Baryon
Encyclopedia
A baryon is a composite particle
made up of three quark
s (as distinct from meson
s, which comprise one quark and one antiquark). Baryons and mesons belong to the hadron
family, which are the quark-based particles. The name "baryon" comes from the Greek
word for "heavy" (βαρύς, barys), because, at the time of their naming, most known particles had lower masses than the baryons.
As quark-based particles, baryons participate in the strong interaction
, whereas lepton
s, which are not quark-based, do not. The most familiar baryons are the proton
s and neutron
s that make up most of the mass of the visible matter
in the universe
. Electron
s (the other major component of the atom
) are leptons. Each baryon has a corresponding antiparticle
(antibaryon) where quarks are replaced by their corresponding antiquarks. For example, a proton is made of two up quarks and one down quark; and its corresponding antiparticle, the antiproton
, is made of two up antiquarks and one down antiquark.
Until recently, it was believed that some experiments showed the existence of pentaquark
s — "exotic" baryons made of four quarks and one antiquark. The particle physics community as a whole did not view their existence as likely in 2006, and in 2008, considered evidence to be overwhelmingly against the existence of the reported pentaquarks.
s — that is, they experience the strong nuclear force and are described by Fermi−Dirac statistics, which apply to all particles obeying the Pauli exclusion principle
. This is in contrast to the boson
s, which do not obey the exclusion principle.
Baryons, along with meson
s, are hadron
s, meaning they are particles composed of quark
s. Quarks have baryon numbers of B = and antiquarks have baryon number of B = −. The term "baryon" usually refers to triquarks - baryons made of three quarks (B = + + = 1). Other exotic baryon
s have been proposed, such as pentaquark
s — baryons made of four quarks and one antiquark (B = + + + − = 1), but their existence is not generally accepted. In theory, heptaquarks (5 quarks, 2 antiquarks), nonaquarks (6 quarks, 3 antiquarks), etc. could also exist.
is matter composed mostly of baryons (by mass), which includes atom
s of any sort (and thus includes nearly all matter that we may encounter or experience
in everyday life, including our bodies). Non-baryonic matter, as implied by the name, is any sort of matter that is not composed primarily of baryons. This might include such ordinary matter as neutrino
s or free electron
s; however, it may also include exotic species of non-baryonic dark matter
, such as supersymmetric particles
, axion
s, or black hole
s. The distinction between baryonic and non-baryonic matter is important in cosmology
, because Big Bang nucleosynthesis
models set tight constraints on the amount of baryonic matter present in the early universe
.
The very existence of baryons is also a significant issue in cosmology because we have assumed that the Big Bang produced a state with equal amounts of baryons and antibaryons. The process by which baryons come to outnumber their antiparticles is called baryogenesis
(in contrast to a process by which lepton
s account for the predominance of matter over antimatter, leptogenesis
).
. Within the prevailing Standard Model
of particle physics, the number of baryons may change in multiples of three due to the action of sphaleron
s, although this is rare and has not been observed under experiment. Some grand unified theories of particle physics also predict that a single proton
can decay, changing the baryon number by one; however, this has not yet been observed under experiment. The excess of baryons over antibaryons in the present universe is thought to be due to non-conservation of baryon number in the very early universe, though this is not well understood.
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.
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 then 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 four Deltas all have different charges ( (uuu), (uud), (udd), (ddd)), but have similar masses (~1,232 MeV/c2) as they are each made of a combination of three u and d quarks. 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 "Delta particle
" had four "charged states", it was said to be of isospin I = . Its "charged states" , , , and , corresponded to the isospin projections I3 = +, I3 = +, I3 = −, and I3 = −, respectively. Another example is the "nucleon particle". As there were two nucleon "charged states", it was said to be of isospin . The positive nucleon (proton) was identified with I3 = + and the neutral nucleon (neutron) with I3 = −. 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 four Deltas and the two nucleons were thought to be the different states of two particles. However in the quark model, Deltas are different states of nucleons (the N++ or N− are forbidden by Pauli's exclusion principle). Isospin, although conveying an inaccurate picture of things, is still used to classify baryons, leading to unnatural and often confusing nomenclature.
flavour 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 octet and decuplet figures on the right). As other quarks were discovered, new quantum numbers were made to have similar description of udc and udb octets and decuplets. Since only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers works well only for octet and decuplet made of one u, one d, and one other quark, and breaks down for the other octets and decuplets (for example, ucb octet and decuplet). 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-Mann–Nishijima formula is equivalent to the expression of charge in terms of quark content:
(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 anywhere.
Quark
s are fermion
ic particles of spin (S = ). Because spin projections varies 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). If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and has only one spin projection (Sz = 0), etc. Since baryons are made of three quarks, their spin vectors can add to make a vector of length S = , which has four spin projections (Sz = +, Sz = +, Sz = −, and Sz = −), or a vector of length S = with two spin projections (Sz = +, and Sz = −).
There is another quantity of 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 baryons with no orbital angular momentum (L = 0), as they correspond to ground state
s—states of minimal energy. Therefore the two groups of baryons most studied are the S = ; L = 0 and S = ; L = 0, which corresponds to J = + and J = +, respectively, although they are not the only ones. It is also possible to obtain J = + particles from S = and L = 2, as well as S = and L = 2. This phenomenon of having multiple particles in the same total angular momentum configuration is called degeneracy
. How to distinguish between these degenerate baryons is an active area of research in baryon spectroscopy.
or parity (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 (in more precise terms, 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 baryons, the parity is related to the orbital angular momentum by the relation:
As a consequence, baryons with no orbital angular momentum (L = 0) all have even parity (P = +).
(I) values and quark
(q) content. There are six groups of baryons—nucleon
, Delta
, Lambda , Sigma
, Xi , and Omega . The rules for classification are defined by the Particle Data Group
. These rules consider the up
, down
and strange
quarks to be light and the charm
, bottom quark
, and top
to be heavy. The rules cover all the particles that can be made from three of each of the six quarks, even though baryons made of t quarks are not expected to exist because of the t quark's short lifetime
. The rules do not cover pentaquarks.
It is also a widespread (but not universal) practice to follow some additional rules when distinguishing between some states that would otherwise have the same symbol.
Quarks carry charge, so knowing the charge of a particle indirectly gives the quark content. For example, the rules above say that a contains a c quark and some combination of two u and/or d quarks. The c quark as a charge of (Q = +), therefore the other two must be a u quark (Q = +), and a d quark (Q = −) to have the correct total charge (Q = +1).
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...
made up of three 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 (as distinct from meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s, which comprise one quark and one antiquark). Baryons and mesons belong to the hadron
Hadron
In particle physics, a hadron is a composite particle made of quarks held together by the strong force...
family, which are the quark-based particles. The name "baryon" comes from the Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
word for "heavy" (βαρύς, barys), because, at the time of their naming, most known particles had lower masses than the baryons.
As quark-based particles, baryons participate in 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...
, whereas 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...
s, which are not quark-based, do not. The most familiar baryons are the 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 and neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
s that make up most of the mass of the visible matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
in the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
. 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...
s (the other major component of the atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
) are leptons. Each baryon 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...
(antibaryon) where quarks are replaced by their corresponding antiquarks. For example, a proton is made of two up quarks and one down quark; and its corresponding antiparticle, the antiproton
Antiproton
The antiproton is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived since any collision with a proton will cause both particles to be annihilated in a burst of energy....
, is made of two up antiquarks and one down antiquark.
Until recently, it was believed that some experiments showed the existence of pentaquark
Pentaquark
A pentaquark is a hypothetical subatomic particle consisting of four quarks and one antiquark bound together . As quarks have a baryon number of +, and antiquarks of −, it would have a total baryon number of 1, thus being classified as an exotic baryon...
s — "exotic" baryons made of four quarks and one antiquark. The particle physics community as a whole did not view their existence as likely in 2006, and in 2008, considered evidence to be overwhelmingly against the existence of the reported pentaquarks.
Background
Baryons are strongly interacting fermionFermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s — that is, they experience the strong nuclear force and are described by Fermi−Dirac statistics, which apply to all particles obeying the Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...
. This is in contrast to the 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, which do not obey the exclusion principle.
Baryons, along with meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s, are hadron
Hadron
In particle physics, a hadron is a composite particle made of quarks held together by the strong force...
s, meaning they are particles composed of 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. Quarks have baryon numbers of B = and antiquarks have baryon number of B = −. The term "baryon" usually refers to triquarks - baryons made of three quarks (B = + + = 1). Other exotic baryon
Exotic baryon
Exotic baryons are hypothetical composite particles which are bound states of 3 quarks and additional elementary particles. This is to be contrasted with ordinary baryons, which are bound states of just 3 quarks. The additional particles may include quarks, antiquarks or gluons.One such exotic...
s have been proposed, such as pentaquark
Pentaquark
A pentaquark is a hypothetical subatomic particle consisting of four quarks and one antiquark bound together . As quarks have a baryon number of +, and antiquarks of −, it would have a total baryon number of 1, thus being classified as an exotic baryon...
s — baryons made of four quarks and one antiquark (B = + + + − = 1), but their existence is not generally accepted. In theory, heptaquarks (5 quarks, 2 antiquarks), nonaquarks (6 quarks, 3 antiquarks), etc. could also exist.
Baryonic matter
Baryonic matterMatter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
is matter composed mostly of baryons (by mass), which includes atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s of any sort (and thus includes nearly all matter that we may encounter or experience
Experience
Experience as a general concept comprises knowledge of or skill in or observation of some thing or some event gained through involvement in or exposure to that thing or event....
in everyday life, including our bodies). Non-baryonic matter, as implied by the name, is any sort of matter that is not composed primarily of baryons. This might include such ordinary matter as neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
s or free 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...
s; however, it may also include exotic species of non-baryonic dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
, such as supersymmetric particles
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
, axion
Axion
The axion is a hypothetical elementary particle postulated by the Peccei-Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics...
s, or black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
s. The distinction between baryonic and non-baryonic matter is important in cosmology
Physical cosmology
Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...
, because Big Bang nucleosynthesis
Big Bang nucleosynthesis
In physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of H-1 during the early phases of the universe...
models set tight constraints on the amount of baryonic matter present in the early universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
.
The very existence of baryons is also a significant issue in cosmology because we have assumed that the Big Bang produced a state with equal amounts of baryons and antibaryons. The process by which baryons come to outnumber their antiparticles is called baryogenesis
Baryogenesis
In physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today.Baryogenesis theories employ...
(in contrast to a process by which 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...
s account for the predominance of matter over antimatter, leptogenesis
Leptogenesis (physics)
In physical cosmology, leptogenesis is the generic term for hypothetical physical processes that produced an asymmetry between leptons and antileptons in the very early universe, resulting in the dominance of leptons over antileptons...
).
Baryogenesis
Experiments are consistent with the number of quarks in the universe being a constant and, to be more specific, the number of baryons being a constant; in technical language, the total baryon number appears to be conservedConservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
. Within the prevailing Standard Model
Standard Model
The 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...
of particle physics, the number of baryons may change in multiples of three due to the action of sphaleron
Sphaleron
A sphaleron is a static solution to the electroweak field equations of the Standard Model of particle physics, and it is involved in processes that violate baryon and lepton number. Such processes cannot be represented by Feynman diagrams, and are therefore called non-perturbative...
s, although this is rare and has not been observed under experiment. Some grand unified theories of particle physics also predict that a single 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....
can decay, changing the baryon number by one; however, this has not yet been observed under experiment. The excess of baryons over antibaryons in the present universe is thought to be due to non-conservation of baryon number in the very early universe, though this is not well understood.
Isospin and charge
The concept of isospin was first proposed by 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...
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.
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 then 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 four Deltas all have different charges ( (uuu), (uud), (udd), (ddd)), but have similar masses (~1,232 MeV/c2) as they are each made of a combination of three u and d quarks. 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 "Delta particle
Delta baryon
The Delta baryons are a family of subatomic hadron particles which have the symbols , , , and and electric charges +2, +1, 0 and -1 elementary charge respectively...
" had four "charged states", it was said to be of isospin I = . Its "charged states" , , , and , corresponded to the isospin projections I3 = +, I3 = +, I3 = −, and I3 = −, respectively. Another example is the "nucleon particle". As there were two nucleon "charged states", it was said to be of isospin . The positive nucleon (proton) was identified with I3 = + and the neutral nucleon (neutron) with I3 = −. 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 four Deltas and the two nucleons were thought to be the different states of two particles. However in the quark model, Deltas are different states of nucleons (the N++ or N− are forbidden by Pauli's exclusion principle). Isospin, although conveying an inaccurate picture of things, is still used to classify baryons, leading to unnatural and often confusing nomenclature.
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...
flavour 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 octet and decuplet figures on the right). As other quarks were discovered, new quantum numbers were made to have similar description of udc and udb octets and decuplets. Since only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers works well only for octet and decuplet made of one u, one d, and one other quark, and breaks down for the other octets and decuplets (for example, ucb octet and decuplet). 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-Mann–Nishijima formula is equivalent to the expression of charge in terms of quark content:
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 anywhere.
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....
ic particles of spin (S = ). Because spin projections varies 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). If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and has only one spin projection (Sz = 0), etc. Since baryons are made of three quarks, their spin vectors can add to make a vector of length S = , which has four spin projections (Sz = +, Sz = +, Sz = −, and Sz = −), or a vector of length S = with two spin projections (Sz = +, and Sz = −).
There is another quantity of 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.
| Spin (S) | Orbital angular momentum (L) | Total angular momentum (J) | Parity (P) (See below) |
Condensed notation (JP) |
|---|---|---|---|---|
| 0 | + | + | ||
| 1 | , | − | −, − | |
| 2 | , | + | +, + | |
| 3 | , | − | −, − | |
| 0 | + | + | ||
| 1 | , , | − | −, −, − | |
| 2 | , , , | + | +, +, +, + | |
| 3 | , , , | − | −, −, −, − |
Particle physicists are most interested in baryons with no orbital angular momentum (L = 0), as they correspond to ground state
Ground state
The 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...
s—states of minimal energy. Therefore the two groups of baryons most studied are the S = ; L = 0 and S = ; L = 0, which corresponds to J = + and J = +, respectively, although they are not the only ones. It is also possible to obtain J = + particles from S = and L = 2, as well as S = and L = 2. This phenomenon of having multiple particles in the same total angular momentum configuration is called degeneracy
Degenerate energy level
In physics, two or more different quantum states are said to be degenerate if they are all at the same energy level. Statistically this means that they are all equally probable of being filled, and in Quantum Mechanics it is represented mathematically by the Hamiltonian for the system having more...
. How to distinguish between these degenerate baryons is an active area of research in baryon 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 intrinsic 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:...
or parity (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 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 (in more precise terms, 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 baryons, the parity is related to the orbital angular momentum by the relation:
As a consequence, baryons with no orbital angular momentum (L = 0) all have even parity (P = +).
Nomenclature
Baryons 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) values 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. There are six groups of baryons—nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
, Delta
Delta baryon
The Delta baryons are a family of subatomic hadron particles which have the symbols , , , and and electric charges +2, +1, 0 and -1 elementary charge respectively...
, Lambda , Sigma
Sigma baryon
The Sigma baryons are a family of subatomic hadron particles which have a +2, +1 or -1 elementary charge or are neutral. They are baryons containing three quarks: two up and/or down quarks, and one third quark, which can be either a strange , a charm , a bottom or a top quark...
, Xi , and Omega . 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...
. These rules consider the up
Up quark
The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
, down
Down quark
The down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...
and strange
Strange quark
The strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...
quarks to be light and the charm
Charm quark
The charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...
, bottom quark
Bottom quark
The bottom quark, also known as the beauty quark, is a third-generation quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...
, and top
Top quark
The top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin-, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
to be heavy. The rules cover all the particles that can be made from three of each of the six quarks, even though baryons made of t quarks are not expected to exist because of the t quark's short lifetime
Top quark
The top quark, also known as the t quark or truth quark, is an elementary particle and a fundamental constituent of matter. Like all quarks, the top quark is an elementary fermion with spin-, and experiences all four fundamental interactions: gravitation, electromagnetism, weak interactions, and...
. The rules do not cover pentaquarks.
- Baryons with three and/or quarks are 's (I = ) or 's (I = ).
- Baryons with two and/or quarks are 's (I = 0) or 's (I = 1). If the third quark is heavy, its identity is given by a subscript.
- Baryons with one or quark are 's (I = ). One or two subscripts are used if one or both of the remaining quarks are heavy.
- Baryons with no or quarks are 's (I = 0), and subscripts indicate any heavy quark content.
- Baryons that decay strongly have their masses as part of their names. For example, Σ0 does not decay strongly, but Δ++(1232) does.
It is also a widespread (but not universal) practice to follow some additional rules when distinguishing between some states that would otherwise have the same symbol.
- Baryons in total angular momentum J = configuration that have the same symbols as their J = counterparts are denoted by an asterisk ( * ).
- Two baryons can be made of three different quarks in J = configuration. In this case, a prime ( ′ ) is used to distinguish between them.
- Exception: When two of the three quarks are one up and one down quark, one baryon is dubbed Λ while the other is dubbed Σ.
Quarks carry charge, so knowing the charge of a particle indirectly gives the quark content. For example, the rules above say that a contains a c quark and some combination of two u and/or d quarks. The c quark as a charge of (Q = +), therefore the other two must be a u quark (Q = +), and a d quark (Q = −) to have the correct total charge (Q = +1).
See also
- Eightfold wayEightfold way (physics)In physics, the Eightfold Way is a term coined by American physicist Murray Gell-Mann for a theory organizing subatomic baryons and mesons into octets...
- List of baryons
- List of particles
- MesonMesonIn particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
- Timeline of particle discoveriesTimeline of particle discoveriesThis is a timeline of subatomic particle discoveries, including all particles thus far discovered which appear to be elementary given the best available evidence...
External links
- Particle Data Group—Review of Particle Physics (2008).
- Georgia State University—HyperPhysics
- Baryons made thinkable, an interactive visualisation allowing physical properties to be compared