down antiquarks, and I3 = − for up antiquarks and down quarks.
quantum number S (not to be confused with spin) was noticed to go up and down along with particle mass. The higher the mass, the lower the strangeness (the more s quarks). Particles could be described with isospin projections (related to charge) and strangeness (mass) (see the uds nonet figures). As other quarks were discovered, new quantum numbers were made to have similar description of udc and udb nonets. Since only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers only works well for the nonets made of one u, one d and one other quark and breaks down for the nonets (for example ucb nonet). If the quarks all had the same mass, their behaviour would be called symmetric, as they would all behave in exactly the same way with respect to the strong interaction. Since quarks do not have the same mass, they do not interact in the same way (exactly like an electron placed in an electric field will accelerate more than a proton placed in the same field because of its lighter mass), and the symmetry is said to be broken.
It was noted that charge (Q) was related to the isospin projection (I3), the baryon number (B) and flavour quantum numbers (S, C, B′, T) by the Gell-Mann–Nishijima formula
:
where S, C, B′, and T represent the strangeness
, charm, bottomness
and topness flavour quantum numbers respectively. They are related to the number of strange, charm, bottom, and top quarks and antiquark according to the relations:
meaning that the Gell-Man–Nishijima formula is equivalent to the expression of charge in terms of quark content:
(I), total angular momentum (J), parity
(P), G-parity
(G) or C-parity (C) when applicable, and quark
(q) content. The rules for classification are defined by the Particle Data Group
, and are rather convoluted. The rules are presented below, in table form for simplicity.
= 0, C = 0, B′
= 0, T = 0). The rules for flavourless mesons are:
† The C parity is only relevant to neutral mesons.
†† For JPC=1−−, the ψ is called the
In addition:
In addition:
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...
, mesons (ˈmiːzɒnz, ˈmɛzɒnz) are 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 composed of one 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...
and one antiquark, bound together by the strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
. 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 or neutron. All mesons are unstable, with the longest-lived lasting for only a few 100-millionths (10−8) of a second. Charged mesons decay (sometimes through intermediate particles) to form electrons and neutrinos. Uncharged mesons may decay to photons.
Mesons are not produced by radioactive decay, but appear in nature only as short-lived products of very high-energy interactions in matter, between particles made of quarks. In 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...
interactions, for example, such particles are ordinary protons and neutrons. Mesons are also frequently produced artificially in high-energy particle accelerators that collide protons, anti-protons, or other particles containing quarks.
In nature, the importance of lighter mesons is that they are the associated quantum-field particles that transmit the nuclear force
Nuclear force
The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...
, in the same way that photons are the particles that transmit the electromagnetic force. The higher energy (more massive) mesons were created momentarily in the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
but are not thought to play a role in nature today. However, such particles are regularly created in experiments, in order to understand the nature of the heavier types of quark which compose the heavier mesons.
Mesons are part of the hadron
Hadron
In particle physics, a hadron is a composite particle made of quarks held together by the strong force...
particle family, defined simply as particles composed of quarks. The other members of the hadron family are the baryon
Baryon
A baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...
s: subatomic particles composed of three quarks rather than two. Some experiments show evidence of tetraquark
Tetraquark
In particle physics a tetraquark is a hypothetical meson composed of four valence quarks. In principle, a tetraquark state may be allowed in quantum chromodynamics, the modern theory of strong interactions. However, there has been no confirmed report of a tetraquark state to date...
s—"exotic" mesons made of two quarks and two antiquarks; the particle physics community regards their existence as unlikely, although possible. Since quarks have a spin of , the difference in quark-number between mesons and baryons results in mesons being boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s while baryons are fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s.
Each type of meson has a corresponding 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...
(antimeson) in which quarks are replaced by their corresponding antiquarks and vice-versa. For example, a positive pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
is made of one up quark and one down antiquark; and its corresponding antiparticle, the negative pion , is made of one up antiquark and one down quark.
Since mesons are composed of quarks, they participate in both the weak
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 strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
s. Mesons with net electric charge
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...
also participate in the electromagnetic interaction. They are classified according to their quark content, total angular momentum, 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:...
, and various other properties such as C-parity and G-parity
G-parity
In theoretical physics, G-parity is a multiplicative quantum number that results from the generalization of C-parity to multiplets of particles....
. While no meson is stable, those of lower 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:...
are nonetheless more stable than the most massive mesons, and are easier to observe and study in 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 or in 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...
experiments. They are also typically less massive than baryons, meaning that they are more easily produced in experiments, and thus exhibit certain higher energy phenomena more readily than baryons composed of the same quarks would. For example, the charm quark was first seen in the J/Psi meson in 1974, and the bottom quark in the upsilon meson in 1977.
History
From theoretical considerations, Hideki YukawaHideki 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 1934 predicted the existence and the approximate mass of the "meson" as the carrier of the nuclear force
Nuclear force
The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...
that holds atomic nuclei
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...
together. If there was no nuclear force, all nuclei with two or more proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
s would fly apart because of the electromagnetic
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
repulsion. Yukawa called his carrier particle the meson, from mesos, the Greek word for intermediate, because its predicted mass was between that of the electron and that of the proton, which has about 1,836 times the mass of the electron. Yukawa had originally named his particle the "mesotron", but he was corrected by the physicist Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
(whose father was a professor of Greek at the University of Munich). Heisenberg pointed out that there is no "tr" in the Greek word "mesos".
The first candidate for Yukawa's meson, then dubbed the "mu meson
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...
" (or muon) was discovered 1936 by Carl David Anderson
Carl David Anderson
Carl David Anderson was an American physicist. He is best known for his discovery of the positron in 1932, an achievement for which he received the 1936 Nobel Prize in Physics, and of the muon in 1936.-Biography:...
and others in the decay product
Decay product
In nuclear physics, a decay product is the remaining nuclide left over from radioactive decay. Radioactive decay often involves a sequence of steps...
s of cosmic ray interactions. The mu meson had about the right mass to be Yukawa's carrier of the strong nuclear force, but over the course of the next decade, it became evident that it was not the right particle. It was eventually found that the mu meson did not participate in the strong nuclear interaction at all, but rather behaved like a heavy version of the 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 is in fact 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...
rather than a meson.
There were years of delays in subatomic particle research during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
in 1939−45, with most physicists working in applied projects for wartime necessities. When the war ended in August 1945, many physicists gradually returned to peacetime research. The first true meson to be discovered was the "pi meson
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
" (or pion) in 1947, by 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...
, and 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...
, who were
investigating cosmic ray products 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
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
. It also had about the right mass, and over the next few years, more experiments showed that the pion was indeed involved in strong interactions. The pion (as a virtual particle
Virtual particle
In physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...
) is the primary force carrier for the nuclear force
Nuclear force
The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...
in atomic nuclei
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...
. Other mesons, such as the rho meson
Rho meson
In particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as , and . After the pions and kaons, the rho mesons are the lightest strongly interacting particle with a mass of roughly for all three states...
s are involved in mediating this force as well, but to lesser extents. Following the discovery of the pion, Yukawa was awarded the 1949 Nobel Prize 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...
for his predictions.
The word meson has at times been used to mean any force carrier, such as "Z0 meson
W and Z bosons
The W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
" which is involved in mediating the weak interaction
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...
. However, this spurious usage has fallen out of favor. Mesons are now defined as particles composed of pairs of quarks and antiquarks.
Spin, orbital angular momentum, and total angular momentum
SpinSpin (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,...
(quantum number S) is a vector quantity that represents the "intrinsic" angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
of a particle. It comes in increments of ħ . The ħ is often dropped because it is the "fundamental" unit of spin, and it is implied that "spin 1" means "spin 1 ħ". (In some systems of natural units
Natural units
In physics, natural units are physical units of measurement based only on universal physical constants. For example the elementary charge e is a natural unit of electric charge, or the speed of light c is a natural unit of speed...
, ħ is chosen to be 1, and therefore does not appear in equations).
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 are fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s—specifically in this case, particles having spin (S = ). Because spin projections vary in increments of 1 (that is 1 ħ), a single quark has a spin vector of length , and has two spin projections (Sz = + and Sz = −). Two quarks can have their spins aligned, in which case the two spin vectors add to make a vector of length S = 1 and three spin projections (Sz = +1, Sz = 0, and Sz = −1), called the spin-1 triplet. If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and only one spin projection (Sz = 0), called the spin-0 singlet. Since mesons are made of one quark and one antiquark, they can be found in triplet and singlet spin states.
There is another quantity of quantized angular momentum, called the orbital angular momentum (quantum number L), that comes in increments of 1 ħ, which represent the angular moment due to quarks orbiting around each other. The total angular momentum (quantum number J) of a particle is therefore the combination of intrinsic angular momentum (spin) and orbital angular momentum. It can take any value from to , in increments of 1.
| S 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,... |
L | J | P 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:... (See below) |
JP |
|---|---|---|---|---|
| 0 | 0 | 0 | − | 0− |
| 1 | 1 | + | 1+ | |
| 2 | 2 | − | 2− | |
| 3 | 3 | + | 3+ | |
| 1 | 0 | 1 | − | 1− |
| 1 | 2, 1, 0 | + | 2+, 1+, 0+ | |
| 2 | 3, 2, 1 | − | 3−, 2−, 1− | |
| 3 | 4, 3, 2 | + | 4+, 3+, 2+ |
Particle physicists are most interested in mesons with no orbital angular momentum (L = 0), therefore the two groups of mesons most studied are the S = 1; L = 0 and S = 0; L = 0, which corresponds to J = 1 and J = 0, although they are not the only ones. It is also possible to obtain J = 1 particles from S = 0 and L = 1. How to distinguish between the S = 1, L = 0 and S = 0, L = 1 mesons is an active area of research in meson spectroscopy.
Parity
If the universe were reflected in a mirror, most of the laws of physics would be identical—things would behave the same way regardless of what we call "left" and what we call "right". This concept of mirror reflection is called parityParity (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:...
(P). Gravity, the electromagnetic force, and the strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
all behave in the same way regardless of whether or not the universe is reflected in a mirror, and thus are said to conserve parity (P-symmetry). However, the weak interaction
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...
does distinguish "left" from "right", a phenomenon called parity violation (P-violation).
Based on this, one might think that if the wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
for each particle (more precisely, the quantum field for each particle type) were simultaneously mirror-reversed, then the new set of wavefunctions would perfectly satisfy the laws of physics (apart from the weak interaction). It turns out that this is not quite true: In order for the equations to be satisfied, the wavefunctions of certain types of particles have to be multiplied by −1, in addition to being mirror-reversed. Such particle types are said to have negative or odd parity (P = −1, or alternatively P = –), while the other particles are said to have positive or even parity (P = +1, or alternatively P = +).
For mesons, the parity is related to the orbital angular momentum by the relation:
where the L is a result of the parity of the corresponding spherical harmonic
Spherical Harmonic
Spherical Harmonic is a science fiction novel from the Saga of the Skolian Empire by Catherine Asaro. It tells the story of Dyhianna Selei , the Ruby Pharaoh of the Skolian Imperialate, as she strives to reform her government and reunite her family in the aftermath of a devastating interstellar...
of the wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
. The '+1' in the exponent comes from the fact that, according to the Dirac equation
Dirac equation
The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...
, a quark and an antiquark have opposite intrinsic parities. Therefore the intrinsic parity of a meson is the product of the intrinsic parities of the quark (+1) and antiquark (−1). As these are different, their product is −1, and so it contributes a +1 in the exponent.
As a consequence, mesons with no orbital angular momentum (L = 0) all have odd parity (P = −1).
C-parity
C-parity is only defined for mesons that are their own antiparticle (i.e. neutral mesons). It represents whether or not the wavefunction of the meson remains the same under the interchange of their quark with their antiquark. Ifthen, the meson is "C even" (C = +1). On the other hand, if
then the meson is "C odd" (C = −1).
C-parity rarely is studied on its own, but the combination of C- and P-parity into CP-parity. CP-parity was thought to be conserved, but was later found to be violated in weak interaction
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...
s.
G-parity
G parity is a generalizations of the C-parity. Instead of simply comparing the wavefunction after exchanging quarks and antiquarks, it compares the wavefunction after exchanging the meson for the corresponding antimeson, regardless of quark content. In the case of neutral meson, G-parity is equivalent to C-parity because neutral mesons are their own antiparticles.If
then, the meson is "G even" (G = +1). On the other hand, if
then the meson is "G odd" (G = −1).
Isospin and charge
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
in 1932 to explain the similarities between protons and neutrons under the strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
. Although they had different electric charges, their masses were so similar that physicists believed they were actually the same particle. The different electric charges were explained as being the result of some unknown excitation similar to spin. This unknown excitation was later dubbed isospin by Eugene Wigner in 1937. When the first mesons were discovered, they too were seen through the eyes of isospin. The three pions were believed to be the same particle, but in different isospin states.
This belief lasted until Murray Gell-Mann
Murray Gell-Mann
Murray Gell-Mann is an American physicist and linguist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles...
proposed 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....
in 1964 (containing originally only the u, d, and s quarks). The success of the isospin model is now understood to be the result of the similar masses of the u and d quarks. Since the u and d quarks have similar masses, particles made of the same number of them also have similar masses. The exact specific u and d quark composition determines the charge, as u quarks carry charge + while d quarks carry charge −. For example the three pions all have different charges ( , (a quantum 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...
of and states), ), but have similar masses (~) as they are each made of a same number of total of up and down quarks and antiquarks. Under the isospin model, they were considered to be a single particle in different charged states.
The mathematics of isospin was modeled after that of spin. Isospin projections varied in increments of 1 just like those of spin, and to each projection was associated a "charged state". Since the "pion particle" had three "charged states", it was said to be of isospin I = 1. Its "charged states" , , and , corresponded to the isospin projections I3 = +1, I3 = 0, and I3 = −1 respectively. Another example is the "rho particle
Rho meson
In particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as , and . After the pions and kaons, the rho mesons are the lightest strongly interacting particle with a mass of roughly for all three states...
", also with three charged states. Its "charged states" , , and , corresponded to the isospin projections I3 = +1, I3 = 0, and I3 = −1 respectively. It was later noted that the isospin projections were related to the up and down quark content of particles by the relation
where the ns are the number of up and down quarks and antiquarks.
In the "isospin picture", the three pions and three rhos were thought to be the different states of two particles. However in the quark model, the rhos are excited states of pions. Isospin, although conveying an inaccurate picture of things, is still used to classify hadrons, leading to unnatural and often confusing nomenclature. Since mesons are hadrons, the isospin classification is also used, with I3 = + for up quarks and down antiquarks, and I3 = − for up antiquarks and down quarks.
Flavour quantum numbers
The strangenessStrangeness
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...
quantum number S (not to be confused with spin) was noticed to go up and down along with particle mass. The higher the mass, the lower the strangeness (the more s quarks). Particles could be described with isospin projections (related to charge) and strangeness (mass) (see the uds nonet figures). As other quarks were discovered, new quantum numbers were made to have similar description of udc and udb nonets. Since only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers only works well for the nonets made of one u, one d and one other quark and breaks down for the nonets (for example ucb nonet). If the quarks all had the same mass, their behaviour would be called symmetric, as they would all behave in exactly the same way with respect to the strong interaction. Since quarks do not have the same mass, they do not interact in the same way (exactly like an electron placed in an electric field will accelerate more than a proton placed in the same field because of its lighter mass), and the symmetry is said to be broken.
It was noted that charge (Q) was related to the isospin projection (I3), the baryon number (B) and flavour quantum numbers (S, C, B′, T) by the Gell-Mann–Nishijima formula
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"...
:
where S, C, B′, and T represent the strangeness
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...
, charm, bottomness
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...
and topness flavour quantum numbers respectively. They are related to the number of strange, charm, bottom, and top quarks and antiquark according to the relations:
meaning that the Gell-Man–Nishijima formula is equivalent to the expression of charge in terms of quark content:
Classification
Mesons are classified into groups according to their isospinIsospin
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...
(I), total angular momentum (J), 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:...
(P), G-parity
G-parity
In theoretical physics, G-parity is a multiplicative quantum number that results from the generalization of C-parity to multiplets of particles....
(G) or C-parity (C) when applicable, and 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...
(q) content. The rules for classification are defined by the Particle Data Group
Particle Data Group
The Particle Data Group is an international collaboration of particle physicists that compiles and reanalyzes published results related to the properties of particles and fundamental interactions. It also publishes reviews of theoretical results that are phenomenologically relevant, including...
, and are rather convoluted. The rules are presented below, in table form for simplicity.
Types of meson
Mesons are classified into types according to their spin configurations. Some specific configurations are given special names based on the mathematical properties of their spin configuration.| Type | S 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,... |
L | P 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:... |
J | JP |
|---|---|---|---|---|---|
| Pseudoscalar meson Pseudoscalar meson In high energy physics, a pseudoscalar meson is a meson with total spin 0 and odd parity . Compare to scalar meson.Pseudoscalar mesons are commonly seen in proton-proton scattering and proton-antiproton annihilation... |
0 | 0 | − | 0 | 0− |
| Pseudovector meson Pseudovector meson In high energy physics, a pseudovector meson or axial vector meson is a meson with total spin 1 and even parity . Compare to a vector meson, which has a total spin 1 and odd parity.... |
0 | 1 | + | 1 | 1+ |
| Vector meson Vector meson In high energy physics, a vector meson is a meson with total spin 1 and odd parity . Compare to a pseudovector meson, which has a total spin 1 and even parity.... |
1 | 0 | − | 1 | 1− |
| Scalar meson Scalar meson In high energy physics, a scalar meson is a meson with total spin 0 and even parity . Compare to pseudoscalar meson.... |
1 | 1 | + | 0 | 0+ |
| Tensor meson | 1 | 1 | + | 2 | 2+ |
Flavourless mesons
Flavourless mesons are mesons made of pair of quark and antiquarks of the same flavour (all their flavour quantum numbers are zero: SStrangeness
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...
= 0, C = 0, 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...
= 0, T = 0). The rules for flavourless mesons are:
| P 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→ 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... ↓ | 0−+, 2−+, 4−+, ... | 1+−, 3+−, 5+−, ... | 1−−, 2−−, 3−−, ... | 0++, 1++, 2++, ... | |
|---|---|---|---|---|---|
 |
1 | |
b+ b0 b− |
|
a+ a0 a− |
| Mix of , , | 0 | |
h h′ |
|
f f′ |
| 0 | hc | ψ | χc | ||
| 0 | hb | χb | |||
| 0 | ht | χt |
† The C parity is only relevant to neutral mesons.
†† For JPC=1−−, the ψ is called the
In addition:
- When the spectroscopic state of the meson is known, it is added in parentheses.
- When the spectroscopic state is unknown, mass (in MeVElectronvoltIn physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...
/cSpeed of lightThe 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) is added in parentheses. - When the meson is in its ground stateGround stateThe ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
, nothing is added in parentheses.
Flavourful mesons
Flavourful mesons are mesons made of pair of quark and antiquarks of different flavours. The rules are simpler in this case: the main symbol depends on the heavier quark, the superscript depends on the charge, and the subscript (if any) depends on the lighter quark. In table form, they are:| antiquark → quark ↓ | up | down | charm | strange | top | bottom |
|---|---|---|---|---|---|---|
| up | — | |||||
| down | — | |||||
| charm | — | |||||
| strange | — | |||||
| top | — | |||||
| bottom | — |
In addition:
- If JPParity (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:...
is in the "normal series" (i.e., JPParity (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:...
= 0+, 1−, 2+, 3−, ...), a superscript ∗ is added. - If the meson is not pseudoscalar (JPParity (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:...
= 0−) or vector (JPParity (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:...
= 1−), J is added as a subscript. - When the spectroscopic state of the meson is known, it is added in parentheses.
- When the spectroscopic state is unknown, mass (in MeVElectronvoltIn physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...
/cSpeed of lightThe 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) is added in parentheses. - When the meson is in its ground stateGround stateThe ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
, nothing is added in parentheses.
See also
- Standard ModelStandard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
External links
- A table of some mesons and their properties
- Particle Data Group—Compiles authoritative information on particle properties
- hep-ph/0211411: The light scalar mesons within quark models
- Naming scheme for hadrons (a PDF file)
- Mesons made thinkable, an interactive visualisation allowing physical properties to be compared