Editing Baryon

{{short description|Hadron (subatomic particle) that is composed of three quarks}}
{{distinguish|Barium}}
{{Redirect|Baryonic|the dinosaur|Baryonyx}}
{{Standard model of particle physics}}

In [[particle physics]], a '''baryon''' is a type of [[composite particle|composite]] [[subatomic particle]] that contains an odd number of [[valence quark]]s, conventionally three.<ref name="Gell-Mann 1964">{{cite journal |doi=10.1016/S0031-9163(64)92001-3 |bibcode=1964PhL.....8..214G |title=A schematic model of baryons and mesons |journal=Physics Letters |volume=8 |issue=3 |pages=214–215 |last1=Gell-Mann |first1=M. |year=1964 }}</ref> [[proton|Protons]] and [[neutron|neutrons]] are examples of baryons; because baryons are composed of [[quark]]s, they belong to the [[hadron]] [[list of particles|family of particles]]. Baryons are also classified as [[fermion]]s because they have half-integer [[Spin (physics)|spin]].

The name "baryon", introduced by [[Abraham Pais]],<ref>{{cite journal |last1=Nakano |first1=Tadao |author-link1=Tadao Nakano |last2=Nishijima |first2=Kazuhiko |author-link2=Kazuhiko Nishijima |date=November 1953 |title=Charge Independence for ''V''-particles |journal=Progress of Theoretical Physics |doi=10.1143/PTP.10.581 |volume=10 |issue=5 |pages=581–582 |quote=The 'baryon' is the collective name for the members of the nucleon family. This name is due to [[Abraham Pais|Pais]]. See ref. (6).|doi-access=free |bibcode=1953PThPh..10..581N }}</ref><ref>Pais, A. (1953). On the baryon-meson-photon system. Progress of Theoretical Physics, 10(4), 457-469.</ref>{{rp|457|q=... it seems practical to have a collective name for these particles and other which possibly may still be discovered and which may also have to be taken along in the conservation principle just mentioned. It is proposed to use the fitting name "baryon" for this purpose.}} comes from the [[Ancient Greek|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 quark]]s 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 [[force carrier|mediated]] by particles known as [[meson]]s. The most familiar baryons are [[proton]]s and [[neutron]]s, 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 [[atomic nucleus|nucleus]] of every [[atom]] ([[electron]]s, the other major component of the atom, are members of a different family of particles called [[lepton]]s; leptons do not interact via the strong force). [[Exotic baryon]]s containing five quarks, called [[pentaquark]]s, 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 [[wikt:circumgalactic medium|circumgalactic medium]],<ref>{{cite news<!--|authors=J. Michael Shull; Britton D. Smith and Charles W. Danforth-->|author=J. Michael Shull|display-authors=etal|title=The Baryon Census in a Multiphase Intergalactic Medium: 30% of the Baryons May Still be Missing|publisher=The Astrophysical Journal|year=2012|volume=759|issue=1|doi=10.1088/0004-637X/759/1/23}}</ref> and the remaining 30 to 40% could be located in the [[warm–hot intergalactic medium]] (WHIM).<ref>{{cite news<!--|authors=J.-P. Macquart; J. X. Prochaska; M. McQuinn; K. W. Bannister; S. Bhandari; C. K. Day; A. T. Deller; R. D. Ekers; C. W. James; L. Marnoch; S. Osłowski; C. Phillips; S. D. Ryder; D. R. Scott; R. M. Shannon & N. Tejos -->|author=J.-P. Macquart|display-authors=etal|title=A census of baryons in the Universe from localized fast radio bursts|publisher=Nature|year=2020|volume=581|pages=391–395|doi=10.1038/s41586-020-2300-2}}</ref>

== Background ==
Baryons are strongly interacting [[fermion]]s; 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 [[boson]]s, which do not obey the exclusion principle.

Baryons, alongside [[meson]]s, are [[hadron]]s, composite particles composed of [[quark]]s. Quarks have [[baryon number]]s of ''B''&nbsp;=&nbsp;{{sfrac|1|3}} and antiquarks have baryon numbers of ''B''&nbsp;=&nbsp;−{{sfrac|1|3}}. The term "baryon" usually refers to ''triquarks''—baryons made of three quarks (''B''&nbsp;=&nbsp;{{sfrac|1|3}}&nbsp;+&nbsp;{{sfrac|1|3}}&nbsp;+&nbsp;{{sfrac|1|3}}&nbsp;=&nbsp;1).

Other [[exotic baryon]]s have been proposed, such as [[pentaquark]]s—baryons made of four quarks and one antiquark (''B''&nbsp;=&nbsp;{{sfrac|1|3}}&nbsp;+&nbsp;{{sfrac|1|3}}&nbsp;+&nbsp;{{sfrac|1|3}}&nbsp;+&nbsp;{{sfrac|1|3}}&nbsp;−&nbsp;{{sfrac|1|3}}&nbsp;=&nbsp;1),<ref>H. Muir (2003)</ref><ref>K. Carter (2003)</ref> but their existence is not generally accepted. The particle physics community as a whole did not view their existence as likely in 2006,<ref name=PDGPentaquarks2006>W.-M. Yao et al. (2006): [http://pdg.lbl.gov/2006/reviews/theta_b152.pdf Particle listings – Θ<sup>+</sup>]</ref> and in 2008, considered evidence to be overwhelmingly against the existence of the reported pentaquarks.<ref name=PDGPentaquarks2008>C. Amsler et al. (2008): [http://pdg.lbl.gov/2008/reviews/pentaquarks_b801.pdf Pentaquarks]</ref> However, in July 2015, the [[LHCb]] experiment observed two resonances consistent with pentaquark states in the Λ{{su|p=0|b=b}} → J/ψK{{su|p=−}}p decay, with a combined [[statistical significance]] of 15σ<!-- YES, FIFTEEN SIGMA. See Talk:Pentaquark-->.<ref name="LHCb-public">
{{cite web
 |author=LHCb
 |date=14 July 2015
 |title=Observation of particles composed of five quarks, pentaquark-charmonium states, seen in Λ{{su|b=b|p=0}} → J/ψpK<sup>−</sup> decays.
 |url=http://lhcb-public.web.cern.ch/lhcb-public/Welcome.html#Penta
 |publisher=[[CERN]]
 |access-date=2015-07-14
}}</ref><ref name="LHCb2015">
{{cite journal
 |author=R. Aaij et al. ([[LHCb]] collaboration)
 |year=2015
 |title=Observation of J/ψp resonances consistent with pentaquark states in Λ{{su|p=0|b=b→J/ψK}}<sup>−</sup>p decays
 |journal=[[Physical Review Letters]]
 |volume=115 |issue=7
 |pages=072001
 |doi=10.1103/PhysRevLett.115.072001
 |bibcode = 2015PhRvL.115g2001A |arxiv = 1507.03414
 |pmid=26317714 |s2cid=119204136
}}</ref>

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 [[atom]]s 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 [[neutrino]]s and free [[electron]]s, [[dark matter]], [[supersymmetry|supersymmetric particles]], [[axion]]s, and [[black hole]]s.

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 [[antiparticle]]s is called [[baryogenesis]].

== Baryogenesis ==
{{Main|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.<ref>{{Cite web |date=November 1, 2016 |title=11.3: Particle Conservation Laws |url=https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/11%3A_Particle_Physics_and_Cosmology/11.03%3A_Particle_Conservation_Laws |url-status=live |archive-url=https://web.archive.org/web/20220810163918/https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/11%3A_Particle_Physics_and_Cosmology/11.03%3A_Particle_Conservation_Laws |archive-date=August 10, 2022 |access-date=December 26, 2023 |website=[[LibreTexts]]}}</ref> 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 theory|grand unified theories]] of particle physics also predict that a single [[proton]] can [[Proton decay|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 ===
{{Main|Isospin}}

[[File:Baryon-decuplet-small.svg|thumb|200px|
Combinations of three '''[[up quark|u]], [[down quark|d]]''' or '''[[strange quark|s]]''' quarks forming baryons with a spin-{{sfrac|3|2}} form the ''[[Eightfold way (physics)|uds baryon decuplet]]'']]
[[File:Baryon-octet-small.svg|thumb|200px|Combinations of three '''[[up quark|u]], [[down quark|d]]''' or '''[[strange quark|s]]''' quarks forming baryons with a spin-{{sfrac|1|2}} form the ''[[Eightfold way (physics)|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]].<ref>W. Heisenberg (1932)</ref> 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.<ref>E. Wigner (1937)</ref>

This belief lasted until [[Murray Gell-Mann]] proposed the [[quark model]] in 1964 (containing originally only the u, d, and s quarks).<ref>M. Gell-Mann (1964)</ref> 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 +{{sfrac|2|3}} while d quarks carry charge −{{sfrac|1|3}}. For example, the four [[Delta baryon|Deltas]] all have different charges ({{SubatomicParticle|Delta++}} (uuu), {{SubatomicParticle|Delta+}} (uud), {{SubatomicParticle|Delta0}} (udd), {{SubatomicParticle|Delta-}} (ddd)), but have similar masses (~1,232&nbsp;MeV/c<sup>2</sup>) 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 "[[Quantum state|charged state]]". Since the "[[Delta baryon|Delta particle]]" had four "charged states", it was said to be of isospin ''I''&nbsp;=&nbsp;{{sfrac|3|2}}. Its "charged states" {{SubatomicParticle|Delta++}}, {{SubatomicParticle|Delta+}}, {{SubatomicParticle|Delta0}}, and {{SubatomicParticle|Delta-}}, corresponded to the isospin projections ''I''<sub>3</sub>&nbsp;=&nbsp;+{{sfrac|3|2}}, ''I''<sub>3</sub>&nbsp;=&nbsp;+{{sfrac|1|2}}, ''I''<sub>3</sub>&nbsp;=&nbsp;−{{sfrac|1|2}}, and ''I''<sub>3</sub>&nbsp;=&nbsp;−{{sfrac|3|2}}, respectively. Another example is the "nucleon particle". As there were two nucleon "charged states", it was said to be of isospin {{sfrac|1|2}}. The positive nucleon {{SubatomicParticle|Nucleon+}} (proton) was identified with ''I''<sub>3</sub>&nbsp;=&nbsp;+{{sfrac|1|2}} and the neutral nucleon {{SubatomicParticle|Nucleon0}} (neutron) with ''I''<sub>3</sub>&nbsp;=&nbsp;−{{sfrac|1|2}}.<ref name=WongA>S.S.M. Wong (1998a)</ref> It was later noted that the isospin projections were related to the up and down quark content of particles by the relation:
: <math>I_\mathrm{3}=\frac{1}{2}[(n_\mathrm{u}-n_\mathrm{\bar{u}})-(n_\mathrm{d}-n_\mathrm{\bar{d}})],</math>
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<sup>++</sup> or N<sup>−</sup> 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 ===
{{Main|Flavour (particle physics)#Flavour quantum numbers}}

The [[strangeness]] [[flavour (particle physics)#Flavour quantum numbers|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 [[Eightfold way (physics)#Baryon octet|octet]] and [[Eightfold way (physics)#Baryon decuplet|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 symmetry|broken]].

It was noted that charge (''Q'') was related to the isospin projection (''I''<sub>3</sub>), the [[baryon number]] (''B'') and flavour quantum numbers (''S'', ''C'', ''B''′, ''T'') by the [[Gell-Mann–Nishijima formula]]:<ref name="WongA" />
: <math>Q = I_3 +\frac{1}{2}\left(B + S + C + B^\prime + T\right),</math>
where ''S'', ''C'', ''B''′, and ''T'' represent the [[strangeness]], [[charm (quantum number)|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:
: <math>\begin{align}
         S &= -\left(n_\mathrm{s} - n_\mathrm{\bar{s}}\right), \\
         C &= +\left(n_\mathrm{c} - n_\mathrm{\bar{c}}\right), \\
  B^\prime &= -\left(n_\mathrm{b} - n_\mathrm{\bar{b}}\right), \\
         T &= +\left(n_\mathrm{t} - n_\mathrm{\bar{t}}\right),
\end{align}</math>
meaning that the Gell-Mann–Nishijima formula is equivalent to the expression of charge in terms of quark content:
: <math>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].</math>

=== Spin, orbital angular momentum, and total angular momentum ===
{{Main|Spin (physics)|Angular momentum operator|Quantum numbers|Clebsch–Gordan coefficients}}
[[Spin (physics)|Spin]] (quantum number ''S'') is a [[Euclidean vector|vector]] quantity that represents the "intrinsic" [[angular momentum]] of a particle. It comes in increments of {{sfrac|1|2}}&nbsp;[[Planck constant|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&nbsp;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 {{sfrac|1|2}} (''S''&nbsp;=&nbsp;{{sfrac|1|2}}). Because spin projections vary in increments of 1 (that is 1&nbsp;ħ), a single quark has a spin vector of length {{sfrac|1|2}}, and has two spin projections (''S''<sub>z</sub>&nbsp;=&nbsp;+{{sfrac|1|2}} and ''S''<sub>z</sub>&nbsp;=&nbsp;−{{sfrac|1|2}}). Two quarks can have their spins aligned, in which case the two spin vectors add to make a vector of length ''S''&nbsp;=&nbsp;1 and three spin projections (''S''<sub>z</sub>&nbsp;=&nbsp;+1, ''S''<sub>z</sub>&nbsp;=&nbsp;0, and ''S''<sub>z</sub>&nbsp;=&nbsp;−1). If two quarks have unaligned spins, the spin vectors add up to make a vector of length ''S''&nbsp;=&nbsp;0 and has only one spin projection (''S''<sub>z</sub>&nbsp;=&nbsp;0), etc. Since baryons are made of three quarks, their spin vectors can add to make a vector of length ''S''&nbsp;=&nbsp;{{sfrac|3|2}}, which has four spin projections (''S''<sub>z</sub>&nbsp;=&nbsp;+{{sfrac|3|2}}, ''S''<sub>z</sub>&nbsp;=&nbsp;+{{sfrac|1|2}}, ''S''<sub>z</sub>&nbsp;=&nbsp;−{{sfrac|1|2}}, and ''S''<sub>z</sub>&nbsp;=&nbsp;−{{sfrac|3|2}}), or a vector of length ''S''&nbsp;=&nbsp;{{sfrac|1|2}} with two spin projections (''S''<sub>z</sub>&nbsp;=&nbsp;+{{sfrac|1|2}}, and ''S''<sub>z</sub>&nbsp;=&nbsp;−{{sfrac|1|2}}).<ref name=Shankar>R. Shankar (1994)</ref>

There is another quantity of angular momentum, called the [[angular momentum operator|orbital angular momentum]] ([[azimuthal quantum number]] ''L''), that comes in increments of 1&nbsp;ħ, which represent the angular moment due to quarks orbiting around each other. The [[angular momentum operator|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 {{nowrap|''J'' {{=}} {{!}}''L'' − ''S''{{!}}}} to {{nowrap|''J'' {{=}} {{!}}''L'' + ''S''{{!}}}}, in increments of 1.
{|class="wikitable" style="margin:1em auto; text-align: center;"
|+ Baryon angular momentum quantum numbers for ''L'' = 0, 1, 2, 3
|-
! Spin, <br />''S''
! Orbital angular <br />momentum, ''L''
! Total angular <br />momentum, ''J''
! [[#Parity|Parity]], <br />''P''
! Condensed <br />notation, ''J''<sup>''P''</sup>
|-
|rowspan="4"| {{sfrac|1|2}}
| 0 || {{sfrac|1|2}} || + || {{sfrac|1|2}}<sup>+</sup>
|-
| 1 || {{sfrac|3|2}}, {{sfrac|1|2}} || − || {{sfrac|3|2}}<sup>−</sup>, {{sfrac|1|2}}<sup>−</sup>
|-
| 2 || {{sfrac|5|2}}, {{sfrac|3|2}} || + || {{sfrac|5|2}}<sup>+</sup>, {{sfrac|3|2}}<sup>+</sup>
|-
| 3 || {{sfrac|7|2}}, {{sfrac|5|2}} || − || {{sfrac|7|2}}<sup>−</sup>, {{sfrac|5|2}}<sup>−</sup>
|-
|rowspan="4"| {{sfrac|3|2}}
| 0 || {{sfrac|3|2}} || + || {{sfrac|3|2}}<sup>+</sup>
|-
| 1 || {{sfrac|5|2}}, {{sfrac|3|2}}, {{sfrac|1|2}} || − || {{sfrac|5|2}}<sup>−</sup>, {{sfrac|3|2}}<sup>−</sup>, {{sfrac|1|2}}<sup>−</sup>
|-
| 2 || {{sfrac|7|2}}, {{sfrac|5|2}}, {{sfrac|3|2}}, {{sfrac|1|2}} || + || {{sfrac|7|2}}<sup>+</sup>, {{sfrac|5|2}}<sup>+</sup>, {{sfrac|3|2}}<sup>+</sup>, {{sfrac|1|2}}<sup>+</sup>
|-
| 3 || {{sfrac|9|2}}, {{sfrac|7|2}}, {{sfrac|5|2}}, {{sfrac|3|2}} || − || {{sfrac|9|2}}<sup>−</sup>, {{sfrac|7|2}}<sup>−</sup>, {{sfrac|5|2}}<sup>−</sup>, {{sfrac|3|2}}<sup>−</sup>
|}

Particle physicists are most interested in baryons with no orbital angular momentum (''L''&nbsp;=&nbsp;0), as they correspond to [[ground state]]s—states of minimal energy. Therefore, the two groups of baryons most studied are the ''S''&nbsp;=&nbsp;{{sfrac|1|2}}; ''L''&nbsp;=&nbsp;0 and ''S''&nbsp;=&nbsp;{{sfrac|3|2}}; ''L''&nbsp;=&nbsp;0, which corresponds to ''J''&nbsp;=&nbsp;{{sfrac|1|2}}<sup>+</sup> and ''J''&nbsp;=&nbsp;{{sfrac|3|2}}<sup>+</sup>, respectively, although they are not the only ones. It is also possible to obtain ''J''&nbsp;=&nbsp;{{sfrac|3|2}}<sup>+</sup> particles from ''S''&nbsp;=&nbsp;{{sfrac|1|2}} and ''L''&nbsp;=&nbsp;2, as well as ''S''&nbsp;=&nbsp;{{sfrac|3|2}} and ''L''&nbsp;=&nbsp;2. This phenomenon of having multiple particles in the same total angular momentum configuration is called ''[[degenerate energy level|degeneracy]]''. How to distinguish between these degenerate baryons is an active area of research in [[baryon spectroscopy]].<ref>H. Garcilazo et al. (2007)</ref><ref>D.M. Manley (2005)</ref>

=== Parity ===
{{Main|Parity (physics)}}

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 "[[parity (physics)|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 [[P-symmetry|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''&nbsp;=&nbsp;−1, or alternatively ''P''&nbsp;=&nbsp;–), while the other particles are said to have positive or even parity (''P''&nbsp;=&nbsp;+1, or alternatively ''P''&nbsp;=&nbsp;+).

For baryons, the parity is related to the orbital angular momentum by the relation:<ref name=WongB>S.S.M. Wong (1998b)</ref>
: <math>P=(-1)^L.\ </math>

As a consequence, baryons with no orbital angular momentum (''L''&nbsp;=&nbsp;0) all have even parity (''P''&nbsp;=&nbsp;+).

== Nomenclature ==
Baryons are classified into groups according to their [[isospin]] (''I'') values and [[quark]] (''q'') content. There are six groups of baryons: [[nucleon]] ({{SubatomicParticle|Nucleon}}), [[Delta baryon|Delta]] ({{SubatomicParticle|Delta}}), [[Lambda baryon|Lambda]] ({{SubatomicParticle|Lambda}}), [[Sigma baryon|Sigma]] ({{SubatomicParticle|Sigma}}), [[Xi baryon|Xi]] ({{SubatomicParticle|Xi}}), and [[Omega baryon|Omega]] ({{SubatomicParticle|Omega}}). The rules for classification are defined by the [[Particle Data Group]]. These rules consider the [[up quark|up]] ({{SubatomicParticle|Up quark}}), [[down quark|down]] ({{SubatomicParticle|Down quark}}) and [[strange quark|strange]] ({{SubatomicParticle|Strange quark}}) quarks to be ''light'' and the [[charm quark|charm]] ({{SubatomicParticle|Charm quark}}), [[bottom quark|bottom]] ({{SubatomicParticle|Bottom quark}}), and [[top quark|top]] ({{SubatomicParticle|Top quark}}) 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.<ref name=PDGBaryonsymbols>C. Amsler et al. (2008): [http://pdg.lbl.gov/2008/reviews/namingrpp.pdf Naming scheme for hadrons]</ref>
* Baryons with (any combination of) three {{SubatomicParticle|link=yes|Up quark}} and/or {{SubatomicParticle|link=yes|Down quark}} quarks are {{SubatomicParticle|link=yes|Nucleon}}s (''I'' = {{sfrac|1|2}}) or {{SubatomicParticle|link=yes|Delta}} baryons (''I'' = {{sfrac|3|2}}).
* Baryons containing two {{SubatomicParticle|link=yes|Up quark}} and/or {{SubatomicParticle|link=yes|Down quark}} quarks are {{SubatomicParticle|link=yes|Lambda}} baryons (''I'' = 0) or {{SubatomicParticle|link=yes|Sigma}} baryons (''I'' = 1). If the third quark is heavy, its identity is given by a subscript.
* Baryons containing one {{SubatomicParticle|link=yes|Up quark}} or {{SubatomicParticle|link=yes|Down quark}} quark are {{SubatomicParticle|link=yes|Xi}} baryons (''I'' = {{sfrac|1|2}}). One or two subscripts are used if one or both of the remaining quarks are heavy.
* Baryons containing no {{SubatomicParticle|link=yes|Up quark}} or {{SubatomicParticle|link=yes|Down quark}} quarks are {{SubatomicParticle|link=yes|Omega}} baryons (''I'' = 0), and subscripts indicate any heavy quark content.
* Baryons that decay strongly have their masses as part of their names. For example, Σ<sup>0</sup> does not decay strongly, but Δ<sup>++</sup>(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.<ref name="WongA" />
* Baryons in [[total angular momentum]] ''J''&nbsp;=&nbsp;{{sfrac|3|2}} configuration that have the same symbols as their ''J''&nbsp;=&nbsp;{{sfrac|1|2}} counterparts are denoted by an asterisk (&nbsp;*&nbsp;).
* Two baryons can be made of three different quarks in ''J''&nbsp;=&nbsp;{{sfrac|1|2}} configuration. In this case, a prime (&nbsp;′&nbsp;) 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 {{SubatomicParticle|charmed Lambda+}} contains a c quark and some combination of two u and/or d quarks. The c quark has a charge of (''Q''&nbsp;=&nbsp;+{{sfrac|2|3}}), therefore the other two must be a u quark (''Q''&nbsp;=&nbsp;+{{sfrac|2|3}}), and a d quark (''Q''&nbsp;=&nbsp;−{{sfrac|1|3}}) to have the correct total charge (''Q''&nbsp;=&nbsp;+1).

== See also ==
* [[Eightfold way (physics)|Eightfold way]]
* [[List of baryons]]
* [[Meson]]
* [[Timeline of particle discoveries]]

== Citations ==
{{reflist}}

== General references ==
{{refbegin}}
* {{cite journal |author=C. Amsler et al. ([[Particle Data Group]]) |title=Review of Particle Physics |journal=[[Physics Letters B]] |volume=667 |issue=1 |pages=1–1340 |year=2008 |doi=10.1016/j.physletb.2008.07.018|pmid=10020536 |bibcode = 2008PhLB..667....1A |url=http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf |archive-date=2022-10-09 |url-status=live |hdl=1854/LU-685594 |s2cid=227119789 |hdl-access=free }}
* {{cite journal |author1=H. Garcilazo |author2=J. Vijande |author3=A. Valcarce  |name-list-style=amp |title=Faddeev study of heavy-baryon spectroscopy |journal=[[Journal of Physics G]] |volume=34 |issue=5 |pages=961–976 |year=2007 |doi=10.1088/0954-3899/34/5/014|arxiv=hep-ph/0703257 |bibcode=2007hep.ph....3257G |s2cid=15445714 }}
* {{cite web |url=http://www.symmetrymagazine.org/cms/?pid=1000377 |archive-url=https://web.archive.org/web/20070708143911/http://www.symmetrymagazine.org/cms/?pid=1000377 |url-status=dead |archive-date=2007-07-08 |title=The rise and fall of the pentaquark |access-date=2008-05-27 |author=K. Carter |year=2006 |publisher=[[Fermilab]] and [[Stanford Linear Accelerator Center|SLAC]] }}
* {{cite journal |author=W.-M. Yao et al. ([[Particle Data Group]]) |title=Review of Particle Physics |journal=Journal of Physics G |volume=33 |issue=1 |pages=1–1232 |year=2006 |doi=10.1088/0954-3899/33/1/001|arxiv = astro-ph/0601168 |bibcode = 2006JPhG...33....1Y }}
* {{cite journal |author=D.M. Manley |title=Status of baryon spectroscopy |journal=[[Journal of Physics: Conference Series]] |volume=5 |issue=1 |pages=230–237 |year=2005 |doi=10.1088/1742-6596/9/1/043 |bibcode = 2005JPhCS...9..230M |doi-access=free }}
* {{cite magazine |url=https://www.newscientist.com/article/dn3903 |title=Pentaquark discovery confounds sceptics |access-date=2008-05-27 |author=H. Muir |year=2003 |magazine=[[New Scientist]]}}
* {{cite book |title=Introductory Nuclear Physics |edition=2nd |author=S.S.M. Wong |year=1998a |publisher=[[John Wiley & Sons]] |location=New York (NY) |isbn=978-0-471-23973-4|chapter=Chapter 2—Nucleon Structure |pages=21–56}}
* {{cite book |title=Introductory Nuclear Physics |edition=2nd |author=S.S.M. Wong |year=1998b |publisher=John Wiley & Sons |location=New York (NY) |isbn=978-0-471-23973-4|chapter=Chapter 3—The Deuteron |pages=57–104}}
* {{cite book |title=Principles of Quantum Mechanics |edition=2nd |author=R. Shankar |year=1994 |publisher=[[Plenum Press]] |location=New York (NY) |isbn=978-0-306-44790-7}}
* {{cite journal |author=E. Wigner |title=On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei |journal=[[Physical Review]] |volume=51 |issue=2 |year=1937|pages=106–119 |doi=10.1103/PhysRev.51.106|bibcode = 1937PhRv...51..106W }}
* {{cite journal |author=M. Gell-Mann |title=A Schematic of Baryons and Mesons |journal=[[Physics Letters]] |volume=8 |issue=3 |pages=214–215 |year=1964 |doi=10.1016/S0031-9163(64)92001-3 |bibcode = 1964PhL.....8..214G }}
* {{cite journal |author=W. Heisenberg |year=1932 |title=Über den Bau der Atomkerne I |journal=[[Zeitschrift für Physik]] |volume=77 |issue=1–2 |pages=1–11 |doi=10.1007/BF01342433|bibcode = 1932ZPhy...77....1H |s2cid=186218053 |language=de}}
* {{cite journal |author=W. Heisenberg |year=1932 |title=Über den Bau der Atomkerne II |journal=Zeitschrift für Physik |volume=78 |pages=156–164 |doi=10.1007/BF01337585|bibcode = 1932ZPhy...78..156H |issue=3–4 |s2cid=186221789 |language=de}}
* {{cite journal |author=W. Heisenberg |year=1932 |title=Über den Bau der Atomkerne III |journal=Zeitschrift für Physik |volume=80 |pages=587–596 |doi=10.1007/BF01335696|bibcode = 1933ZPhy...80..587H |issue=9–10 |s2cid=126422047 |language=de}}
{{refend}}

== External links ==
* Particle Data Group—[http://pdg.lbl.gov/index.html Review of Particle Physics (2018).]
* Georgia State University—[http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html HyperPhysics]

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[[Category:Baryons| ]]