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| [[Image:8foldway.png|thumb|right|'''Figure 1:''' The pseudoscalar meson nonet. Members of the octet are shown in green, the singlet in magenta. The name of the ''[[Eightfold way (physics)|Eightfold Way]]'' derives from this classification.]]
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| In [[physics]], the '''quark model''' is a classification scheme for [[hadron]]s in terms of their valence [[quark]]s—the quarks and antiquarks which give rise to the [[quantum number]]s of the hadrons.
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| The quark model was originally just a very good classification scheme to organize the depressingly large number of [[hadron]]s that were being discovered starting in the 1950s and continuing through the 1960s but it received experimental verification beginning in the late 1960s and continuing to the present. Hadrons are not "fundamental", but their "valence quarks" are thought to be, the quarks and antiquarks which give rise to the [[quantum number]]s of the hadrons.
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| These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the [[Poincaré symmetry]]—''J''<sup>''PC''</sup>, where ''J'', ''P'' and ''C'' stand for the [[total angular momentum]], [[P-symmetry]], and [[C-symmetry]] respectively. The remainder are [[flavour quantum numbers]] such as the [[isospin]], [[strangeness]], [[charm (quantum number)|charm]], and so on. The quark model is the follow-up to the [[Eightfold way (physics)|''Eightfold Way'']] classification scheme.
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| All quarks are assigned a [[baryon number]] of {{frac|1|3}}. [[Up quark|Up]], [[charm quark|charm]] and [[top quark]]s have an [[electric charge]] of +{{frac|2|3}}, while the [[down quark|down]], [[strange quark|strange]], and [[bottom quark]]s have an electric charge of −{{frac|1|3}}. Antiquarks have the opposite quantum numbers. Quarks are also [[spin-1/2|spin-{{frac|1|2}}]] particles, meaning they are [[fermion]]s.
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| [[Meson]]s are made of a valence quark−antiquark pair (thus have a baryon number of 0), while [[baryon]]s are made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavours of quark (which form an approximate [[SU(3)|SU(3) symmetry]]). There are generalizations to larger number of flavours.
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| ==History==
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| Developing classification schemes for [[hadron]]s became a burning question after new experimental techniques uncovered so many of them that it became clear that they could not all be elementary. These discoveries led [[Wolfgang Pauli]] to exclaim "Had I foreseen that, I would have gone into botany," and [[Enrico Fermi]] to advise his student [[Leon Lederman]]: "Young man, if I could remember the names of these particles, I would have been a botanist." These new schemes earned Nobel prizes for experimental particle physicists, including [[Luis Walter Alvarez|Luis Alvarez]], who was at the forefront of many of these developments. Several early proposals, such as the one by [[Shoichi Sakata]], were unable to explain all the data. A version developed by [[Moo-Young Han]] and [[Yoichiro Nambu]] was also eventually found untenable. The [[Gell-Mann–Nishijima formula|quark model in its modern form]] was developed by [[Murray Gell-Mann]] and [[Kazuhiko Nishijima]]. The model received important contributions from [[Yuval Ne'eman]] and [[George Zweig]]. The spin {{frac|3|2}} [[Omega baryon|{{SubatomicParticle|Omega-}} baryon]], a member of the ground state decuplet, was a prediction of the model. When it was discovered in an experiment at [[Brookhaven National Laboratory]], Gell-Mann received a Nobel prize for his work on the quark model.
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| ==Mesons==
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| {{see also|Meson|List of mesons}}
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| [[Image:Noneto mesônico de spin 0.png|thumb|'''Figure 2:''' [[Pseudoscalar]] mesons of spin 0 form a nonet]]
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| [[Image:Noneto mesônico de spin 1.png|thumb|'''Figure 3:''' Mesons of spin 1 form a nonet]]
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| The Eightfold Way classification is named after the following fact. If we take three flavours of quarks, then the quarks lie in the [[fundamental representation]], '''3''' (called the triplet) of [[flavour (particle physics)|flavour]] [[SU(3)]]. The antiquarks lie in the complex conjugate representation {{overline|'''3'''}}. The nine states (nonet) made out of a pair can be decomposed into the [[trivial representation]], '''1''' (called the singlet), and the [[Adjoint representation of a Lie group|adjoint representation]], '''8''' (called the octet). The notation for this decomposition is
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| :<math>\mathbf{3}\otimes \mathbf{\overline{3}} = \mathbf{8} \oplus \mathbf{1}</math>. | |
| Figure 1 shows the application of this decomposition to the mesons. If the flavour symmetry were exact, then all nine mesons would have the same mass. The physical content of the theory includes consideration of the symmetry breaking induced by the quark mass differences, and considerations of mixing between various multiplets (such as the octet and the singlet). The splitting between the {{SubatomicParticle|Eta}} and the {{SubatomicParticle|Eta prime}} is larger than the quark model can accommodate. This "[[QCD vacuum#The η'|{{SubatomicParticle|Eta}}–{{SubatomicParticle|Eta prime}} puzzle]]" is resolved by [[instanton]]s.
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| Mesons are hadrons with zero [[baryon number]]. If the quark–antiquark pair are in an [[angular momentum operator|orbital angular momentum]] ''L'' state, and have [[spin (physics)|spin]] ''S'', then
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| *|''L'' − ''S''| ≤ ''J'' ≤ ''L'' + ''S'', where ''S'' = 0 or 1,
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| *''P'' = (−1)<sup>''L'' + 1</sup>, where the 1 in the exponent arises from the [[intrinsic parity]] of the quark–antiquark pair.
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| *''C'' = (−1)<sup>''L'' + ''S''</sup> for mesons which have no [[flavour (particle physics)|flavour]]. Flavoured mesons have indefinite value of ''C''.
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| *For [[isospin]] ''I'' = 1 and 0 states, one can define a new [[multiplicative quantum number]] called the ''[[G-parity]]'' such that {{nowrap|''G'' {{=}} (−1)<sup>''I'' + ''L'' + ''S''</sup>'''}}.
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| If ''P'' = (−1)<sup>''J''</sup>, then it follows that ''S'' = 1, thus ''PC''= 1. States with these quantum numbers are called ''natural parity states'' while all other quantum numbers are called ''exotic'' (for example the state {{nowrap|''J''<sup>''PC''</sup> {{=}} 0<sup>−−</sup>}}).
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| {{clr}}
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| ==Baryons==
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| {{see also|Baryon|List of baryons}}
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| [[Image:Baryon octet.png|thumb|200px|right|'''Figure 4'''. The ''S'' = {{frac|1|2}} ground state baryon octet]][[Image:Baryon decuplet.png|thumb|200px|right|'''Figure 5'''. The ''S'' = {{frac|3|2}} baryon decuplet]]
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| Since quarks are [[fermion]]s, the [[spin-statistics theorem]] implies that the [[wavefunction]] of a baryon must be antisymmetric under exchange of any two quarks. This antisymmetric wavefunction is obtained by making it fully antisymmetric in colour and symmetric in flavour, spin and space put together. With three flavours, the decomposition in flavour is
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| :<math>\mathbf{3}\otimes\mathbf{3}\otimes\mathbf{3}=\mathbf{10}_S\oplus\mathbf{8}_M\oplus\mathbf{8}_M\oplus\mathbf{1}_A</math>. | |
| The decuplet is symmetric in flavour, the singlet antisymmetric and the two octets have mixed symmetry. The space and spin parts of the states are thereby fixed once the orbital angular momentum is given.
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| It is sometimes useful to think of the [[quantum state#Basis states|basis state]]s of quarks as the six states of three flavours and two spins per flavour. This approximate symmetry is called spin-flavour [[SU(6)]]. In terms of this, the decomposition is
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| ::<math>\mathbf{6}\otimes\mathbf{6}\otimes\mathbf{6}=\mathbf{56}_S\oplus\mathbf{70}_M\oplus\mathbf{70}_M\oplus\mathbf{20}_A</math>
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| The 56 states with symmetric combination of spin and flavour decompose under flavour [[SU(3)]] into
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| ::<math>\mathbf{56}=\mathbf{10}^\frac{3}{2}\oplus\mathbf{8}^\frac{1}{2}</math>
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| where the superscript denotes the spin, ''S'', of the baryon. Since these states are symmetric in spin and flavour, they should also be symmetric in space—a condition that is easily satisfied by making the orbital angular momentum ''L'' = 0. These are the ground state baryons. The ''S'' = {{frac|1|2}} octet baryons are the two [[nucleon]]s ({{SubatomicParticle|Proton+}}, {{SubatomicParticle|Neutron0}}), the three [[Sigma baryon|Sigmas]] ({{SubatomicParticle|Sigma+}}, {{SubatomicParticle|Sigma0}}, {{SubatomicParticle|Sigma-}}), the two [[Xi baryon|Xis]] ({{SubatomicParticle|Xi0}}, {{SubatomicParticle|Xi-}}), and the [[Lambda baryon|Lambda]] ({{SubatomicParticle|Lambda0}}). The ''S'' = {{frac|3|2}} decuplet baryons are the four [[Delta baryon|Deltas]] ({{SubatomicParticle|Delta++}}, {{SubatomicParticle|Delta+}}, {{SubatomicParticle|Delta0}}, {{SubatomicParticle|Delta-}}), three [[Sigma baryon|Sigmas]] ({{SubatomicParticle|Sigma*+}}, {{SubatomicParticle|Sigma*0}}, {{SubatomicParticle|Sigma*-}}), two [[Xi baryon|Xis]] ({{SubatomicParticle|Xi*0}}, {{SubatomicParticle|Xi*-}}), and the [[Omega]] ({{SubatomicParticle|Omega-}}). Mixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other questions that the model deals with.
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| {{clr}}
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| ===The discovery of colour===
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| {{Main|Color charge}}
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| Colour quantum numbers have been used from the beginning. However, colour was discovered as a consequence of this classification when it was realized that the spin ''S'' = {{frac|3|2}} baryon, the {{SubatomicParticle|Delta++}} required three up quarks with parallel spins and vanishing orbital angular momentum, and therefore could not have an antisymmetric wavefunction unless there was a hidden quantum number (due to the [[Pauli exclusion principle]]). [[Oscar Greenberg]] noted this problem in 1964, suggesting that quarks should be [[para-fermion]]s.<ref>
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| {{cite journal
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| |author=O.W. Greenberg
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| |year=1964
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| |title=Spin and Unitary-Spin Independence in a Paraquark Model of Baryons and Mesons
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| |journal=[[Physical Review Letters]]
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| |volume=13 |pages=598
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| |doi=10.1103/PhysRevLett.13.598
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| |bibcode = 1964PhRvL..13..598G
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| |issue=20 }}</ref> Six months later [[Moo-Young Han]] and [[Yoichiro Nambu]] suggested the existence of three triplets of quarks to solve this problem.<ref>
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| {{cite journal
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| |author=M.Y. Han, Y. Nambu
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| |year=1965
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| |title=Three-Triplet Model with Double SU(3) Symmetry
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| |journal=[[Physical Review]]
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| |volume=139 |pages=B1006
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| |doi=10.1103/PhysRev.139.B1006
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| |bibcode = 1965PhRv..139.1006H
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| |issue=4B }}</ref> The concept of colour was definitely established in the 1973 article written jointly by [[William A. Bardeen|William Bardeen]], [[Harald Fritzsch]] and [[Murray Gell-Mann]].<ref>
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| {{cite conference
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| |author=W. Bardeen, H. Fritzsch, M. Gell-Mann
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| |year=1973
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| |title=Light cone current algebra, ''π''<sup>0</sup> decay, and ''e''<sup>+</sup> ''e''<sup>−</sup> annihilation
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| |arxiv=hep-ph/0211388
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| |editor=R. Gatto
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| |booktitle=Scale and conformal symmetry in hadron physics
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| |page=139
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| |publisher=[[John Wiley & Sons]]
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| |id=ISBN 0-471-29292-3
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| }}</ref>
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| ==States outside the quark model==
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| While the quark model is derivable from the theory of [[quantum chromodynamics]], the structure of hadrons is more complicated than this model reveals. The full [[quantum mechanics|quantum mechanical]] [[wave function]] of any hadron must include virtual quark pairs as well as virtual [[gluon]]s. Also, there may be hadrons which lie outside the quark model. Among these are the ''[[glueball]]s'' (which contain only valence gluons), ''hybrids'' (which contain valence quarks as well as gluons) and "[[exotic hadron]]s" (such as [[tetraquark]]s or [[pentaquark]]s).
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| ==See also==
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| *[[Subatomic particles]]
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| *[[Hadron]]s, [[baryon]]s, [[meson]]s and [[quark]]s
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| *[[Exotic hadron]]s: [[exotic meson]]s and [[exotic baryon]]s
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| *[[Quantum chromodynamics]], [[flavour (particle physics)|flavour]], the [[QCD vacuum]]
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| ==References and external links==
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| {{reflist}}
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| *{{cite web
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| |author=J.R. Christman
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| |year=2001
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| |url=http://35.9.69.219/home/modules/pdf_modules/m282.pdf
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| |title=SU(3) and the quark model
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| |id=MISN-0-282
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| |work=[[Project PHYSNET]]
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| |publisher=[[University of Michigan]]
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| |accessdate=2009-07-24
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| }}
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| *{{cite journal
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| |author=S. Eidelman ''et al.'' [[Particle Data Group]]
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| |year=2004
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| |url=http://pdg.lbl.gov/2004/reviews/quarkmodrpp.pdf
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| |title=Review of Particle Physics
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| |journal=[[Physics Letters B]]
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| |volume=592 |page=1
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| |doi=10.1016/j.physletb.2004.06.001
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| |arxiv = astro-ph/0406663 |bibcode = 2004PhLB..592....1P }}
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| *{{cite book
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| |author=H. Georgi
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| |authorlink=Howard Georgi
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| |year=1999
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| |title=Lie algebras in particle physics
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| |publisher=[[Perseus Books]]
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| |isbn=0-7382-0233-9
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| }}
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| *{{cite book
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| |author=J.J.J. Kokkedee
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| |year=1969
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| |title=The quark model
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| |publisher=[[W. A. Benjamin]]
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| |asin=B001RAVDIA
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| }}
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| [[Category:Hadrons]]
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