In particle physics, a baryon is a type of composite subatomic particle that contains an odd number of valence quarks, conventionally three.Protons and neutrons are examples of baryons; because baryons are composed of quarks, they belong to the hadron family of particles. Baryons are also classified as fermions because they have half-integer spin.
The name "baryon", introduced by Abraham Pais,: 457 comes from the Greek word for "heavy" (βαρύς, barýs), because, at the time of their naming, most known elementary particles had lower masses than the baryons. Each baryon has a corresponding antiparticle (antibaryon) where their corresponding antiquarks replace quarks. 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.
Baryons participate in the residual strong force, which is mediated by particles known as mesons. The most familiar baryons are protons and neutrons, both of which contain three quarks, and for this reason they are sometimes called triquarks. These particles make up most of the mass of the visible matter in the universe and compose the nucleus of every atom (electrons, the other major component of the atom, are members of a different family of particles called leptons; leptons do not interact via the strong force). Exotic baryons containing five quarks, called pentaquarks, have also been discovered and studied.
A census of the Universe's baryons indicates that 10% of them could be found inside galaxies, 50 to 60% in the circumgalactic medium, and the remaining 30 to 40% could be located in the warm–hot intergalactic medium (WHIM).
Background
Baryons are strongly interacting fermions; that is, they are acted on by 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 bosons, which do not obey the exclusion principle.
Baryons, alongside mesons, are hadrons, composite particles composed of quarks. Quarks have baryon numbers of B = 1/3 and antiquarks have baryon numbers of B = −1/3. The term "baryon" usually refers to triquarks—baryons made of three quarks (B = 1/3 + 1/3 + 1/3 = 1).
Other exotic baryons have been proposed, such as pentaquarks—baryons made of four quarks and one antiquark (B = 1/3 + 1/3 + 1/3 + 1/3 − 1/3 = 1), but their existence is not generally accepted. 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. However, in July 2015, the LHCb experiment observed two resonances consistent with pentaquark states in the Λ0
b → J/ψK−
p decay, with a combined statistical significance of 15σ.
In theory, heptaquarks (5 quarks, 2 antiquarks), nonaquarks (6 quarks, 3 antiquarks), etc. could also exist.
Baryonic matter
Nearly all matter that may be encountered or experienced in everyday life is baryonic matter, which includes atoms of any sort, and provides them with the property of mass. Non-baryonic matter, as implied by the name, is any sort of matter that is not composed primarily of baryons. This might include neutrinos and free electrons, dark matter, supersymmetric particles, axions, and black holes.
The very existence of baryons is also a significant issue in cosmology because it is assumed that the Big Bang produced a state with equal amounts of baryons and antibaryons. The process by which baryons came to outnumber their antiparticles is called baryogenesis.
Baryogenesis
Experiments are consistent with the number of quarks in the universe being conserved alongside the total baryon number, with antibaryons being counted as negative quantities. Within the prevailing Standard Model of particle physics, the number of baryons may change in multiples of three due to the action of sphalerons, 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.
Properties
Isospin and charge
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 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 u and d quarks. Since 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 +2/3 while d quarks carry charge −1/3. For example, the four Deltas all have different charges (
Δ++
(uuu),
Δ+
(uud),
Δ0
(udd),
Δ−
(ddd)), but have similar masses (~1,232 MeV/c2) as they are each made of a combination of three u or 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 = 3/2. Its "charged states"
Δ++
,
Δ+
,
Δ0
, and
Δ−
, corresponded to the isospin projections I3 = +3/2, I3 = +1/2, I3 = −1/2, and I3 = −3/2, respectively. Another example is the "nucleon particle". As there were two nucleon "charged states", it was said to be of isospin 1/2. The positive nucleon
N+
(proton) was identified with I3 = +1/2 and the neutral nucleon
N0
(neutron) with I3 = −1/2. It was later noted that the isospin projections were related to the up and down quark content of particles by the relation:
![{\displaystyle I_{\mathrm {3} }={\frac {1}{2}}[(n_{\mathrm {u} }-n_{\mathrm {\bar {u}} })-(n_{\mathrm {d} }-n_{\mathrm {\bar {d}} })],}](https://www.english.nina.az/wikipedia/image/aHR0cHM6Ly93d3cuZW5nbGlzaC5uaW5hLmF6L3dpa2lwZWRpYS9pbWFnZS9hSFIwY0hNNkx5OTNhV3RwYldWa2FXRXViM0puTDJGd2FTOXlaWE4wWDNZeEwyMWxaR2xoTDIxaGRHZ3ZjbVZ1WkdWeUwzTjJaeTg1WldVek9UVTRZekUzWTJaaE9ERTJOalF4WlRZeU1XSXdOR0ZpWm1Ka09HWmtPRGcyT0RsaC5zdmc=.svg)
where the n's 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 strangeness 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 the same way 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:
![{\displaystyle Q={\frac {2}{3}}\left[(n_{\mathrm {u} }-n_{\mathrm {\bar {u}} })+(n_{\mathrm {c} }-n_{\mathrm {\bar {c}} })+(n_{\mathrm {t} }-n_{\mathrm {\bar {t}} })\right]-{\frac {1}{3}}\left[(n_{\mathrm {d} }-n_{\mathrm {\bar {d}} })+(n_{\mathrm {s} }-n_{\mathrm {\bar {s}} })+(n_{\mathrm {b} }-n_{\mathrm {\bar {b}} })\right].}](https://www.english.nina.az/wikipedia/image/aHR0cHM6Ly93d3cuZW5nbGlzaC5uaW5hLmF6L3dpa2lwZWRpYS9pbWFnZS9hSFIwY0hNNkx5OTNhV3RwYldWa2FXRXViM0puTDJGd2FTOXlaWE4wWDNZeEwyMWxaR2xoTDIxaGRHZ3ZjbVZ1WkdWeUwzTjJaeTgxTVRjM1l6ZGpNRE16Tm1JeU9HVXhNRGcxTkdFd01HRm1aakZrWkRJM05EUTJOREZtTnpJNC5zdmc=.svg)
Spin, orbital angular momentum, and total angular momentum
Spin (quantum number S) is a vector quantity that represents the "intrinsic" angular momentum of a particle. It comes in increments of 1/2 ħ (pronounced "h-bar"). 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.
Quarks are fermionic particles of spin 1/2 (S = 1/2). Because spin projections vary in increments of 1 (that is 1 ħ), a single quark has a spin vector of length 1/2, and has two spin projections (Sz = +1/2 and Sz = −1/2). 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 = 3/2, which has four spin projections (Sz = +3/2, Sz = +1/2, Sz = −1/2, and Sz = −3/2), or a vector of length S = 1/2 with two spin projections (Sz = +1/2, and Sz = −1/2).
There is another quantity of angular momentum, called the orbital angular momentum (azimuthal 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 (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 J = |L − S| to J = |L + S|, in increments of 1.
| Spin, S | Orbital angular momentum, L | Total angular momentum, J | Parity, P | Condensed notation, JP |
|---|---|---|---|---|
| 1/2 | 0 | 1/2 | + | 1/2+ |
| 1 | 3/2, 1/2 | − | 3/2−, 1/2− | |
| 2 | 5/2, 3/2 | + | 5/2+, 3/2+ | |
| 3 | 7/2, 5/2 | − | 7/2−, 5/2− | |
| 3/2 | 0 | 3/2 | + | 3/2+ |
| 1 | 5/2, 3/2, 1/2 | − | 5/2−, 3/2−, 1/2− | |
| 2 | 7/2, 5/2, 3/2, 1/2 | + | 7/2+, 5/2+, 3/2+, 1/2+ | |
| 3 | 9/2, 7/2, 5/2, 3/2 | − | 9/2−, 7/2−, 5/2−, 3/2− |
Particle physicists are most interested in baryons with no orbital angular momentum (L = 0), as they correspond to ground states—states of minimal energy. Therefore, the two groups of baryons most studied are the S = 1/2; L = 0 and S = 3/2; L = 0, which corresponds to J = 1/2+ and J = 3/2+, respectively, although they are not the only ones. It is also possible to obtain J = 3/2+ particles from S = 1/2 and L = 2, as well as S = 3/2 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.
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 parity" or simply "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, 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: 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 isospin (I) values and quark (q) content. There are six groups of baryons: nucleon (
N
), Delta (
Δ
), Lambda (
Λ
), Sigma (
Σ
), Xi (
Ξ
), and Omega (
Ω
). The rules for classification are defined by the Particle Data Group. These rules consider the up (
u
), down (
d
) and strange (
s
) quarks to be light and the charm (
c
), bottom (
b
), and top (
t
) quarks 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 top quarks are not expected to exist because of the top quark's short lifetime. The rules do not cover pentaquarks.
- Baryons with (any combination of) three
u
and/or
d
quarks are
N
s (I = 1/2) or
Δ
baryons (I = 3/2). - Baryons containing two
u
and/or
d
quarks are
Λ
baryons (I = 0) or
Σ
baryons (I = 1). If the third quark is heavy, its identity is given by a subscript. - Baryons containing one
u
or
d
quark are
Ξ
baryons (I = 1/2). One or two subscripts are used if one or both of the remaining quarks are heavy. - Baryons containing no
u
or
d
quarks are
Ω
baryons (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 = 3/2 configuration that have the same symbols as their J = 1/2 counterparts are denoted by an asterisk ( * ).
- Two baryons can be made of three different quarks in J = 1/2 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 a charge, so knowing the charge of a particle indirectly gives the quark content. For example, the rules above say that a
Λ+
c contains a c quark and some combination of two u and/or d quarks. The c quark has a charge of (Q = +2/3), therefore the other two must be a u quark (Q = +2/3), and a d quark (Q = −1/3) to have the correct total charge (Q = +1).
See also
- Eightfold way
- List of baryons
- Meson
- Timeline of particle discoveries
Citations
- Gell-Mann, M. (1964). "A schematic model of baryons and mesons". Physics Letters. 8 (3): 214–215. Bibcode:1964PhL.....8..214G. doi:10.1016/S0031-9163(64)92001-3.
- ; Nishijima, Kazuhiko (November 1953). "Charge Independence for V-particles". Progress of Theoretical Physics. 10 (5): 581–582. Bibcode:1953PThPh..10..581N. doi:10.1143/PTP.10.581.
The 'baryon' is the collective name for the members of the nucleon family. This name is due to Pais. See ref. (6).
- Pais, A. (1953). On the baryon-meson-photon system. Progress of Theoretical Physics, 10(4), 457-469.
- J. Michael Shull; et al. (2012). "The Baryon Census in a Multiphase Intergalactic Medium: 30% of the Baryons May Still be Missing". Vol. 759, no. 1. The Astrophysical Journal. doi:10.1088/0004-637X/759/1/23.
- J.-P. Macquart; et al. (2020). "A census of baryons in the Universe from localized fast radio bursts". Vol. 581. Nature. pp. 391–395. doi:10.1038/s41586-020-2300-2.
- H. Muir (2003)
- K. Carter (2003)
- W.-M. Yao et al. (2006): Particle listings – Θ+
- C. Amsler et al. (2008): Pentaquarks
- LHCb (14 July 2015). "Observation of particles composed of five quarks, pentaquark-charmonium states, seen in Λ0
b → J/ψpK− decays". CERN. Retrieved 2015-07-14. - R. Aaij et al. (LHCb collaboration) (2015). "Observation of J/ψp resonances consistent with pentaquark states in Λ0
b→J/ψK−p decays". Physical Review Letters. 115 (7): 072001. arXiv:1507.03414. Bibcode:2015PhRvL.115g2001A. doi:10.1103/PhysRevLett.115.072001. PMID 26317714. S2CID 119204136. - "11.3: Particle Conservation Laws". LibreTexts. November 1, 2016. Archived from the original on August 10, 2022. Retrieved December 26, 2023.
- W. Heisenberg (1932)
- E. Wigner (1937)
- M. Gell-Mann (1964)
- S.S.M. Wong (1998a)
- R. Shankar (1994)
- H. Garcilazo et al. (2007)
- D.M. Manley (2005)
- S.S.M. Wong (1998b)
- C. Amsler et al. (2008): Naming scheme for hadrons
General references
- C. Amsler et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1–1340. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. PMID 10020536. S2CID 227119789. Archived (PDF) from the original on 2022-10-09.
- H. Garcilazo; J. Vijande & A. Valcarce (2007). "Faddeev study of heavy-baryon spectroscopy". Journal of Physics G. 34 (5): 961–976. arXiv:hep-ph/0703257. Bibcode:2007hep.ph....3257G. doi:10.1088/0954-3899/34/5/014. S2CID 15445714.
- K. Carter (2006). "The rise and fall of the pentaquark". Fermilab and SLAC. Archived from the original on 2007-07-08. Retrieved 2008-05-27.
- W.-M. Yao et al. (Particle Data Group) (2006). "Review of Particle Physics". Journal of Physics G. 33 (1): 1–1232. arXiv:astro-ph/0601168. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001.
- D.M. Manley (2005). "Status of baryon spectroscopy". Journal of Physics: Conference Series. 5 (1): 230–237. Bibcode:2005JPhCS...9..230M. doi:10.1088/1742-6596/9/1/043.
- H. Muir (2003). "Pentaquark discovery confounds sceptics". New Scientist. Retrieved 2008-05-27.
- S.S.M. Wong (1998a). "Chapter 2—Nucleon Structure". Introductory Nuclear Physics (2nd ed.). New York (NY): John Wiley & Sons. pp. 21–56. ISBN 978-0-471-23973-4.
- S.S.M. Wong (1998b). "Chapter 3—The Deuteron". Introductory Nuclear Physics (2nd ed.). New York (NY): John Wiley & Sons. pp. 57–104. ISBN 978-0-471-23973-4.
- R. Shankar (1994). Principles of Quantum Mechanics (2nd ed.). New York (NY): Plenum Press. ISBN 978-0-306-44790-7.
- E. Wigner (1937). "On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei". Physical Review. 51 (2): 106–119. Bibcode:1937PhRv...51..106W. doi:10.1103/PhysRev.51.106.
- M. Gell-Mann (1964). "A Schematic of Baryons and Mesons". Physics Letters. 8 (3): 214–215. Bibcode:1964PhL.....8..214G. doi:10.1016/S0031-9163(64)92001-3.
- W. Heisenberg (1932). "Über den Bau der Atomkerne I". Zeitschrift für Physik (in German). 77 (1–2): 1–11. Bibcode:1932ZPhy...77....1H. doi:10.1007/BF01342433. S2CID 186218053.
- W. Heisenberg (1932). "Über den Bau der Atomkerne II". Zeitschrift für Physik (in German). 78 (3–4): 156–164. Bibcode:1932ZPhy...78..156H. doi:10.1007/BF01337585. S2CID 186221789.
- W. Heisenberg (1932). "Über den Bau der Atomkerne III". Zeitschrift für Physik (in German). 80 (9–10): 587–596. Bibcode:1933ZPhy...80..587H. doi:10.1007/BF01335696. S2CID 126422047.
External links
- Particle Data Group—Review of Particle Physics (2018).
- Georgia State University—HyperPhysics
- Baryons made thinkable, an interactive visualisation allowing physical properties to be compared
In particle physics a baryon is a type of composite subatomic particle that contains an odd number of valence quarks conventionally three Protons and neutrons are examples of baryons because baryons are composed of quarks they belong to the hadron family of particles Baryons are also classified as fermions because they have half integer spin The name baryon introduced by Abraham Pais 457 comes from the Greek word for heavy barys barys because at the time of their naming most known elementary particles had lower masses than the baryons Each baryon has a corresponding antiparticle antibaryon where their corresponding antiquarks replace quarks 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 Baryons participate in the residual strong force which is mediated by particles known as mesons The most familiar baryons are protons and neutrons both of which contain three quarks and for this reason they are sometimes called triquarks These particles make up most of the mass of the visible matter in the universe and compose the nucleus of every atom electrons the other major component of the atom are members of a different family of particles called leptons leptons do not interact via the strong force Exotic baryons containing five quarks called pentaquarks have also been discovered and studied A census of the Universe s baryons indicates that 10 of them could be found inside galaxies 50 to 60 in the circumgalactic medium and the remaining 30 to 40 could be located in the warm hot intergalactic medium WHIM BackgroundBaryons are strongly interacting fermions that is they are acted on by 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 bosons which do not obey the exclusion principle Baryons alongside mesons are hadrons composite particles composed of quarks Quarks have baryon numbers of B 1 3 and antiquarks have baryon numbers of B 1 3 The term baryon usually refers to triquarks baryons made of three quarks B 1 3 1 3 1 3 1 Other exotic baryons have been proposed such as pentaquarks baryons made of four quarks and one antiquark B 1 3 1 3 1 3 1 3 1 3 1 but their existence is not generally accepted 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 However in July 2015 the LHCb experiment observed two resonances consistent with pentaquark states in the L0 b J psK p decay with a combined statistical significance of 15s In theory heptaquarks 5 quarks 2 antiquarks nonaquarks 6 quarks 3 antiquarks etc could also exist Baryonic matterNearly all matter that may be encountered or experienced in everyday life is baryonic matter which includes atoms of any sort and provides them with the property of mass Non baryonic matter as implied by the name is any sort of matter that is not composed primarily of baryons This might include neutrinos and free electrons dark matter supersymmetric particles axions and black holes The very existence of baryons is also a significant issue in cosmology because it is assumed that the Big Bang produced a state with equal amounts of baryons and antibaryons The process by which baryons came to outnumber their antiparticles is called baryogenesis BaryogenesisExperiments are consistent with the number of quarks in the universe being conserved alongside the total baryon number with antibaryons being counted as negative quantities Within the prevailing Standard Model of particle physics the number of baryons may change in multiples of three due to the action of sphalerons 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 PropertiesIsospin and charge Combinations of three u d or s quarks forming baryons with a spin 3 2 form the uds baryon decupletCombinations of three u d or s quarks forming baryons with a spin 1 2 form the uds baryon octet 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 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 u and d quarks Since 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 2 3 while d quarks carry charge 1 3 For example the four Deltas all have different charges D uuu D uud D0 udd D ddd but have similar masses 1 232 MeV c2 as they are each made of a combination of three u or 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 3 2 Its charged states D D D0 and D corresponded to the isospin projections I3 3 2 I3 1 2 I3 1 2 and I3 3 2 respectively Another example is the nucleon particle As there were two nucleon charged states it was said to be of isospin 1 2 The positive nucleon N proton was identified with I3 1 2 and the neutral nucleon N0 neutron with I3 1 2 It was later noted that the isospin projections were related to the up and down quark content of particles by the relation I3 12 nu nu nd nd displaystyle I mathrm 3 frac 1 2 n mathrm u n mathrm bar u n mathrm d n mathrm bar d where the n s 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 strangeness 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 the same way 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 Q I3 12 B S C B T displaystyle Q I 3 frac 1 2 left B S C B prime T right 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 S ns ns C nc nc B nb nb T nt nt displaystyle begin aligned S amp left n mathrm s n mathrm bar s right C amp left n mathrm c n mathrm bar c right B prime amp left n mathrm b n mathrm bar b right T amp left n mathrm t n mathrm bar t right end aligned meaning that the Gell Mann Nishijima formula is equivalent to the expression of charge in terms of quark content Q 23 nu nu nc nc nt nt 13 nd nd ns ns nb nb displaystyle Q frac 2 3 left n mathrm u n mathrm bar u n mathrm c n mathrm bar c n mathrm t n mathrm bar t right frac 1 3 left n mathrm d n mathrm bar d n mathrm s n mathrm bar s n mathrm b n mathrm bar b right Spin orbital angular momentum and total angular momentum Spin quantum number S is a vector quantity that represents the intrinsic angular momentum of a particle It comes in increments of 1 2 ħ pronounced h bar 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 Quarks are fermionic particles of spin 1 2 S 1 2 Because spin projections vary in increments of 1 that is 1 ħ a single quark has a spin vector of length 1 2 and has two spin projections Sz 1 2 and Sz 1 2 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 3 2 which has four spin projections Sz 3 2 Sz 1 2 Sz 1 2 and Sz 3 2 or a vector of length S 1 2 with two spin projections Sz 1 2 and Sz 1 2 There is another quantity of angular momentum called the orbital angular momentum azimuthal 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 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 J L S to J L S in increments of 1 Baryon angular momentum quantum numbers for L 0 1 2 3 Spin S Orbital angular momentum L Total angular momentum J Parity P Condensed notation JP 1 2 0 1 2 1 2 1 3 2 1 2 3 2 1 2 2 5 2 3 2 5 2 3 2 3 7 2 5 2 7 2 5 2 3 2 0 3 2 3 2 1 5 2 3 2 1 2 5 2 3 2 1 2 2 7 2 5 2 3 2 1 2 7 2 5 2 3 2 1 2 3 9 2 7 2 5 2 3 2 9 2 7 2 5 2 3 2 Particle physicists are most interested in baryons with no orbital angular momentum L 0 as they correspond to ground states states of minimal energy Therefore the two groups of baryons most studied are the S 1 2 L 0 and S 3 2 L 0 which corresponds to J 1 2 and J 3 2 respectively although they are not the only ones It is also possible to obtain J 3 2 particles from S 1 2 and L 2 as well as S 3 2 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 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 parity or simply 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 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 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 P 1 L displaystyle P 1 L As a consequence baryons with no orbital angular momentum L 0 all have even parity P NomenclatureBaryons are classified into groups according to their isospin I values and quark q content There are six groups of baryons nucleon N Delta D Lambda L Sigma S Xi 3 and Omega W The rules for classification are defined by the Particle Data Group These rules consider the up u down d and strange s quarks to be light and the charm c bottom b and top t quarks 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 top quarks are not expected to exist because of the top quark s short lifetime The rules do not cover pentaquarks Baryons with any combination of three u and or d quarks are N s I 1 2 or D baryons I 3 2 Baryons containing two u and or d quarks are L baryons I 0 or S baryons I 1 If the third quark is heavy its identity is given by a subscript Baryons containing one u or d quark are 3 baryons I 1 2 One or two subscripts are used if one or both of the remaining quarks are heavy Baryons containing no u or d quarks are W baryons I 0 and subscripts indicate any heavy quark content Baryons that decay strongly have their masses as part of their names For example S0 does not decay strongly but D 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 3 2 configuration that have the same symbols as their J 1 2 counterparts are denoted by an asterisk Two baryons can be made of three different quarks in J 1 2 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 L while the other is dubbed S Quarks carry a charge so knowing the charge of a particle indirectly gives the quark content For example the rules above say that a L c contains a c quark and some combination of two u and or d quarks The c quark has a charge of Q 2 3 therefore the other two must be a u quark Q 2 3 and a d quark Q 1 3 to have the correct total charge Q 1 See alsoEightfold way List of baryons Meson Timeline of particle discoveriesCitationsGell Mann M 1964 A schematic model of baryons and mesons Physics Letters 8 3 214 215 Bibcode 1964PhL 8 214G doi 10 1016 S0031 9163 64 92001 3 Nishijima Kazuhiko November 1953 Charge Independence for V particles Progress of Theoretical Physics 10 5 581 582 Bibcode 1953PThPh 10 581N doi 10 1143 PTP 10 581 The baryon is the collective name for the members of the nucleon family This name is due to Pais See ref 6 Pais A 1953 On the baryon meson photon system Progress of Theoretical Physics 10 4 457 469 J Michael Shull et al 2012 The Baryon Census in a Multiphase Intergalactic Medium 30 of the Baryons May Still be Missing Vol 759 no 1 The Astrophysical Journal doi 10 1088 0004 637X 759 1 23 J P Macquart et al 2020 A census of baryons in the Universe from localized fast radio bursts Vol 581 Nature pp 391 395 doi 10 1038 s41586 020 2300 2 H Muir 2003 K Carter 2003 W M Yao et al 2006 Particle listings 8 C Amsler et al 2008 Pentaquarks LHCb 14 July 2015 Observation of particles composed of five quarks pentaquark charmonium states seen in L0 b J pspK decays CERN Retrieved 2015 07 14 R Aaij et al LHCb collaboration 2015 Observation of J psp resonances consistent with pentaquark states in L0 b J psK p decays Physical Review Letters 115 7 072001 arXiv 1507 03414 Bibcode 2015PhRvL 115g2001A doi 10 1103 PhysRevLett 115 072001 PMID 26317714 S2CID 119204136 11 3 Particle Conservation Laws LibreTexts November 1 2016 Archived from the original on August 10 2022 Retrieved December 26 2023 W Heisenberg 1932 E Wigner 1937 M Gell Mann 1964 S S M Wong 1998a R Shankar 1994 H Garcilazo et al 2007 D M Manley 2005 S S M Wong 1998b C Amsler et al 2008 Naming scheme for hadronsGeneral referencesC Amsler et al Particle Data Group 2008 Review of Particle Physics PDF Physics Letters B 667 1 1 1340 Bibcode 2008PhLB 667 1A doi 10 1016 j physletb 2008 07 018 hdl 1854 LU 685594 PMID 10020536 S2CID 227119789 Archived PDF from the original on 2022 10 09 H Garcilazo J Vijande amp A Valcarce 2007 Faddeev study of heavy baryon spectroscopy Journal of Physics G 34 5 961 976 arXiv hep ph 0703257 Bibcode 2007hep ph 3257G doi 10 1088 0954 3899 34 5 014 S2CID 15445714 K Carter 2006 The rise and fall of the pentaquark Fermilab and SLAC Archived from the original on 2007 07 08 Retrieved 2008 05 27 W M Yao et al Particle Data Group 2006 Review of Particle Physics Journal of Physics G 33 1 1 1232 arXiv astro ph 0601168 Bibcode 2006JPhG 33 1Y doi 10 1088 0954 3899 33 1 001 D M Manley 2005 Status of baryon spectroscopy Journal of Physics Conference Series 5 1 230 237 Bibcode 2005JPhCS 9 230M doi 10 1088 1742 6596 9 1 043 H Muir 2003 Pentaquark discovery confounds sceptics New Scientist Retrieved 2008 05 27 S S M Wong 1998a Chapter 2 Nucleon Structure Introductory Nuclear Physics 2nd ed New York NY John Wiley amp Sons pp 21 56 ISBN 978 0 471 23973 4 S S M Wong 1998b Chapter 3 The Deuteron Introductory Nuclear Physics 2nd ed New York NY John Wiley amp Sons pp 57 104 ISBN 978 0 471 23973 4 R Shankar 1994 Principles of Quantum Mechanics 2nd ed New York NY Plenum Press ISBN 978 0 306 44790 7 E Wigner 1937 On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei Physical Review 51 2 106 119 Bibcode 1937PhRv 51 106W doi 10 1103 PhysRev 51 106 M Gell Mann 1964 A Schematic of Baryons and Mesons Physics Letters 8 3 214 215 Bibcode 1964PhL 8 214G doi 10 1016 S0031 9163 64 92001 3 W Heisenberg 1932 Uber den Bau der Atomkerne I Zeitschrift fur Physik in German 77 1 2 1 11 Bibcode 1932ZPhy 77 1H doi 10 1007 BF01342433 S2CID 186218053 W Heisenberg 1932 Uber den Bau der Atomkerne II Zeitschrift fur Physik in German 78 3 4 156 164 Bibcode 1932ZPhy 78 156H doi 10 1007 BF01337585 S2CID 186221789 W Heisenberg 1932 Uber den Bau der Atomkerne III Zeitschrift fur Physik in German 80 9 10 587 596 Bibcode 1933ZPhy 80 587H doi 10 1007 BF01335696 S2CID 126422047 External linksParticle Data Group Review of Particle Physics 2018 Georgia State University HyperPhysics Baryons made thinkable an interactive visualisation allowing physical properties to be compared
