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1. Shard Calculation

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Calculated Shard: 152 (from laksa099)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa152.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://en.wikipedia.org/wiki/Quark_model\')), getAhrefsUnparsedNoserviceFromURL(\'https://en.wikipedia.org/wiki/Quark_model\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/en.wikipedia.org\/wiki\/Quark_model","crawl_time":1774644622,"first_indexed_time":1382274218,"http_code":200,"src_unparsed":"org,wikipedia!en,\/wiki\/Quark_model s443","src_root_hash":"17790707453426894952","history_drop_reason":null,"meta_title":"Quark model - Wikipedia","meta_descriptions":[],"attrs_boilerpipe_text":"From Wikipedia, the free encyclopedia\nFigure 1\n: The\npseudoscalar meson\nnonet. Members of the original meson \"octet\" are shown in green, the singlet in magenta. Although these mesons are now grouped into a nonet, the\nEightfold Way\nname derives from the patterns of eight for the mesons and baryons in the original classification scheme.\nIn\nparticle physics\n, the\nquark model\nis a classification scheme for\nhadrons\nin terms of their valence\nquarks\n—the quarks and antiquarks that give rise to the\nquantum numbers\nof the hadrons. The quark model  underlies\n\"flavor SU(3)\"\n, or the\nEightfold Way\n, the successful\nclassification scheme\norganizing the large number of lighter\nhadrons\nthat were being discovered starting in the 1950s and continuing through the 1960s. It received experimental\nverification\nbeginning in the late 1960s and is a valid and effective classification of them to date. The model was independently proposed by physicists\nMurray Gell-Mann\n,\n[\n1\n]\nwho dubbed them \"quarks\" in a concise paper, and\nGeorge Zweig\n,\n[\n2\n]\n[\n3\n]\nwho suggested \"aces\" in a longer manuscript.\nAndré Petermann\nalso touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation.\n[\n4\n]\n[\n5\n]\nToday, the model has essentially been absorbed as a component of the established\nquantum field theory\nof strong and electroweak particle interactions, dubbed the\nStandard Model\n.\nHadrons are not really \"elementary\", and can be regarded as bound states of their \"valence quarks\" and antiquarks, which give rise to the\nquantum numbers\nof the hadrons. These quantum numbers are labels identifying the  hadrons, and are of two kinds. One set comes from the\nPoincaré symmetry\n—\nJ\nPC\n, where\nJ\n,\nP\nand\nC\nstand for the\ntotal angular momentum\n,\nP-symmetry\n, and\nC-symmetry\n, respectively.\nThe other set is the\nflavor quantum numbers\nsuch as the\nisospin\n,\nstrangeness\n,\ncharm\n, and so on. The strong interactions binding the quarks together are insensitive to these quantum numbers, so variation of them leads to systematic mass and coupling relationships among the hadrons in the same flavor multiplet.\nAll quarks are assigned a\nbaryon number\nof\n⁠\n1\n\/\n3\n⁠\n.\nUp\n,\ncharm\nand\ntop quarks\nhave an\nelectric charge\nof +\n⁠\n2\n\/\n3\n⁠\n, while the\ndown\n,\nstrange\n, and\nbottom quarks\nhave an electric charge of −\n⁠\n1\n\/\n3\n⁠\n. Antiquarks have the opposite quantum numbers. Quarks are\nspin-\n⁠\n1\n\/\n2\n⁠\nparticles, and thus\nfermions\n. Each quark or antiquark obeys the Gell-Mann–Nishijima formula individually, so any additive assembly of them will as well.\nMesons\nare made of a valence quark–antiquark pair (thus have a baryon number of 0), while\nbaryons\nare made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavors of quark (which form an approximate flavor\nSU(3) symmetry\n). There are generalizations to larger number of flavors.\nDeveloping classification schemes for\nhadrons\nbecame a timely question after new experimental techniques uncovered so many of them that it became clear that they could not all be elementary. These discoveries led\nWolfgang Pauli\nto exclaim \"Had I foreseen that, I would have gone into botany.\" and\nEnrico Fermi\nto advise his student\nLeon Lederman\n: \"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\nLuis Alvarez\n, who was at the forefront of many of these developments. Constructing hadrons as bound states of fewer constituents would thus organize the \"zoo\" at hand. Several early proposals, such as the ones by\nEnrico Fermi\nand\nChen-Ning Yang\n(1949), and the\nSakata model\n(1956), ended up satisfactorily covering the mesons, but failed with baryons, and so were unable to explain all the data.\nThe\nGell-Mann–Nishijima formula\n, developed by\nMurray Gell-Mann\nand\nKazuhiko Nishijima\n, led to the\nEightfold Way\nclassification, invented by Gell-Mann, with important independent contributions from\nYuval Ne'eman\n, in 1961. The hadrons were organized into SU(3) representation multiplets, octets and decuplets, of roughly the same mass, due to the strong interactions; and smaller mass differences linked to the flavor quantum numbers, invisible to the strong interactions. The\nGell-Mann–Okubo mass formula\nsystematized the quantification of these small mass differences among members of a hadronic multiplet, controlled by the\nexplicit symmetry breaking\nof SU(3).\nThe spin-\n⁠\n3\n\/\n2\n⁠\nΩ\n−\nbaryon\n, a member of the ground-state decuplet, was a crucial prediction of that classification. After it was discovered in an experiment at\nBrookhaven National Laboratory\n, Gell-Mann received a\nNobel Prize in Physics\nfor his work on the Eightfold Way, in 1969.\nFinally, in 1964, Gell-Mann and\nGeorge Zweig\n, discerned independently what the Eightfold Way picture encodes: They posited three elementary fermionic constituents—the \"\nup\n\", \"\ndown\n\", and \"\nstrange\n\" quarks—which are unobserved, and possibly unobservable in a free form. Simple pairwise or triplet combinations of these three constituents and their antiparticles underlie and elegantly encode the Eightfold Way classification, in an economical, tight structure, resulting in further simplicity. Hadronic mass differences were now linked to the different masses of the constituent quarks.\nIt would take about a decade for the unexpected nature—and physical reality—of these quarks to be appreciated more fully (See\nQuarks\n). Counter-intuitively, they cannot ever be observed in isolation (\ncolor confinement\n), but instead always combine with other quarks to form full hadrons, which then furnish ample indirect information on the trapped quarks themselves. Conversely, the quarks serve in the definition of\nquantum chromodynamics\n, the fundamental theory fully describing the strong interactions; and the Eightfold Way is now understood to be a consequence of the flavor symmetry structure of the lightest three of them.\nFigure 2\n:\nPseudoscalar mesons\nof spin-0 form a nonet\nFigure 3\n:\nVector mesons\nof spin-1 form a nonet\nThe Eightfold Way classification is named after the following fact: If we take three flavors of quarks, then the quarks lie in the\nfundamental representation\n,\n3\n(called the triplet) of\nflavor\nSU(3)\n. The antiquarks lie in the complex conjugate representation\n3\n. The nine states (nonet) made out of a pair can be decomposed into the\ntrivial representation\n,\n1\n(called the singlet), and the\nadjoint representation\n,\n8\n(called the octet). The notation for this decomposition is\nFigure 1 shows the application of this decomposition to the mesons. If the flavor symmetry were exact (as in the limit that only the strong interactions operate, but the electroweak interactions are notionally switched off), then all nine mesons would have the same mass. However, the physical content of the full theory\n[\nclarification needed\n]\nincludes 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).\nN.B. Nevertheless, the mass splitting between the\nη\nand the\nη′\nis larger than the quark model can accommodate, and  this \"\nη\n–\nη′\npuzzle\n\" has its origin in topological peculiarities of the strong interaction vacuum, such as\ninstanton\nconfigurations.\nMesons are hadrons with zero\nbaryon number\n. If the quark–antiquark pair are in an\norbital angular momentum\nL\nstate, and have\nspin\nS\n, then\n|\nL\n−\nS\n| ≤\nJ\n≤\nL\n+\nS\n, where\nS\n= 0 or 1,\nP\n= (−1)\nL\n+1\n, where the 1 in the exponent arises from the\nintrinsic parity\nof the quark–antiquark pair.\nC\n= (−1)\nL\n+\nS\nfor mesons which have no\nflavor\n. Flavored mesons have indefinite value of\nC\n.\nFor\nisospin\nI\n= 1\nand 0 states, one can define a new\nmultiplicative quantum number\ncalled the\nG-parity\nsuch that\nG\n= (−1)\nI\n+\nL\n+\nS\n.\nIf\nP\n= (−1)\nJ\n, then it follows that\nS\n= 1, thus\nPC\n= 1. States with these quantum numbers are called\nnatural parity states\n; while all other quantum numbers are thus called\nexotic\n(for example, the state\nJ\nPC\n= 0\n−−\n).\nFigure 4\n. The\nS\n=\n⁠\n1\n\/\n2\n⁠\nground state\nbaryon\noctet\nFigure 5\n. The\nS\n=\n⁠\n3\n\/\n2\n⁠\nbaryon\ndecuplet\nSince quarks are\nfermions\n, the\nspin–statistics theorem\nimplies that the\nwavefunction\nof a baryon must be antisymmetric under the exchange of any two quarks. This antisymmetric wavefunction is obtained by making it fully antisymmetric in color, discussed below, and symmetric in flavor, spin and space put together. With three flavors, the decomposition in flavor is\nThe decuplet is symmetric in flavor, 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.\nIt is sometimes useful to think of the\nbasis states\nof quarks as the six states of three flavors and two spins per flavor. This approximate symmetry is called spin-flavor\nSU(6)\n. In terms of this, the decomposition is\nThe 56 states with symmetric combination of spin and flavour decompose under flavor\nSU(3)\ninto\nwhere the superscript denotes the spin,\nS\n, of the baryon. Since these states are symmetric in spin and flavor, they should also be symmetric in space—a condition that is easily satisfied by making the orbital angular momentum\nL\n= 0\n. These are the ground-state baryons.\nThe\nS\n=\n⁠\n1\n\/\n2\n⁠\noctet baryons are the two\nnucleons\n(\np\n+\n,\nn\n0\n), the three\nSigmas\n(\nΣ\n+\n,\nΣ\n0\n,\nΣ\n−\n), the two\nXis\n(\nΞ\n0\n,\nΞ\n−\n), and the\nLambda\n(\nΛ\n0\n). The\nS\n=\n⁠\n3\n\/\n2\n⁠\ndecuplet baryons are the four\nDeltas\n(\nΔ\n++\n,\nΔ\n+\n,\nΔ\n0\n,\nΔ\n−\n), three\nSigmas\n(\nΣ\n∗+\n,\nΣ\n∗0\n,\nΣ\n∗−\n), two\nXis\n(\nΞ\n∗0\n,\nΞ\n∗−\n), and the\nOmega\n(\nΩ\n−\n).\nFor example, the constituent quark model wavefunction for the proton is\nMixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other quantities that the model predicts successfully.\nThe group theory approach described above assumes that the quarks are eight components of a single particle, so the anti-symmetrization applies to all the quarks.  A simpler approach is to consider the eight flavored quarks as eight separate, distinguishable, non-identical particles.  Then the anti-symmetrization applies only to two identical quarks (like uu, for instance).\n[\n6\n]\nThen, the proton wavefunction can be written in a simpler form:\nand the\nIf quark–quark interactions are limited to two-body interactions, then all the successful quark model predictions, including sum rules for baryon masses and magnetic moments, can be derived.\nColor quantum numbers are the characteristic charges of the strong force, and are completely uninvolved in electroweak interactions. They were discovered as a consequence of the quark model classification, when it was appreciated that the spin\nS\n=\n⁠\n3\n\/\n2\n⁠\nbaryon, the\nΔ\n++\n, required three up quarks with parallel spins and vanishing orbital angular momentum. Therefore, it could not have an antisymmetric wavefunction, (required by the\nPauli exclusion principle\n).\nOscar Greenberg\nnoted this problem in 1964, suggesting that quarks should be\npara-fermions\n.\n[\n7\n]\nInstead, six months later,\nMoo-Young Han\nand\nYoichiro Nambu\nsuggested the existence of a hidden degree of freedom, they labeled as the group SU(3)' (but later called 'color). This led to three triplets of quarks whose wavefunction was anti-symmetric in the color degree of freedom.\nFlavor and color were intertwined in that model: they did not commute.\n[\n8\n]\nThe modern concept of color completely commuting with all other charges and providing the strong force charge was articulated in 1973, by\nWilliam Bardeen\n,\nHarald Fritzsch\n, and\nMurray Gell-Mann\n.\n[\n9\n]\n[\n10\n]\nStates outside the quark model\n[\nedit\n]\nWhile the quark model is derivable from the theory of\nquantum chromodynamics\n, the structure of hadrons is more complicated than this model allows. The full\nquantum mechanical\nwavefunction\nof any hadron must include virtual quark pairs as well as virtual\ngluons\n, and allows for a variety of mixings. There may be hadrons which lie outside the quark model. Among these are the\nglueballs\n(which contain only valence gluons),\nhybrids\n(which contain valence quarks as well as gluons) and\nexotic hadrons\n(such as\ntetraquarks\nor\npentaquarks\n).\nSubatomic particles\nHadrons\n,\nbaryons\n,\nmesons\nand\nquarks\nExotic hadrons\n:\nexotic mesons\nand\nexotic baryons\nQuantum chromodynamics\n,\nflavor\n, the\nQCD vacuum\n^\nGell-Mann, M.\n(4 January 1964). \"A Schematic Model of Baryons and Mesons\".\nPhysics Letters\n.\n8\n(3):\n214–\n215.\nBibcode\n:\n1964PhL.....8..214G\n.\ndoi\n:\n10.1016\/S0031-9163(64)92001-3\n.\n^\nZweig, G.\n(17 January 1964).\nAn SU(3) Model for Strong Interaction Symmetry and its Breaking\n(PDF)\n(Report). CERN Report No.8182\/TH.401.\n^\nZweig, G.\n(1964).\nAn SU(3) Model for Strong Interaction Symmetry and its Breaking: II\n(PDF)\n(Report). CERN Report No.8419\/TH.412.\n^\nPetermann, A.\n(1965). \"Propriétés de l'étrangeté et une formule de masse pour les mésons vectoriels\" [Strangeness properties and a mass formula for vector meson].\nNuclear Physics\n.\n63\n(2):\n349–\n352.\narXiv\n:\n1412.8681\n.\nBibcode\n:\n1965NucPh..63..349P\n.\ndoi\n:\n10.1016\/0029-5582(65)90348-2\n.\n^\nPetrov, Vladimir A. (June 23–27, 2014).\nHalf a Century with QUARKS\n. XXX-th International Workshop on High Energy Physics.\nProtvino\n,\nMoscow Oblast\n, Russia.\narXiv\n:\n1412.8681\n.\n^\nFranklin, J. (1968). \"A Model of Baryons Made of Quarks with Hidden Spin\".\nPhysical Review\n.\n172\n(3):\n1807–\n1817.\nBibcode\n:\n1968PhRv..172.1807F\n.\ndoi\n:\n10.1103\/PhysRev.172.1807\n.\n^\nGreenberg, O.W. (1964). \"Spin and unitary-spin independence in a paraquark model of baryons and mesons\".\nPhysical Review Letters\n.\n13\n(20):\n598–\n602.\nBibcode\n:\n1964PhRvL..13..598G\n.\ndoi\n:\n10.1103\/PhysRevLett.13.598\n.\n^\nHan, M.Y.; Nambu, Y. (1965).\n\"Three-triplet model with double SU(3) symmetry\"\n.\nPhysical Review B\n.\n139\n(4B): 1006.\nBibcode\n:\n1965PhRv..139.1006H\n.\ndoi\n:\n10.1103\/PhysRev.139.B1006\n.\n^\nBardeen, W.; Fritzsch, H.; Gell-Mann, M. (1973).\n\"Light cone current algebra,\nπ\n0\ndecay, and\ne\n+\ne\n−\nannihilation\"\n. In Gatto, R. (ed.).\nScale and conformal symmetry in hadron physics\n.\nJohn Wiley & Sons\n. p. \n139\n.\narXiv\n:\nhep-ph\/0211388\n.\nBibcode\n:\n2002hep.ph...11388B\n.\nISBN\n \n0-471-29292-3\n.\n^\nFritzsch, H.; Gell-Mann, M.; Leutwyler, H. (1973). \"Advantages of the color octet gluon picture\".\nPhysics Letters B\n.\n47\n(4): 365.\nBibcode\n:\n1973PhLB...47..365F\n.\nCiteSeerX\n \n10.1.1.453.4712\n.\ndoi\n:\n10.1016\/0370-2693(73)90625-4\n.\nS. Eidelman\net al.\nParticle Data Group\n(2004).\n\"Review of Particle Physics\"\n(PDF)\n.\nPhysics Letters B\n.\n592\n(\n1–\n4): 1.\narXiv\n:\nastro-ph\/0406663\n.\nBibcode\n:\n2004PhLB..592....1P\n.\ndoi\n:\n10.1016\/j.physletb.2004.06.001\n.\nS2CID\n \n118588567\n.\nLichtenberg, D B (1970).\nUnitary Symmetry and Elementary Particles\n. Academic Press.\nISBN\n \n978-1483242729\n.\nThomson, M A (2011),\nLecture notes\nJ.J.J. Kokkedee (1969).\nThe quark model\n.\nW. A. Benjamin\n.\nASIN\n \nB001RAVDIA\n.","attrs_markdown":"[Jump to content](https:\/\/en.wikipedia.org\/wiki\/Quark_model#bodyContent)\n\nMain menu\n\nMain menu\n\nmove to sidebar\n\nhide\n\nNavigation\n\n- [Main page](https:\/\/en.wikipedia.org\/wiki\/Main_Page \"Visit the main page [z]\")\n- [Contents](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Contents \"Guides to browsing Wikipedia\")\n- [Current events](https:\/\/en.wikipedia.org\/wiki\/Portal:Current_events \"Articles related to current events\")\n- [Random article](https:\/\/en.wikipedia.org\/wiki\/Special:Random \"Visit a randomly selected article [x]\")\n- [About Wikipedia](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:About \"Learn about Wikipedia and how it works\")\n- [Contact us](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Contact_us \"How to contact Wikipedia\")\n\nContribute\n\n- [Help](https:\/\/en.wikipedia.org\/wiki\/Help:Contents \"Guidance on how to use and edit Wikipedia\")\n- [Learn to edit](https:\/\/en.wikipedia.org\/wiki\/Help:Introduction \"Learn how to edit Wikipedia\")\n- [Community portal](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Community_portal \"The hub for editors\")\n- [Recent changes](https:\/\/en.wikipedia.org\/wiki\/Special:RecentChanges \"A list of recent changes to Wikipedia [r]\")\n- [Upload file](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:File_upload_wizard \"Add images or other media for use on Wikipedia\")\n- [Special pages](https:\/\/en.wikipedia.org\/wiki\/Special:SpecialPages \"A list of all special pages [q]\")\n\n[![](https:\/\/en.wikipedia.org\/static\/images\/icons\/enwiki-25.svg) ![Wikipedia](https:\/\/en.wikipedia.org\/static\/images\/mobile\/copyright\/wikipedia-wordmark-en-25.svg) ![The Free Encyclopedia](https:\/\/en.wikipedia.org\/static\/images\/mobile\/copyright\/wikipedia-tagline-en-25.svg)](https:\/\/en.wikipedia.org\/wiki\/Main_Page)\n\n[Search](https:\/\/en.wikipedia.org\/wiki\/Special:Search \"Search Wikipedia [f]\")\n\nAppearance\n\n- [Donate](https:\/\/donate.wikimedia.org\/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en)\n- [Create account](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:CreateAccount&returnto=Quark+model \"You are encouraged to create an account and log in; however, it is not mandatory\")\n- [Log in](https:\/\/en.wikipedia.org\/w\/index.php?title=Special:UserLogin&returnto=Quark+model \"You're encouraged to log in; however, it's not mandatory. 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[o]\")\n\n## Contents\nmove to sidebar\n\nhide\n\n- [(Top)](https:\/\/en.wikipedia.org\/wiki\/Quark_model)\n- [1 History](https:\/\/en.wikipedia.org\/wiki\/Quark_model#History)\n- [2 Mesons](https:\/\/en.wikipedia.org\/wiki\/Quark_model#Mesons)\n- [3 Baryons](https:\/\/en.wikipedia.org\/wiki\/Quark_model#Baryons)\n  Toggle Baryons subsection\n  - [3\\.1 Discovery of color](https:\/\/en.wikipedia.org\/wiki\/Quark_model#Discovery_of_color)\n- [4 States outside the quark model](https:\/\/en.wikipedia.org\/wiki\/Quark_model#States_outside_the_quark_model)\n- [5 See also](https:\/\/en.wikipedia.org\/wiki\/Quark_model#See_also)\n- [6 Notes](https:\/\/en.wikipedia.org\/wiki\/Quark_model#Notes)\n- [7 References](https:\/\/en.wikipedia.org\/wiki\/Quark_model#References)\n\nToggle the table of contents\n\n# Quark model\n15 languages\n\n- [العربية](https:\/\/ar.wikipedia.org\/wiki\/%D9%86%D9%85%D9%88%D8%B0%D8%AC_%D8%A7%D9%84%D9%83%D9%88%D8%A7%D8%B1%D9%83 \"نموذج الكوارك – Arabic\")\n- [Català](https:\/\/ca.wikipedia.org\/wiki\/Model_de_quarks \"Model de quarks – Catalan\")\n- [Español](https:\/\/es.wikipedia.org\/wiki\/Modelo_de_cuarks \"Modelo de cuarks – Spanish\")\n- [Euskara](https:\/\/eu.wikipedia.org\/wiki\/Quark_eredua \"Quark eredua – Basque\")\n- [فارسی](https:\/\/fa.wikipedia.org\/wiki\/%D9%85%D8%AF%D9%84_%DA%A9%D9%88%D8%A7%D8%B1%DA%A9 \"مدل کوارک – Persian\")\n- [Magyar](https:\/\/hu.wikipedia.org\/wiki\/Kvarkmodell \"Kvarkmodell – Hungarian\")\n- [Italiano](https:\/\/it.wikipedia.org\/wiki\/Modello_a_quark_costituenti \"Modello a quark costituenti – Italian\")\n- [日本語](https:\/\/ja.wikipedia.org\/wiki\/%E3%82%AF%E3%82%A9%E3%83%BC%E3%82%AF%E3%83%A2%E3%83%87%E3%83%AB \"クォークモデル – Japanese\")\n- [한국어](https:\/\/ko.wikipedia.org\/wiki\/%EC%BF%BC%ED%81%AC_%EB%AA%A8%ED%98%95 \"쿼크 모형 – Korean\")\n- [Русский](https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D0%B2%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C \"Кварковая модель – Russian\")\n- [Slovenščina](https:\/\/sl.wikipedia.org\/wiki\/Kvarkovski_model \"Kvarkovski model – Slovenian\")\n- [Türkçe](https:\/\/tr.wikipedia.org\/wiki\/Kuark_modeli \"Kuark modeli – Turkish\")\n- [Українська](https:\/\/uk.wikipedia.org\/wiki\/%D0%9A%D0%B2%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B0_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C \"Кваркова модель – Ukrainian\")\n- [吴语](https:\/\/wuu.wikipedia.org\/wiki\/%E5%A4%B8%E5%85%8B%E6%A8%A1%E5%9E%8B \"夸克模型 – Wu\")\n- [中文](https:\/\/zh.wikipedia.org\/wiki\/%E5%A4%B8%E5%85%8B%E6%A8%A1%E5%9E%8B \"夸克模型 – Chinese\")\n\n[Edit links](https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/Q1890674#sitelinks-wikipedia \"Edit interlanguage links\")\n\n- [Article](https:\/\/en.wikipedia.org\/wiki\/Quark_model \"View the content page [c]\")\n- [Talk](https:\/\/en.wikipedia.org\/wiki\/Talk:Quark_model \"Discuss improvements to the content page [t]\")\n\nEnglish\n\n- [Read](https:\/\/en.wikipedia.org\/wiki\/Quark_model)\n- 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item](https:\/\/www.wikidata.org\/wiki\/Special:EntityPage\/Q1890674 \"Structured data on this page hosted by Wikidata [g]\")\n\nAppearance\n\nmove to sidebar\n\nhide\n\nFrom Wikipedia, the free encyclopedia\n\nClassification scheme of hadrons\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/af\/8foldway.svg\/250px-8foldway.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:8foldway.svg)\n\n**Figure 1**: The [pseudoscalar meson](https:\/\/en.wikipedia.org\/wiki\/Pseudoscalar_meson \"Pseudoscalar meson\") nonet. Members of the original meson \"octet\" are shown in green, the singlet in magenta. Although these mesons are now grouped into a nonet, the [Eightfold Way](https:\/\/en.wikipedia.org\/wiki\/Eightfold_way_\\(physics\\) \"Eightfold way (physics)\") name derives from the patterns of eight for the mesons and baryons in the original classification scheme.\n\nIn [particle physics](https:\/\/en.wikipedia.org\/wiki\/Particle_physics \"Particle physics\"), the **quark model** is a classification scheme for [hadrons](https:\/\/en.wikipedia.org\/wiki\/Hadron \"Hadron\") in terms of their valence [quarks](https:\/\/en.wikipedia.org\/wiki\/Quark \"Quark\")—the quarks and antiquarks that give rise to the [quantum numbers](https:\/\/en.wikipedia.org\/wiki\/Quantum_number \"Quantum number\") of the hadrons. The quark model underlies [\"flavor SU(3)\"](https:\/\/en.wikipedia.org\/wiki\/Flavour_\\(particle_physics\\) \"Flavour (particle physics)\"), or the [Eightfold Way](https:\/\/en.wikipedia.org\/wiki\/Eightfold_way_\\(physics\\) \"Eightfold way (physics)\"), the successful [classification scheme](https:\/\/en.wikipedia.org\/wiki\/Classification_scheme_\\(information_science\\) \"Classification scheme (information science)\") organizing the large number of lighter [hadrons](https:\/\/en.wikipedia.org\/wiki\/Hadron \"Hadron\") that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental [verification](https:\/\/en.wikipedia.org\/wiki\/Verification_and_validation \"Verification and validation\") beginning in the late 1960s and is a valid and effective classification of them to date. The model was independently proposed by physicists [Murray Gell-Mann](https:\/\/en.wikipedia.org\/wiki\/Murray_Gell-Mann \"Murray Gell-Mann\"),[\\[1\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-Gell-Man1964-1) who dubbed them \"quarks\" in a concise paper, and [George Zweig](https:\/\/en.wikipedia.org\/wiki\/George_Zweig \"George Zweig\"),[\\[2\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-Zweig1964a-2)[\\[3\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-Zweig1964b-3) who suggested \"aces\" in a longer manuscript. [André Petermann](https:\/\/en.wikipedia.org\/wiki\/Andr%C3%A9_Petermann \"André Petermann\") also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation.[\\[4\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-4)[\\[5\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-5) Today, the model has essentially been absorbed as a component of the established [quantum field theory](https:\/\/en.wikipedia.org\/wiki\/Quantum_field_theory \"Quantum field theory\") of strong and electroweak particle interactions, dubbed the [Standard Model](https:\/\/en.wikipedia.org\/wiki\/Standard_Model \"Standard Model\").\n\nHadrons are not really \"elementary\", and can be regarded as bound states of their \"valence quarks\" and antiquarks, which give rise to the [quantum numbers](https:\/\/en.wikipedia.org\/wiki\/Quantum_number \"Quantum number\") of the hadrons. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the [Poincaré symmetry](https:\/\/en.wikipedia.org\/wiki\/Poincar%C3%A9_symmetry \"Poincaré symmetry\")—*J**PC*, where *J*, *P* and *C* stand for the [total angular momentum](https:\/\/en.wikipedia.org\/wiki\/Total_angular_momentum \"Total angular momentum\"), [P-symmetry](https:\/\/en.wikipedia.org\/wiki\/P-symmetry \"P-symmetry\"), and [C-symmetry](https:\/\/en.wikipedia.org\/wiki\/C-symmetry \"C-symmetry\"), respectively.\n\nThe other set is the [flavor quantum numbers](https:\/\/en.wikipedia.org\/wiki\/Flavour_quantum_numbers \"Flavour quantum numbers\") such as the [isospin](https:\/\/en.wikipedia.org\/wiki\/Isospin \"Isospin\"), [strangeness](https:\/\/en.wikipedia.org\/wiki\/Strangeness \"Strangeness\"), [charm](https:\/\/en.wikipedia.org\/wiki\/Charm_\\(quantum_number\\) \"Charm (quantum number)\"), and so on. The strong interactions binding the quarks together are insensitive to these quantum numbers, so variation of them leads to systematic mass and coupling relationships among the hadrons in the same flavor multiplet.\n\nAll quarks are assigned a [baryon number](https:\/\/en.wikipedia.org\/wiki\/Baryon_number \"Baryon number\") of ⁠1\/3⁠. [Up](https:\/\/en.wikipedia.org\/wiki\/Up_quark \"Up quark\"), [charm](https:\/\/en.wikipedia.org\/wiki\/Charm_quark \"Charm quark\") and [top quarks](https:\/\/en.wikipedia.org\/wiki\/Top_quark \"Top quark\") have an [electric charge](https:\/\/en.wikipedia.org\/wiki\/Electric_charge \"Electric charge\") of +⁠2\/3⁠, while the [down](https:\/\/en.wikipedia.org\/wiki\/Down_quark \"Down quark\"), [strange](https:\/\/en.wikipedia.org\/wiki\/Strange_quark \"Strange quark\"), and [bottom quarks](https:\/\/en.wikipedia.org\/wiki\/Bottom_quark \"Bottom quark\") have an electric charge of −⁠1\/3⁠. Antiquarks have the opposite quantum numbers. Quarks are [spin-⁠1\/2⁠](https:\/\/en.wikipedia.org\/wiki\/Spin-1\/2 \"Spin-1\/2\") particles, and thus [fermions](https:\/\/en.wikipedia.org\/wiki\/Fermion \"Fermion\"). Each quark or antiquark obeys the Gell-Mann–Nishijima formula individually, so any additive assembly of them will as well.\n\n[Mesons](https:\/\/en.wikipedia.org\/wiki\/Meson \"Meson\") are made of a valence quark–antiquark pair (thus have a baryon number of 0), while [baryons](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\") are made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavors of quark (which form an approximate flavor [SU(3) symmetry](https:\/\/en.wikipedia.org\/wiki\/SU\\(3\\) \"SU(3)\")). There are generalizations to larger number of flavors.\n\n## History\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&action=edit&section=1 \"Edit section: History\")\\]\n\nDeveloping classification schemes for [hadrons](https:\/\/en.wikipedia.org\/wiki\/Hadron \"Hadron\") became a timely 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](https:\/\/en.wikipedia.org\/wiki\/Wolfgang_Pauli \"Wolfgang Pauli\") to exclaim \"Had I foreseen that, I would have gone into botany.\" and [Enrico Fermi](https:\/\/en.wikipedia.org\/wiki\/Enrico_Fermi \"Enrico Fermi\") to advise his student [Leon Lederman](https:\/\/en.wikipedia.org\/wiki\/Leon_Lederman \"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 Alvarez](https:\/\/en.wikipedia.org\/wiki\/Luis_Walter_Alvarez \"Luis Walter Alvarez\"), who was at the forefront of many of these developments. Constructing hadrons as bound states of fewer constituents would thus organize the \"zoo\" at hand. Several early proposals, such as the ones by [Enrico Fermi](https:\/\/en.wikipedia.org\/wiki\/Enrico_Fermi \"Enrico Fermi\") and [Chen-Ning Yang](https:\/\/en.wikipedia.org\/wiki\/Chen-Ning_Yang \"Chen-Ning Yang\") (1949), and the [Sakata model](https:\/\/en.wikipedia.org\/wiki\/Sakata_model \"Sakata model\") (1956), ended up satisfactorily covering the mesons, but failed with baryons, and so were unable to explain all the data.\n\nThe [Gell-Mann–Nishijima formula](https:\/\/en.wikipedia.org\/wiki\/Gell-Mann%E2%80%93Nishijima_formula \"Gell-Mann–Nishijima formula\"), developed by [Murray Gell-Mann](https:\/\/en.wikipedia.org\/wiki\/Murray_Gell-Mann \"Murray Gell-Mann\") and [Kazuhiko Nishijima](https:\/\/en.wikipedia.org\/wiki\/Kazuhiko_Nishijima \"Kazuhiko Nishijima\"), led to the [Eightfold Way](https:\/\/en.wikipedia.org\/wiki\/Eightfold_way_\\(physics\\) \"Eightfold way (physics)\") classification, invented by Gell-Mann, with important independent contributions from [Yuval Ne'eman](https:\/\/en.wikipedia.org\/wiki\/Yuval_Ne%27eman \"Yuval Ne'eman\"), in 1961. The hadrons were organized into SU(3) representation multiplets, octets and decuplets, of roughly the same mass, due to the strong interactions; and smaller mass differences linked to the flavor quantum numbers, invisible to the strong interactions. The [Gell-Mann–Okubo mass formula](https:\/\/en.wikipedia.org\/wiki\/Gell-Mann%E2%80%93Okubo_mass_formula \"Gell-Mann–Okubo mass formula\") systematized the quantification of these small mass differences among members of a hadronic multiplet, controlled by the [explicit symmetry breaking](https:\/\/en.wikipedia.org\/wiki\/Explicit_symmetry_breaking \"Explicit symmetry breaking\") of SU(3).\n\nThe spin-⁠3\/2⁠ [Ω−  baryon](https:\/\/en.wikipedia.org\/wiki\/Omega_baryon \"Omega baryon\"), a member of the ground-state decuplet, was a crucial prediction of that classification. After it was discovered in an experiment at [Brookhaven National Laboratory](https:\/\/en.wikipedia.org\/wiki\/Brookhaven_National_Laboratory \"Brookhaven National Laboratory\"), Gell-Mann received a [Nobel Prize in Physics](https:\/\/en.wikipedia.org\/wiki\/Nobel_Prize_in_Physics \"Nobel Prize in Physics\") for his work on the Eightfold Way, in 1969.\n\nFinally, in 1964, Gell-Mann and [George Zweig](https:\/\/en.wikipedia.org\/wiki\/George_Zweig \"George Zweig\"), discerned independently what the Eightfold Way picture encodes: They posited three elementary fermionic constituents—the \"[up](https:\/\/en.wikipedia.org\/wiki\/Up_quark \"Up quark\")\", \"[down](https:\/\/en.wikipedia.org\/wiki\/Down_quark \"Down quark\")\", and \"[strange](https:\/\/en.wikipedia.org\/wiki\/Strange_quark \"Strange quark\")\" quarks—which are unobserved, and possibly unobservable in a free form. Simple pairwise or triplet combinations of these three constituents and their antiparticles underlie and elegantly encode the Eightfold Way classification, in an economical, tight structure, resulting in further simplicity. Hadronic mass differences were now linked to the different masses of the constituent quarks.\n\nIt would take about a decade for the unexpected nature—and physical reality—of these quarks to be appreciated more fully (See [Quarks](https:\/\/en.wikipedia.org\/wiki\/Quarks \"Quarks\")). Counter-intuitively, they cannot ever be observed in isolation ([color confinement](https:\/\/en.wikipedia.org\/wiki\/Color_confinement \"Color confinement\")), but instead always combine with other quarks to form full hadrons, which then furnish ample indirect information on the trapped quarks themselves. Conversely, the quarks serve in the definition of [quantum chromodynamics](https:\/\/en.wikipedia.org\/wiki\/Quantum_chromodynamics \"Quantum chromodynamics\"), the fundamental theory fully describing the strong interactions; and the Eightfold Way is now understood to be a consequence of the flavor symmetry structure of the lightest three of them.\n\n## Mesons\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&action=edit&section=2 \"Edit section: Mesons\")\\]\n\nSee also: [Meson](https:\/\/en.wikipedia.org\/wiki\/Meson \"Meson\") and [List of mesons](https:\/\/en.wikipedia.org\/wiki\/List_of_mesons \"List of mesons\")\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/c0\/Meson_nonet_-_spin_0.svg\/250px-Meson_nonet_-_spin_0.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:Meson_nonet_-_spin_0.svg)\n\n**Figure 2**: [Pseudoscalar mesons](https:\/\/en.wikipedia.org\/wiki\/Pseudoscalar_meson \"Pseudoscalar meson\") of spin-0 form a nonet\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/1\/13\/Meson_nonet_-_spin_1.svg\/250px-Meson_nonet_-_spin_1.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:Meson_nonet_-_spin_1.svg)\n\n**Figure 3**: [Vector mesons](https:\/\/en.wikipedia.org\/wiki\/Vector_mesons \"Vector mesons\") of spin-1 form a nonet\n\nThe Eightfold Way classification is named after the following fact: If we take three flavors of quarks, then the quarks lie in the [fundamental representation](https:\/\/en.wikipedia.org\/wiki\/Fundamental_representation \"Fundamental representation\"), **3** (called the triplet) of [flavor](https:\/\/en.wikipedia.org\/wiki\/Flavour_\\(particle_physics\\) \"Flavour (particle physics)\") [SU(3)](https:\/\/en.wikipedia.org\/wiki\/SU\\(3\\) \"SU(3)\"). The antiquarks lie in the complex conjugate representation **3**. The nine states (nonet) made out of a pair can be decomposed into the [trivial representation](https:\/\/en.wikipedia.org\/wiki\/Trivial_representation \"Trivial representation\"), **1** (called the singlet), and the [adjoint representation](https:\/\/en.wikipedia.org\/wiki\/Adjoint_representation_of_a_Lie_group \"Adjoint representation of a Lie group\"), **8** (called the octet). The notation for this decomposition is\n\n3\n\n⊗\n\n3\n\n¯\n\n\\=\n\n8\n\n⊕\n\n1\n\n.\n\n{\\\\displaystyle \\\\mathbf {3} \\\\otimes \\\\mathbf {\\\\overline {3}} =\\\\mathbf {8} \\\\oplus \\\\mathbf {1} ~.}\n\n![{\\\\displaystyle \\\\mathbf {3} \\\\otimes \\\\mathbf {\\\\overline {3}} =\\\\mathbf {8} \\\\oplus \\\\mathbf {1} ~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/ac6f83cd866c815a8e296a97b3abd91cde4c78cc)\n\nFigure 1 shows the application of this decomposition to the mesons. If the flavor symmetry were exact (as in the limit that only the strong interactions operate, but the electroweak interactions are notionally switched off), then all nine mesons would have the same mass. However, the physical content of the full theory\\[*[clarification needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Please_clarify \"Wikipedia:Please clarify\")*\\] 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).\n\nN.B. Nevertheless, the mass splitting between the η and the η′ is larger than the quark model can accommodate, and this \"[η–η′ puzzle](https:\/\/en.wikipedia.org\/wiki\/QCD_vacuum#Eta_prime_meson \"QCD vacuum\")\" has its origin in topological peculiarities of the strong interaction vacuum, such as [instanton](https:\/\/en.wikipedia.org\/wiki\/Instanton \"Instanton\") configurations.\n\nMesons are hadrons with zero [baryon number](https:\/\/en.wikipedia.org\/wiki\/Baryon_number \"Baryon number\"). If the quark–antiquark pair are in an [orbital angular momentum](https:\/\/en.wikipedia.org\/wiki\/Angular_momentum_operator \"Angular momentum operator\") L state, and have [spin](https:\/\/en.wikipedia.org\/wiki\/Spin_\\(physics\\) \"Spin (physics)\") S, then\n\n- \\|*L* − *S*\\| ≤ *J* ≤ *L* + *S*, where *S* = 0 or 1,\n- *P* = (−1)*L*\\+1, where the 1 in the exponent arises from the [intrinsic parity](https:\/\/en.wikipedia.org\/wiki\/Intrinsic_parity \"Intrinsic parity\") of the quark–antiquark pair.\n- *C* = (−1)*L*\\+*S* for mesons which have no [flavor](https:\/\/en.wikipedia.org\/wiki\/Flavour_\\(particle_physics\\) \"Flavour (particle physics)\"). Flavored mesons have indefinite value of [*C*](https:\/\/en.wikipedia.org\/wiki\/C_parity \"C parity\").\n- For [isospin](https:\/\/en.wikipedia.org\/wiki\/Isospin \"Isospin\") *I* = 1 and 0 states, one can define a new [multiplicative quantum number](https:\/\/en.wikipedia.org\/wiki\/Multiplicative_quantum_number \"Multiplicative quantum number\") called the *[G-parity](https:\/\/en.wikipedia.org\/wiki\/G-parity \"G-parity\")* such that *G* = (−1)*I*\\+*L*\\+*S*.\n\nIf *P* = (−1)*J*, 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 thus called *exotic* (for example, the state *J**PC* = 0−−).\n\n## Baryons\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&action=edit&section=3 \"Edit section: Baryons\")\\]\n\nMain article: [Baryon](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\")\n\nSee also: [List of baryons](https:\/\/en.wikipedia.org\/wiki\/List_of_baryons \"List of baryons\")\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/4\/4b\/Baryon_octet.png\/250px-Baryon_octet.png)](https:\/\/en.wikipedia.org\/wiki\/File:Baryon_octet.png)\n\n**Figure 4**. The\n\n*S* =\n\n⁠1\/2⁠\n\nground state [baryon](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\") octet\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/ec\/Baryon_decuplet.png\/250px-Baryon_decuplet.png)](https:\/\/en.wikipedia.org\/wiki\/File:Baryon_decuplet.png)\n\n**Figure 5**. The\n\n*S* =\n\n⁠3\/2⁠\n\n[baryon](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\") decuplet\n\nSince quarks are [fermions](https:\/\/en.wikipedia.org\/wiki\/Fermion \"Fermion\"), the [spin–statistics theorem](https:\/\/en.wikipedia.org\/wiki\/Spin%E2%80%93statistics_theorem \"Spin–statistics theorem\") implies that the [wavefunction](https:\/\/en.wikipedia.org\/wiki\/Wavefunction \"Wavefunction\") of a baryon must be antisymmetric under the exchange of any two quarks. This antisymmetric wavefunction is obtained by making it fully antisymmetric in color, discussed below, and symmetric in flavor, spin and space put together. With three flavors, the decomposition in flavor is 3 ⊗ 3 ⊗ 3 \\= 10 S ⊕ 8 M ⊕ 8 M ⊕ 1 A . {\\\\displaystyle \\\\mathbf {3} \\\\otimes \\\\mathbf {3} \\\\otimes \\\\mathbf {3} =\\\\mathbf {10} \\_{S}\\\\oplus \\\\mathbf {8} \\_{M}\\\\oplus \\\\mathbf {8} \\_{M}\\\\oplus \\\\mathbf {1} \\_{A}~.} ![{\\\\displaystyle \\\\mathbf {3} \\\\otimes \\\\mathbf {3} \\\\otimes \\\\mathbf {3} =\\\\mathbf {10} \\_{S}\\\\oplus \\\\mathbf {8} \\_{M}\\\\oplus \\\\mathbf {8} \\_{M}\\\\oplus \\\\mathbf {1} \\_{A}~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/efe21e8ee3332d4c573b43eea5321da19262e2c6) The decuplet is symmetric in flavor, 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.\n\nIt is sometimes useful to think of the [basis states](https:\/\/en.wikipedia.org\/wiki\/Quantum_state#Basis_states_of_one-particle_systems \"Quantum state\") of quarks as the six states of three flavors and two spins per flavor. This approximate symmetry is called spin-flavor [SU(6)](https:\/\/en.wikipedia.org\/wiki\/SU\\(6\\) \"SU(6)\"). In terms of this, the decomposition is 6 ⊗ 6 ⊗ 6 \\= 56 S ⊕ 70 M ⊕ 70 M ⊕ 20 A . {\\\\displaystyle \\\\mathbf {6} \\\\otimes \\\\mathbf {6} \\\\otimes \\\\mathbf {6} =\\\\mathbf {56} \\_{S}\\\\oplus \\\\mathbf {70} \\_{M}\\\\oplus \\\\mathbf {70} \\_{M}\\\\oplus \\\\mathbf {20} \\_{A}~.} ![{\\\\displaystyle \\\\mathbf {6} \\\\otimes \\\\mathbf {6} \\\\otimes \\\\mathbf {6} =\\\\mathbf {56} \\_{S}\\\\oplus \\\\mathbf {70} \\_{M}\\\\oplus \\\\mathbf {70} \\_{M}\\\\oplus \\\\mathbf {20} \\_{A}~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/613eb3fb4d716059f31551e9166f05abe035a79b)\n\nThe 56 states with symmetric combination of spin and flavour decompose under flavor [SU(3)](https:\/\/en.wikipedia.org\/wiki\/SU\\(3\\) \"SU(3)\") into 56 \\= 10 3 2 ⊕ 8 1 2 , {\\\\displaystyle \\\\mathbf {56} =\\\\mathbf {10} ^{\\\\frac {3}{2}}\\\\oplus \\\\mathbf {8} ^{\\\\frac {1}{2}}~,} ![{\\\\displaystyle \\\\mathbf {56} =\\\\mathbf {10} ^{\\\\frac {3}{2}}\\\\oplus \\\\mathbf {8} ^{\\\\frac {1}{2}}~,}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/6289d9cac1a1b9aceb282456deed0142207abff1) where the superscript denotes the spin, *S*, of the baryon. Since these states are symmetric in spin and flavor, 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.\n\nThe *S* = ⁠1\/2⁠ octet baryons are the two [nucleons](https:\/\/en.wikipedia.org\/wiki\/Nucleon \"Nucleon\") (p\\+  \n, n0  \n), the three [Sigmas](https:\/\/en.wikipedia.org\/wiki\/Sigma_baryon \"Sigma baryon\") (Σ\\+  \n, Σ0  \n, Σ−  \n), the two [Xis](https:\/\/en.wikipedia.org\/wiki\/Xi_baryon \"Xi baryon\") (Ξ0  \n, Ξ−  \n), and the [Lambda](https:\/\/en.wikipedia.org\/wiki\/Lambda_baryon \"Lambda baryon\") (Λ0  \n). The *S* = ⁠3\/2⁠ decuplet baryons are the four [Deltas](https:\/\/en.wikipedia.org\/wiki\/Delta_baryon \"Delta baryon\") (Δ\\++  \n, Δ\\+  \n, Δ0  \n, Δ−  \n), three [Sigmas](https:\/\/en.wikipedia.org\/wiki\/Sigma_baryon \"Sigma baryon\") (Σ∗+  \n, Σ∗0  \n, Σ∗−  \n), two [Xis](https:\/\/en.wikipedia.org\/wiki\/Xi_baryon \"Xi baryon\") (Ξ∗0  \n, Ξ∗−  \n), and the [Omega](https:\/\/en.wikipedia.org\/wiki\/Omega_particle \"Omega particle\") (Ω−  \n).\n\nFor example, the constituent quark model wavefunction for the proton is \\| p ↑ ⟩ \\= 1 18 \\[ 2 \\| u ↑ d ↓ u ↑ ⟩ \\+ 2 \\| u ↑ u ↑ d ↓ ⟩ \\+ 2 \\| d ↓ u ↑ u ↑ ⟩ − \\| u ↑ u ↓ d ↑ ⟩ − \\| u ↑ d ↑ u ↓ ⟩ − \\| u ↓ d ↑ u ↑ ⟩ − \\| d ↑ u ↓ u ↑ ⟩ − \\| d ↑ u ↑ u ↓ ⟩ − \\| u ↓ u ↑ d ↑ ⟩ \\] . {\\\\displaystyle \\|{\\\\text{p}}\\_{\\\\uparrow }\\\\rangle ={\\\\frac {1}{\\\\sqrt {18}}}\\[2\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle +2\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\downarrow }\\\\rangle +2\\|{\\\\text{d}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{d}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\uparrow }\\\\rangle \\]~.} ![{\\\\displaystyle \\|{\\\\text{p}}\\_{\\\\uparrow }\\\\rangle ={\\\\frac {1}{\\\\sqrt {18}}}\\[2\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle +2\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\downarrow }\\\\rangle +2\\|{\\\\text{d}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{d}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\uparrow }\\\\rangle \\]~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c5d84892af6c62784c12f0b691cd79d4d8584b3a)\n\nMixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other quantities that the model predicts successfully.\n\nThe group theory approach described above assumes that the quarks are eight components of a single particle, so the anti-symmetrization applies to all the quarks. A simpler approach is to consider the eight flavored quarks as eight separate, distinguishable, non-identical particles. Then the anti-symmetrization applies only to two identical quarks (like uu, for instance).[\\[6\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-JF1968-6)\n\nThen, the proton wavefunction can be written in a simpler form:\n\np\n\n(\n\n1\n\n2\n\n,\n\n1\n\n2\n\n)\n\n\\=\n\nu\n\nu\n\nd\n\n6\n\n\\[\n\n2\n\n↑↑↓\n\n−\n\n↑↓↑\n\n−\n\n↓↑↑\n\n\\]\n\n{\\\\displaystyle {\\\\text{p}}\\\\left({\\\\frac {1}{2}},{\\\\frac {1}{2}}\\\\right)={\\\\frac {{\\\\text{u}}{\\\\text{u}}{\\\\text{d}}}{\\\\sqrt {6}}}\\[2\\\\uparrow \\\\uparrow \\\\downarrow -\\\\uparrow \\\\downarrow \\\\uparrow -\\\\downarrow \\\\uparrow \\\\uparrow \\]}\n\n![{\\\\displaystyle {\\\\text{p}}\\\\left({\\\\frac {1}{2}},{\\\\frac {1}{2}}\\\\right)={\\\\frac {{\\\\text{u}}{\\\\text{u}}{\\\\text{d}}}{\\\\sqrt {6}}}\\[2\\\\uparrow \\\\uparrow \\\\downarrow -\\\\uparrow \\\\downarrow \\\\uparrow -\\\\downarrow \\\\uparrow \\\\uparrow \\]}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/530602aa73765eab71fa2e8847f9f2764325d62c)\n\nand the\n\nΔ\n\n\\+\n\n(\n\n3\n\n3\n\n,\n\n3\n\n2\n\n)\n\n\\=\n\nu\n\nu\n\nd\n\n\\[\n\n↑↑↑\n\n\\]\n\n.\n\n{\\\\displaystyle \\\\Delta ^{+}\\\\left({\\\\frac {3}{3}},{\\\\frac {3}{2}}\\\\right)={\\\\text{u}}{\\\\text{u}}{\\\\text{d}}\\[\\\\uparrow \\\\uparrow \\\\uparrow \\]~.}\n\n![{\\\\displaystyle \\\\Delta ^{+}\\\\left({\\\\frac {3}{3}},{\\\\frac {3}{2}}\\\\right)={\\\\text{u}}{\\\\text{u}}{\\\\text{d}}\\[\\\\uparrow \\\\uparrow \\\\uparrow \\]~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/89c6b137d6e75df3c098948d8107f061ceafa1b8)\n\nIf quark–quark interactions are limited to two-body interactions, then all the successful quark model predictions, including sum rules for baryon masses and magnetic moments, can be derived.\n\n### Discovery of color\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&action=edit&section=4 \"Edit section: Discovery of color\")\\]\n\nMain article: [Color charge](https:\/\/en.wikipedia.org\/wiki\/Color_charge \"Color charge\")\n\nColor quantum numbers are the characteristic charges of the strong force, and are completely uninvolved in electroweak interactions. They were discovered as a consequence of the quark model classification, when it was appreciated that the spin *S* = ⁠3\/2⁠ baryon, the Δ\\++  \n, required three up quarks with parallel spins and vanishing orbital angular momentum. Therefore, it could not have an antisymmetric wavefunction, (required by the [Pauli exclusion principle](https:\/\/en.wikipedia.org\/wiki\/Pauli_exclusion_principle \"Pauli exclusion principle\")). [Oscar Greenberg](https:\/\/en.wikipedia.org\/wiki\/Oscar_Greenberg \"Oscar Greenberg\") noted this problem in 1964, suggesting that quarks should be [para-fermions](https:\/\/en.wikipedia.org\/wiki\/Para-fermion \"Para-fermion\").[\\[7\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-7)\n\nInstead, six months later, [Moo-Young Han](https:\/\/en.wikipedia.org\/wiki\/Moo-Young_Han \"Moo-Young Han\") and [Yoichiro Nambu](https:\/\/en.wikipedia.org\/wiki\/Yoichiro_Nambu \"Yoichiro Nambu\") suggested the existence of a hidden degree of freedom, they labeled as the group SU(3)' (but later called 'color). This led to three triplets of quarks whose wavefunction was anti-symmetric in the color degree of freedom. Flavor and color were intertwined in that model: they did not commute.[\\[8\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-8)\n\nThe modern concept of color completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [William Bardeen](https:\/\/en.wikipedia.org\/wiki\/William_A._Bardeen \"William A. Bardeen\"), [Harald Fritzsch](https:\/\/de.wikipedia.org\/wiki\/Harald_Fritzsch \"de:Harald Fritzsch\"), and [Murray Gell-Mann](https:\/\/en.wikipedia.org\/wiki\/Murray_Gell-Mann \"Murray Gell-Mann\").[\\[9\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-9)[\\[10\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-10)\n\n## States outside the quark model\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&action=edit&section=5 \"Edit section: States outside the quark model\")\\]\n\nWhile the quark model is derivable from the theory of [quantum chromodynamics](https:\/\/en.wikipedia.org\/wiki\/Quantum_chromodynamics \"Quantum chromodynamics\"), the structure of hadrons is more complicated than this model allows. The full [quantum mechanical](https:\/\/en.wikipedia.org\/wiki\/Quantum_mechanics \"Quantum mechanics\") [wavefunction](https:\/\/en.wikipedia.org\/wiki\/Wavefunction \"Wavefunction\") of any hadron must include virtual quark pairs as well as virtual [gluons](https:\/\/en.wikipedia.org\/wiki\/Gluon \"Gluon\"), and allows for a variety of mixings. There may be hadrons which lie outside the quark model. Among these are the *[glueballs](https:\/\/en.wikipedia.org\/wiki\/Glueball \"Glueball\")* (which contain only valence gluons), *hybrids* (which contain valence quarks as well as gluons) and *[exotic hadrons](https:\/\/en.wikipedia.org\/wiki\/Exotic_hadron \"Exotic hadron\")* (such as [tetraquarks](https:\/\/en.wikipedia.org\/wiki\/Tetraquark \"Tetraquark\") or [pentaquarks](https:\/\/en.wikipedia.org\/wiki\/Pentaquark \"Pentaquark\")).\n\n## See also\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&action=edit&section=6 \"Edit section: See also\")\\]\n\n- [Subatomic particles](https:\/\/en.wikipedia.org\/wiki\/Subatomic_particles \"Subatomic particles\")\n- [Hadrons](https:\/\/en.wikipedia.org\/wiki\/Hadron \"Hadron\"), [baryons](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\"), [mesons](https:\/\/en.wikipedia.org\/wiki\/Meson \"Meson\") and [quarks](https:\/\/en.wikipedia.org\/wiki\/Quark \"Quark\")\n- [Exotic hadrons](https:\/\/en.wikipedia.org\/wiki\/Exotic_hadron \"Exotic hadron\"): [exotic mesons](https:\/\/en.wikipedia.org\/wiki\/Exotic_meson \"Exotic meson\") and [exotic baryons](https:\/\/en.wikipedia.org\/wiki\/Exotic_baryon \"Exotic baryon\")\n- [Quantum chromodynamics](https:\/\/en.wikipedia.org\/wiki\/Quantum_chromodynamics \"Quantum chromodynamics\"), [flavor](https:\/\/en.wikipedia.org\/wiki\/Flavour_\\(particle_physics\\) \"Flavour (particle physics)\"), the [QCD vacuum](https:\/\/en.wikipedia.org\/wiki\/QCD_vacuum \"QCD vacuum\")\n\n## Notes\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&action=edit&section=7 \"Edit section: Notes\")\\]\n\n1. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-Gell-Man1964_1-0)**\n   [Gell-Mann, M.](https:\/\/en.wikipedia.org\/wiki\/Murray_Gell-Mann \"Murray Gell-Mann\") (4 January 1964). \"A Schematic Model of Baryons and Mesons\". *[Physics Letters](https:\/\/en.wikipedia.org\/wiki\/Physics_Letters \"Physics Letters\")*. **8** (3): 214–215\\. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1964PhL.....8..214G](https:\/\/ui.adsabs.harvard.edu\/abs\/1964PhL.....8..214G). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/S0031-9163(64)92001-3](https:\/\/doi.org\/10.1016%2FS0031-9163%2864%2992001-3).\n2. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-Zweig1964a_2-0)**\n   [Zweig, G.](https:\/\/en.wikipedia.org\/wiki\/George_Zweig \"George Zweig\") (17 January 1964). [An SU(3) Model for Strong Interaction Symmetry and its Breaking](https:\/\/cds.cern.ch\/record\/352337\/files\/CERN-TH-401.pdf) (PDF) (Report). CERN Report No.8182\/TH.401.\n3. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-Zweig1964b_3-0)**\n   [Zweig, G.](https:\/\/en.wikipedia.org\/wiki\/George_Zweig \"George Zweig\") (1964). [An SU(3) Model for Strong Interaction Symmetry and its Breaking: II](https:\/\/cds.cern.ch\/record\/570209\/files\/CERN-TH-412.pdf) (PDF) (Report). CERN Report No.8419\/TH.412.\n4. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-4)**\n   [Petermann, A.](https:\/\/en.wikipedia.org\/wiki\/Andr%C3%A9_Petermann \"André Petermann\") (1965). \"Propriétés de l'étrangeté et une formule de masse pour les mésons vectoriels\" \\[Strangeness properties and a mass formula for vector meson\\]. *[Nuclear Physics](https:\/\/en.wikipedia.org\/wiki\/Nuclear_Physics_\\(journal\\) \"Nuclear Physics (journal)\")*. **63** (2): 349–352\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1412\\.8681](https:\/\/arxiv.org\/abs\/1412.8681). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1965NucPh..63..349P](https:\/\/ui.adsabs.harvard.edu\/abs\/1965NucPh..63..349P). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/0029-5582(65)90348-2](https:\/\/doi.org\/10.1016%2F0029-5582%2865%2990348-2).\n5. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-5)**\n   Petrov, Vladimir A. (June 23–27, 2014). *Half a Century with QUARKS*. XXX-th International Workshop on High Energy Physics. [Protvino](https:\/\/en.wikipedia.org\/wiki\/Protvino \"Protvino\"), [Moscow Oblast](https:\/\/en.wikipedia.org\/wiki\/Moscow_Oblast \"Moscow Oblast\"), Russia. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1412\\.8681](https:\/\/arxiv.org\/abs\/1412.8681).\n6. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-JF1968_6-0)**\n   Franklin, J. (1968). \"A Model of Baryons Made of Quarks with Hidden Spin\". *[Physical Review](https:\/\/en.wikipedia.org\/wiki\/Physical_Review \"Physical Review\")*. **172** (3): 1807–1817\\. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1968PhRv..172.1807F](https:\/\/ui.adsabs.harvard.edu\/abs\/1968PhRv..172.1807F). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1103\/PhysRev.172.1807](https:\/\/doi.org\/10.1103%2FPhysRev.172.1807).\n7. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-7)**\n   Greenberg, O.W. (1964). \"Spin and unitary-spin independence in a paraquark model of baryons and mesons\". *[Physical Review Letters](https:\/\/en.wikipedia.org\/wiki\/Physical_Review_Letters \"Physical Review Letters\")*. **13** (20): 598–602\\. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1964PhRvL..13..598G](https:\/\/ui.adsabs.harvard.edu\/abs\/1964PhRvL..13..598G). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1103\/PhysRevLett.13.598](https:\/\/doi.org\/10.1103%2FPhysRevLett.13.598).\n8. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-8)**\n   Han, M.Y.; Nambu, Y. (1965). [\"Three-triplet model with double SU(3) symmetry\"](https:\/\/digital.library.unt.edu\/ark:\/67531\/metadc1031342\/). *[Physical Review B](https:\/\/en.wikipedia.org\/wiki\/Physical_Review_B \"Physical Review B\")*. **139** (4B): 1006. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1965PhRv..139.1006H](https:\/\/ui.adsabs.harvard.edu\/abs\/1965PhRv..139.1006H). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1103\/PhysRev.139.B1006](https:\/\/doi.org\/10.1103%2FPhysRev.139.B1006).\n9. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-9)**\n   Bardeen, W.; Fritzsch, H.; Gell-Mann, M. (1973). [\"Light cone current algebra, *π*0 decay, and *e*\\+ *e*− annihilation\"](https:\/\/archive.org\/details\/scaleconformalsy0000unse\/page\/139). In Gatto, R. (ed.). *Scale and conformal symmetry in hadron physics*. [John Wiley & Sons](https:\/\/en.wikipedia.org\/wiki\/John_Wiley_%26_Sons \"John Wiley & Sons\"). p. [139](https:\/\/archive.org\/details\/scaleconformalsy0000unse\/page\/139). [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-ph\/0211388](https:\/\/arxiv.org\/abs\/hep-ph\/0211388). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2002hep.ph...11388B](https:\/\/ui.adsabs.harvard.edu\/abs\/2002hep.ph...11388B). [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n   \n   [0-471-29292-3](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/0-471-29292-3 \"Special:BookSources\/0-471-29292-3\")\n   \n   .\n10. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-10)**\n    Fritzsch, H.; Gell-Mann, M.; Leutwyler, H. (1973). \"Advantages of the color octet gluon picture\". *[Physics Letters B](https:\/\/en.wikipedia.org\/wiki\/Physics_Letters_B \"Physics Letters B\")*. **47** (4): 365. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1973PhLB...47..365F](https:\/\/ui.adsabs.harvard.edu\/abs\/1973PhLB...47..365F). [CiteSeerX](https:\/\/en.wikipedia.org\/wiki\/CiteSeerX_\\(identifier\\) \"CiteSeerX (identifier)\") [10\\.1.1.453.4712](https:\/\/citeseerx.ist.psu.edu\/viewdoc\/summary?doi=10.1.1.453.4712). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/0370-2693(73)90625-4](https:\/\/doi.org\/10.1016%2F0370-2693%2873%2990625-4).\n\n## References\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&action=edit&section=8 \"Edit section: References\")\\]\n\n- S. Eidelman *et al.* [Particle Data Group](https:\/\/en.wikipedia.org\/wiki\/Particle_Data_Group \"Particle Data Group\") (2004). [\"Review of Particle Physics\"](http:\/\/pdg.lbl.gov\/2004\/reviews\/quarkmodrpp.pdf) (PDF). *[Physics Letters B](https:\/\/en.wikipedia.org\/wiki\/Physics_Letters_B \"Physics Letters B\")*. **592** (1–4\\): 1. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[astro-ph\/0406663](https:\/\/arxiv.org\/abs\/astro-ph\/0406663). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2004PhLB..592....1P](https:\/\/ui.adsabs.harvard.edu\/abs\/2004PhLB..592....1P). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/j.physletb.2004.06.001](https:\/\/doi.org\/10.1016%2Fj.physletb.2004.06.001). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [118588567](https:\/\/api.semanticscholar.org\/CorpusID:118588567).\n- Lichtenberg, D B (1970). *Unitary Symmetry and Elementary Particles*. Academic Press. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [978-1483242729](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-1483242729 \"Special:BookSources\/978-1483242729\")\n  \n  .\n- Thomson, M A (2011), [Lecture notes](http:\/\/www.hep.phy.cam.ac.uk\/~thomson\/partIIIparticles\/handouts\/Handout_7_2011.pdf)\n- J.J.J. Kokkedee (1969). [*The quark model*](https:\/\/archive.org\/details\/quarkmodel0000kokk). [W. A. Benjamin](https:\/\/en.wikipedia.org\/wiki\/W._A._Benjamin \"W. A. Benjamin\"). [ASIN](https:\/\/en.wikipedia.org\/wiki\/ASIN_\\(identifier\\) \"ASIN (identifier)\") [B001RAVDIA](https:\/\/www.amazon.com\/dp\/B001RAVDIA).\n\n| [v](https:\/\/en.wikipedia.org\/wiki\/Template:Particles \"Template:Particles\") [t](https:\/\/en.wikipedia.org\/wiki\/Template_talk:Particles \"Template talk:Particles\") [e](https:\/\/en.wikipedia.org\/wiki\/Special:EditPage\/Template:Particles \"Special:EditPage\/Template:Particles\")[Particles in physics](https:\/\/en.wikipedia.org\/wiki\/Particle_physics \"Particle physics\") |   |\n|---|---|\n| [Elementary](https:\/\/en.wikipedia.org\/wiki\/Elementary_particle \"Elementary particle\") |   |\n|   |   |\n| [Fermions](https:\/\/en.wikipedia.org\/wiki\/Fermion \"Fermion\") |   |\n|   |   |\n| [Quarks](https:\/\/en.wikipedia.org\/wiki\/Quark \"Quark\") | [Up (quark](https:\/\/en.wikipedia.org\/wiki\/Up_quark \"Up quark\") [antiquark)](https:\/\/en.wikipedia.org\/wiki\/Up_antiquark \"Up antiquark\") [Down (quark](https:\/\/en.wikipedia.org\/wiki\/Down_quark \"Down quark\") [antiquark)](https:\/\/en.wikipedia.org\/wiki\/Down_antiquark \"Down antiquark\") [Charm (quark](https:\/\/en.wikipedia.org\/wiki\/Charm_quark \"Charm quark\") [antiquark)](https:\/\/en.wikipedia.org\/wiki\/Charm_antiquark \"Charm antiquark\") [Strange (quark](https:\/\/en.wikipedia.org\/wiki\/Strange_quark \"Strange quark\") [antiquark)](https:\/\/en.wikipedia.org\/wiki\/Strange_antiquark \"Strange antiquark\") [Top (quark](https:\/\/en.wikipedia.org\/wiki\/Top_quark \"Top quark\") [antiquark)](https:\/\/en.wikipedia.org\/wiki\/Top_antiquark \"Top antiquark\") [Bottom (quark](https:\/\/en.wikipedia.org\/wiki\/Bottom_quark \"Bottom quark\") [antiquark)](https:\/\/en.wikipedia.org\/wiki\/Bottom_antiquark \"Bottom antiquark\") |\n| [Leptons](https:\/\/en.wikipedia.org\/wiki\/Lepton \"Lepton\") | [Electron](https:\/\/en.wikipedia.org\/wiki\/Electron \"Electron\") [Positron](https:\/\/en.wikipedia.org\/wiki\/Positron \"Positron\") [Muon](https:\/\/en.wikipedia.org\/wiki\/Muon \"Muon\") [Antimuon](https:\/\/en.wikipedia.org\/wiki\/Muon \"Muon\") [Tau](https:\/\/en.wikipedia.org\/wiki\/Tau_\\(particle\\) \"Tau (particle)\") [Antitau](https:\/\/en.wikipedia.org\/wiki\/Tau_\\(particle\\) \"Tau (particle)\") [Neutrino](https:\/\/en.wikipedia.org\/wiki\/Neutrino \"Neutrino\") [Electron neutrino](https:\/\/en.wikipedia.org\/wiki\/Electron_neutrino \"Electron neutrino\") [Electron antineutrino](https:\/\/en.wikipedia.org\/wiki\/Neutrino#Antineutrinos \"Neutrino\") [Muon neutrino](https:\/\/en.wikipedia.org\/wiki\/Muon_neutrino \"Muon neutrino\") [Muon antineutrino](https:\/\/en.wikipedia.org\/wiki\/Neutrino#Antineutrinos \"Neutrino\") [Tau neutrino](https:\/\/en.wikipedia.org\/wiki\/Tau_neutrino \"Tau neutrino\") [Tau antineutrino](https:\/\/en.wikipedia.org\/wiki\/Neutrino#Antineutrinos \"Neutrino\") |\n| [Bosons](https:\/\/en.wikipedia.org\/wiki\/Boson \"Boson\") |   |\n|   |   |\n| [Gauge](https:\/\/en.wikipedia.org\/wiki\/Gauge_boson \"Gauge boson\") | [Photon](https:\/\/en.wikipedia.org\/wiki\/Photon \"Photon\") [Gluon](https:\/\/en.wikipedia.org\/wiki\/Gluon \"Gluon\") [W and Z bosons](https:\/\/en.wikipedia.org\/wiki\/W_and_Z_bosons \"W and Z bosons\") |\n| [Scalar](https:\/\/en.wikipedia.org\/wiki\/Scalar_boson \"Scalar boson\") | [Higgs boson](https:\/\/en.wikipedia.org\/wiki\/Higgs_boson \"Higgs boson\") |\n| [Ghost fields](https:\/\/en.wikipedia.org\/wiki\/Ghost_\\(physics\\) \"Ghost (physics)\") | [Faddeev–Popov ghosts](https:\/\/en.wikipedia.org\/wiki\/Faddeev%E2%80%93Popov_ghost \"Faddeev–Popov ghost\") |\n| [Hypothetical](https:\/\/en.wikipedia.org\/wiki\/List_of_hypothetical_particles \"List of hypothetical particles\") |   |\n|   |   |\n| [Superpartners](https:\/\/en.wikipedia.org\/wiki\/Superpartner \"Superpartner\") |   |\n|   |   |\n| [Gauginos](https:\/\/en.wikipedia.org\/wiki\/Gaugino \"Gaugino\") | [Gluino](https:\/\/en.wikipedia.org\/wiki\/Gluino \"Gluino\") [Gravitino](https:\/\/en.wikipedia.org\/wiki\/Gravitino \"Gravitino\") [Photino](https:\/\/en.wikipedia.org\/wiki\/Photino \"Photino\") |\n| Others | [Axino](https:\/\/en.wikipedia.org\/wiki\/Axino \"Axino\") [Chargino](https:\/\/en.wikipedia.org\/wiki\/Chargino \"Chargino\") [Higgsino](https:\/\/en.wikipedia.org\/wiki\/Higgsino \"Higgsino\") [Neutralino](https:\/\/en.wikipedia.org\/wiki\/Neutralino \"Neutralino\") [Sfermion](https:\/\/en.wikipedia.org\/wiki\/Sfermion \"Sfermion\") ([Stop squark](https:\/\/en.wikipedia.org\/wiki\/Stop_squark \"Stop squark\")) |\n| Others | [Axion](https:\/\/en.wikipedia.org\/wiki\/Axion \"Axion\") [Curvaton](https:\/\/en.wikipedia.org\/wiki\/Curvaton \"Curvaton\") [Dilaton](https:\/\/en.wikipedia.org\/wiki\/Dilaton \"Dilaton\") [Dual graviton](https:\/\/en.wikipedia.org\/wiki\/Dual_graviton \"Dual graviton\") [Graviphoton](https:\/\/en.wikipedia.org\/wiki\/Graviphoton \"Graviphoton\") [Graviton](https:\/\/en.wikipedia.org\/wiki\/Graviton \"Graviton\") [Inflaton](https:\/\/en.wikipedia.org\/wiki\/Inflaton \"Inflaton\") [Leptoquark](https:\/\/en.wikipedia.org\/wiki\/Leptoquark \"Leptoquark\") [Magnetic monopole](https:\/\/en.wikipedia.org\/wiki\/Magnetic_monopole \"Magnetic monopole\") [Majoron](https:\/\/en.wikipedia.org\/wiki\/Majoron \"Majoron\") [Majorana fermion](https:\/\/en.wikipedia.org\/wiki\/Majorana_fermion \"Majorana fermion\") [Dark photon](https:\/\/en.wikipedia.org\/wiki\/Dark_photon \"Dark photon\") [Preon](https:\/\/en.wikipedia.org\/wiki\/Preon \"Preon\") [Sterile neutrino](https:\/\/en.wikipedia.org\/wiki\/Sterile_neutrino \"Sterile neutrino\") [Tachyon](https:\/\/en.wikipedia.org\/wiki\/Tachyon \"Tachyon\") [W′ and Z′ bosons](https:\/\/en.wikipedia.org\/wiki\/W%E2%80%B2_and_Z%E2%80%B2_bosons \"W′ and Z′ bosons\") [X and Y bosons](https:\/\/en.wikipedia.org\/wiki\/X_and_Y_bosons \"X and Y bosons\") |\n| [Composite](https:\/\/en.wikipedia.org\/wiki\/Bound_state \"Bound state\") |   |\n|   |   |\n| [Hadrons](https:\/\/en.wikipedia.org\/wiki\/Hadron \"Hadron\") |   |\n|   |   |\n| [Baryons](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\") | [Nucleon](https:\/\/en.wikipedia.org\/wiki\/Nucleon \"Nucleon\") [Proton](https:\/\/en.wikipedia.org\/wiki\/Proton \"Proton\") [Antiproton](https:\/\/en.wikipedia.org\/wiki\/Antiproton \"Antiproton\") [Neutron](https:\/\/en.wikipedia.org\/wiki\/Neutron \"Neutron\") [Antineutron](https:\/\/en.wikipedia.org\/wiki\/Antineutron \"Antineutron\") [Delta baryon](https:\/\/en.wikipedia.org\/wiki\/Delta_baryon \"Delta baryon\") [Lambda baryon](https:\/\/en.wikipedia.org\/wiki\/Lambda_baryon \"Lambda baryon\") [Sigma baryon](https:\/\/en.wikipedia.org\/wiki\/Sigma_baryon \"Sigma baryon\") [Xi baryon](https:\/\/en.wikipedia.org\/wiki\/Xi_baryon \"Xi baryon\") [Omega baryon](https:\/\/en.wikipedia.org\/wiki\/Omega_baryon \"Omega baryon\") |\n| [Mesons](https:\/\/en.wikipedia.org\/wiki\/Meson \"Meson\") | [Pion](https:\/\/en.wikipedia.org\/wiki\/Pion \"Pion\") [Rho meson](https:\/\/en.wikipedia.org\/wiki\/Rho_meson \"Rho meson\") [Eta and eta prime mesons](https:\/\/en.wikipedia.org\/wiki\/Eta_meson \"Eta meson\") [Bottom eta meson](https:\/\/en.wikipedia.org\/wiki\/Bottom_eta_meson \"Bottom eta meson\") [Phi meson](https:\/\/en.wikipedia.org\/wiki\/Phi_meson \"Phi meson\") [J\/psi meson](https:\/\/en.wikipedia.org\/wiki\/J\/psi_meson \"J\/psi meson\") [Omega meson](https:\/\/en.wikipedia.org\/wiki\/Omega_meson \"Omega meson\") [Upsilon meson](https:\/\/en.wikipedia.org\/wiki\/Upsilon_meson \"Upsilon meson\") [Kaon](https:\/\/en.wikipedia.org\/wiki\/Kaon \"Kaon\") [B meson](https:\/\/en.wikipedia.org\/wiki\/B_meson \"B meson\") [D meson](https:\/\/en.wikipedia.org\/wiki\/D_meson \"D meson\") [Quarkonium](https:\/\/en.wikipedia.org\/wiki\/Quarkonium \"Quarkonium\") |\n| [Exotic hadrons](https:\/\/en.wikipedia.org\/wiki\/Exotic_hadron \"Exotic hadron\") | [Tetraquark](https:\/\/en.wikipedia.org\/wiki\/Tetraquark \"Tetraquark\") ([Double-charm tetraquark](https:\/\/en.wikipedia.org\/wiki\/Double-charm_tetraquark \"Double-charm tetraquark\")) [Pentaquark](https:\/\/en.wikipedia.org\/wiki\/Pentaquark \"Pentaquark\") |\n| Others | [Atomic nuclei](https:\/\/en.wikipedia.org\/wiki\/Atomic_nucleus \"Atomic nucleus\") [Atoms](https:\/\/en.wikipedia.org\/wiki\/Atom \"Atom\") [Exotic atoms](https:\/\/en.wikipedia.org\/wiki\/Exotic_atom \"Exotic atom\") [Positronium](https:\/\/en.wikipedia.org\/wiki\/Positronium \"Positronium\") [Muonium](https:\/\/en.wikipedia.org\/wiki\/Muonium \"Muonium\") [Tauonium](https:\/\/en.wikipedia.org\/wiki\/Tauonium \"Tauonium\") [Onia](https:\/\/en.wikipedia.org\/wiki\/Onium \"Onium\") [Pionium](https:\/\/en.wikipedia.org\/wiki\/Pionium \"Pionium\") [Protonium](https:\/\/en.wikipedia.org\/wiki\/Protonium \"Protonium\") [Antihydrogen](https:\/\/en.wikipedia.org\/wiki\/Antihydrogen \"Antihydrogen\") [Superatoms](https:\/\/en.wikipedia.org\/wiki\/Superatom \"Superatom\") [Molecules](https:\/\/en.wikipedia.org\/wiki\/Molecule \"Molecule\") |\n| [Hypothetical](https:\/\/en.wikipedia.org\/wiki\/List_of_hypothetical_particles \"List of hypothetical particles\") |   |\n|   |   |\n|   |   |\n| Baryons | [Hexaquark](https:\/\/en.wikipedia.org\/wiki\/Hexaquark \"Hexaquark\") [Heptaquark](https:\/\/en.wikipedia.org\/wiki\/Heptaquark \"Heptaquark\") [Skyrmion](https:\/\/en.wikipedia.org\/wiki\/Skyrmion \"Skyrmion\") |\n| Mesons | [Glueball](https:\/\/en.wikipedia.org\/wiki\/Glueball \"Glueball\") [Theta meson](https:\/\/en.wikipedia.org\/wiki\/Theta_meson \"Theta meson\") [T meson](https:\/\/en.wikipedia.org\/wiki\/T_meson \"T meson\") |\n| Others | [Mesonic molecule](https:\/\/en.wikipedia.org\/wiki\/Mesonic_molecule \"Mesonic molecule\") [Pomeron](https:\/\/en.wikipedia.org\/wiki\/Pomeron \"Pomeron\") [Diquark](https:\/\/en.wikipedia.org\/wiki\/Diquark \"Diquark\") [R-hadron](https:\/\/en.wikipedia.org\/wiki\/R-hadron \"R-hadron\") |\n| [Quasiparticles](https:\/\/en.wikipedia.org\/wiki\/Quasiparticle \"Quasiparticle\") | [Anyon](https:\/\/en.wikipedia.org\/wiki\/Anyon \"Anyon\") [Davydov soliton](https:\/\/en.wikipedia.org\/wiki\/Davydov_soliton \"Davydov soliton\") [Dropleton](https:\/\/en.wikipedia.org\/wiki\/Dropleton \"Dropleton\") [Exciton](https:\/\/en.wikipedia.org\/wiki\/Exciton \"Exciton\") [Fracton](https:\/\/en.wikipedia.org\/wiki\/Fracton_\\(subdimensional_particle\\) \"Fracton (subdimensional particle)\") [Hole](https:\/\/en.wikipedia.org\/wiki\/Electron_hole \"Electron hole\") [Magnon](https:\/\/en.wikipedia.org\/wiki\/Magnon \"Magnon\") [Phonon](https:\/\/en.wikipedia.org\/wiki\/Phonon \"Phonon\") [Plasmaron](https:\/\/en.wikipedia.org\/wiki\/Plasmaron \"Plasmaron\") [Plasmon](https:\/\/en.wikipedia.org\/wiki\/Plasmon \"Plasmon\") [Polariton](https:\/\/en.wikipedia.org\/wiki\/Polariton \"Polariton\") [Polaron](https:\/\/en.wikipedia.org\/wiki\/Polaron \"Polaron\") [Roton](https:\/\/en.wikipedia.org\/wiki\/Roton \"Roton\") [Trion](https:\/\/en.wikipedia.org\/wiki\/Trion_\\(physics\\) \"Trion (physics)\") |\n| Lists | [Baryons](https:\/\/en.wikipedia.org\/wiki\/List_of_baryons \"List of baryons\") [Mesons](https:\/\/en.wikipedia.org\/wiki\/List_of_mesons \"List of mesons\") [Particles](https:\/\/en.wikipedia.org\/wiki\/List_of_particles \"List of particles\") [Quasiparticles](https:\/\/en.wikipedia.org\/wiki\/List_of_quasiparticles \"List of quasiparticles\") [Timeline of particle discoveries](https:\/\/en.wikipedia.org\/wiki\/Timeline_of_particle_discoveries \"Timeline of particle discoveries\") |\n| Related | [History of subatomic physics](https:\/\/en.wikipedia.org\/wiki\/History_of_subatomic_physics \"History of subatomic physics\") [timeline](https:\/\/en.wikipedia.org\/wiki\/Timeline_of_atomic_and_subatomic_physics \"Timeline of atomic and subatomic physics\") [Standard Model](https:\/\/en.wikipedia.org\/wiki\/Standard_Model \"Standard Model\") [mathematical formulation](https:\/\/en.wikipedia.org\/wiki\/Mathematical_formulation_of_the_Standard_Model \"Mathematical formulation of the Standard Model\") [Subatomic particles](https:\/\/en.wikipedia.org\/wiki\/Subatomic_particle \"Subatomic particle\") [Particles](https:\/\/en.wikipedia.org\/wiki\/Particle \"Particle\") [Antiparticles](https:\/\/en.wikipedia.org\/wiki\/Antiparticle \"Antiparticle\") [Nuclear physics](https:\/\/en.wikipedia.org\/wiki\/Nuclear_physics \"Nuclear physics\") [Eightfold way](https:\/\/en.wikipedia.org\/wiki\/Eightfold_way_\\(physics\\) \"Eightfold way (physics)\") [Quark model]() [Exotic matter](https:\/\/en.wikipedia.org\/wiki\/Exotic_matter \"Exotic matter\") [Massless particle](https:\/\/en.wikipedia.org\/wiki\/Massless_particle \"Massless particle\") [Relativistic particle](https:\/\/en.wikipedia.org\/wiki\/Relativistic_particle \"Relativistic particle\") [Virtual particle](https:\/\/en.wikipedia.org\/wiki\/Virtual_particle \"Virtual particle\") [Wave–particle duality](https:\/\/en.wikipedia.org\/wiki\/Wave%E2%80%93particle_duality \"Wave–particle duality\") [Particle chauvinism](https:\/\/en.wikipedia.org\/wiki\/Particle_chauvinism \"Particle chauvinism\") |\n| [![](https:\/\/upload.wikimedia.org\/wikipedia\/en\/thumb\/e\/e2\/Symbol_portal_class.svg\/20px-Symbol_portal_class.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:Symbol_portal_class.svg \"Portal\") **[Physics portal](https:\/\/en.wikipedia.org\/wiki\/Portal:Physics \"Portal:Physics\")** |   |\n\n| [v](https:\/\/en.wikipedia.org\/wiki\/Template:Standard_model_of_physics \"Template:Standard model of physics\") [t](https:\/\/en.wikipedia.org\/wiki\/Template_talk:Standard_model_of_physics \"Template talk:Standard model of physics\") [e](https:\/\/en.wikipedia.org\/wiki\/Special:EditPage\/Template:Standard_model_of_physics \"Special:EditPage\/Template:Standard model of physics\")[Standard Model](https:\/\/en.wikipedia.org\/wiki\/Standard_Model \"Standard Model\") |   |   |\n|---|---|---|\n| Background | [Particle physics](https:\/\/en.wikipedia.org\/wiki\/Particle_physics \"Particle physics\") [Fermions](https:\/\/en.wikipedia.org\/wiki\/Fermion \"Fermion\") [Gauge boson](https:\/\/en.wikipedia.org\/wiki\/Gauge_boson \"Gauge boson\") [Higgs boson](https:\/\/en.wikipedia.org\/wiki\/Higgs_boson \"Higgs boson\") [Quantum field theory](https:\/\/en.wikipedia.org\/wiki\/Quantum_field_theory \"Quantum field theory\") [Gauge theory](https:\/\/en.wikipedia.org\/wiki\/Gauge_theory \"Gauge theory\") [Strong interaction](https:\/\/en.wikipedia.org\/wiki\/Strong_interaction \"Strong interaction\") [Color charge](https:\/\/en.wikipedia.org\/wiki\/Color_charge \"Color charge\") [Quantum chromodynamics](https:\/\/en.wikipedia.org\/wiki\/Quantum_chromodynamics \"Quantum chromodynamics\") [Quark model]() [Electroweak interaction](https:\/\/en.wikipedia.org\/wiki\/Electroweak_interaction \"Electroweak interaction\") [Weak interaction](https:\/\/en.wikipedia.org\/wiki\/Weak_interaction \"Weak interaction\") [Quantum electrodynamics](https:\/\/en.wikipedia.org\/wiki\/Quantum_electrodynamics \"Quantum electrodynamics\") [Fermi's interaction](https:\/\/en.wikipedia.org\/wiki\/Fermi%27s_interaction \"Fermi's interaction\") [Weak hypercharge](https:\/\/en.wikipedia.org\/wiki\/Weak_hypercharge \"Weak hypercharge\") [Weak isospin](https:\/\/en.wikipedia.org\/wiki\/Weak_isospin \"Weak isospin\") | ![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/0\/00\/Standard_Model_of_Elementary_Particles.svg\/250px-Standard_Model_of_Elementary_Particles.svg.png) |\n| Constituents | [CKM matrix](https:\/\/en.wikipedia.org\/wiki\/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix \"Cabibbo–Kobayashi–Maskawa matrix\") [Spontaneous symmetry breaking](https:\/\/en.wikipedia.org\/wiki\/Spontaneous_symmetry_breaking \"Spontaneous symmetry breaking\") [Higgs mechanism](https:\/\/en.wikipedia.org\/wiki\/Higgs_mechanism \"Higgs mechanism\") [Mathematical formulation of the Standard Model](https:\/\/en.wikipedia.org\/wiki\/Mathematical_formulation_of_the_Standard_Model \"Mathematical formulation of the Standard Model\") |   |\n| [Beyond the Standard Model](https:\/\/en.wikipedia.org\/wiki\/Physics_beyond_the_Standard_Model \"Physics beyond the Standard Model\") |   |   |\n|   |   |   |\n| Evidence | [Hierarchy problem](https:\/\/en.wikipedia.org\/wiki\/Hierarchy_problem \"Hierarchy problem\") [Dark matter](https:\/\/en.wikipedia.org\/wiki\/Dark_matter \"Dark matter\") [Cosmological constant](https:\/\/en.wikipedia.org\/wiki\/Cosmological_constant \"Cosmological constant\") [problem](https:\/\/en.wikipedia.org\/wiki\/Cosmological_constant_problem \"Cosmological constant problem\") [Strong CP problem](https:\/\/en.wikipedia.org\/wiki\/CP_violation \"CP violation\") [Neutrino oscillation](https:\/\/en.wikipedia.org\/wiki\/Neutrino_oscillation \"Neutrino oscillation\") |   |\n| Theories | [Technicolor](https:\/\/en.wikipedia.org\/wiki\/Technicolor_\\(physics\\) \"Technicolor (physics)\") [Kaluza–Klein theory](https:\/\/en.wikipedia.org\/wiki\/Kaluza%E2%80%93Klein_theory \"Kaluza–Klein theory\") [Grand Unified Theory](https:\/\/en.wikipedia.org\/wiki\/Grand_Unified_Theory \"Grand Unified Theory\") [Theory of everything](https:\/\/en.wikipedia.org\/wiki\/Theory_of_everything \"Theory of everything\") |   |\n| [Supersymmetry](https:\/\/en.wikipedia.org\/wiki\/Supersymmetry \"Supersymmetry\") | [MSSM](https:\/\/en.wikipedia.org\/wiki\/Minimal_Supersymmetric_Standard_Model \"Minimal Supersymmetric Standard Model\") [NMSSM](https:\/\/en.wikipedia.org\/wiki\/Next-to-Minimal_Supersymmetric_Standard_Model \"Next-to-Minimal Supersymmetric Standard Model\") [Split supersymmetry](https:\/\/en.wikipedia.org\/wiki\/Split_supersymmetry \"Split supersymmetry\") [Supergravity](https:\/\/en.wikipedia.org\/wiki\/Supergravity \"Supergravity\") |   |\n| [Quantum gravity](https:\/\/en.wikipedia.org\/wiki\/Quantum_gravity \"Quantum gravity\") | [String theory](https:\/\/en.wikipedia.org\/wiki\/String_theory \"String theory\") [Superstring theory](https:\/\/en.wikipedia.org\/wiki\/Superstring_theory \"Superstring theory\") [Loop quantum gravity](https:\/\/en.wikipedia.org\/wiki\/Loop_quantum_gravity \"Loop quantum gravity\") [Causal dynamical triangulation](https:\/\/en.wikipedia.org\/wiki\/Causal_dynamical_triangulation \"Causal dynamical triangulation\") [Canonical quantum gravity](https:\/\/en.wikipedia.org\/wiki\/Canonical_quantum_gravity \"Canonical quantum gravity\") [Superfluid vacuum theory](https:\/\/en.wikipedia.org\/wiki\/Superfluid_vacuum_theory \"Superfluid vacuum theory\") [Twistor theory](https:\/\/en.wikipedia.org\/wiki\/Twistor_theory \"Twistor theory\") |   |\n| Experiments | [Gran Sasso](https:\/\/en.wikipedia.org\/wiki\/Laboratori_Nazionali_del_Gran_Sasso \"Laboratori Nazionali del Gran Sasso\") [INO](https:\/\/en.wikipedia.org\/wiki\/India-based_Neutrino_Observatory \"India-based Neutrino Observatory\") [LHC](https:\/\/en.wikipedia.org\/wiki\/Large_Hadron_Collider \"Large Hadron Collider\") [SNO](https:\/\/en.wikipedia.org\/wiki\/Sudbury_Neutrino_Observatory \"Sudbury Neutrino Observatory\") [Super-K](https:\/\/en.wikipedia.org\/wiki\/Super-Kamiokande \"Super-Kamiokande\") [Tevatron](https:\/\/en.wikipedia.org\/wiki\/Tevatron \"Tevatron\") |   |\n| ![](https:\/\/upload.wikimedia.org\/wikipedia\/en\/thumb\/9\/96\/Symbol_category_class.svg\/20px-Symbol_category_class.svg.png) **[Category](https:\/\/en.wikipedia.org\/wiki\/Category:Standard_Model \"Category:Standard Model\")** [![](https:\/\/upload.wikimedia.org\/wikipedia\/en\/thumb\/4\/4a\/Commons-logo.svg\/20px-Commons-logo.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:Commons-logo.svg \"Commons page\") **[Commons](https:\/\/commons.wikimedia.org\/wiki\/Category:Standard_Model_\\(physics\\) \"commons:Category:Standard Model (physics)\")** |   |   |\n\n![](https:\/\/en.wikipedia.org\/wiki\/Special:CentralAutoLogin\/start?useformat=desktop&type=1x1&usesul3=1)\n\nRetrieved from \"<https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&oldid=1292342105>\"\n\n[Categories](https:\/\/en.wikipedia.org\/wiki\/Help:Category \"Help:Category\"):\n\n- [Hadrons](https:\/\/en.wikipedia.org\/wiki\/Category:Hadrons \"Category:Hadrons\")\n- [Quarks](https:\/\/en.wikipedia.org\/wiki\/Category:Quarks \"Category:Quarks\")\n- [Particle physics](https:\/\/en.wikipedia.org\/wiki\/Category:Particle_physics \"Category:Particle physics\")\n- [Concepts in physics](https:\/\/en.wikipedia.org\/wiki\/Category:Concepts_in_physics \"Category:Concepts in physics\")\n- [Standard Model](https:\/\/en.wikipedia.org\/wiki\/Category:Standard_Model \"Category:Standard Model\")\n- [Murray Gell-Mann](https:\/\/en.wikipedia.org\/wiki\/Category:Murray_Gell-Mann \"Category:Murray Gell-Mann\")\n\nHidden categories:\n\n- [Articles with short description](https:\/\/en.wikipedia.org\/wiki\/Category:Articles_with_short_description \"Category:Articles with short description\")\n- [Short description matches Wikidata](https:\/\/en.wikipedia.org\/wiki\/Category:Short_description_matches_Wikidata \"Category:Short description matches Wikidata\")\n- [Wikipedia articles needing clarification from February 2016](https:\/\/en.wikipedia.org\/wiki\/Category:Wikipedia_articles_needing_clarification_from_February_2016 \"Category:Wikipedia articles needing clarification from February 2016\")\n\n- This page was last edited on 26 May 2025, at 13:45 (UTC).\n- Text is available under the [Creative Commons Attribution-ShareAlike 4.0 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Wikipedia® is a registered trademark of the [Wikimedia Foundation, Inc.](https:\/\/wikimediafoundation.org\/), a non-profit organization.\n\n- [Privacy policy](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Policy:Privacy_policy)\n- [About Wikipedia](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:About)\n- [Disclaimers](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:General_disclaimer)\n- [Contact Wikipedia](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Contact_us)\n- [Legal & safety contacts](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Legal:Wikimedia_Foundation_Legal_and_Safety_Contact_Information)\n- [Code of Conduct](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Policy:Universal_Code_of_Conduct)\n- [Developers](https:\/\/developer.wikimedia.org\/)\n- [Statistics](https:\/\/stats.wikimedia.org\/#\/en.wikipedia.org)\n- [Cookie statement](https:\/\/foundation.wikimedia.org\/wiki\/Special:MyLanguage\/Policy:Cookie_statement)\n- [Mobile view](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&mobileaction=toggle_view_mobile)\n\n- [![Wikimedia Foundation](https:\/\/en.wikipedia.org\/static\/images\/footer\/wikimedia.svg)](https:\/\/www.wikimedia.org\/)\n- [![Powered by MediaWiki](https:\/\/en.wikipedia.org\/w\/resources\/assets\/mediawiki_compact.svg)](https:\/\/www.mediawiki.org\/)\n\nSearch\n\nToggle the table of contents\n\nQuark model\n\n15 languages\n\n[Add topic](https:\/\/en.wikipedia.org\/wiki\/Quark_model)","attrs_readable_markdown":"From Wikipedia, the free encyclopedia\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/af\/8foldway.svg\/250px-8foldway.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:8foldway.svg)\n\n**Figure 1**: The [pseudoscalar meson](https:\/\/en.wikipedia.org\/wiki\/Pseudoscalar_meson \"Pseudoscalar meson\") nonet. Members of the original meson \"octet\" are shown in green, the singlet in magenta. Although these mesons are now grouped into a nonet, the [Eightfold Way](https:\/\/en.wikipedia.org\/wiki\/Eightfold_way_\\(physics\\) \"Eightfold way (physics)\") name derives from the patterns of eight for the mesons and baryons in the original classification scheme.\n\nIn [particle physics](https:\/\/en.wikipedia.org\/wiki\/Particle_physics \"Particle physics\"), the **quark model** is a classification scheme for [hadrons](https:\/\/en.wikipedia.org\/wiki\/Hadron \"Hadron\") in terms of their valence [quarks](https:\/\/en.wikipedia.org\/wiki\/Quark \"Quark\")—the quarks and antiquarks that give rise to the [quantum numbers](https:\/\/en.wikipedia.org\/wiki\/Quantum_number \"Quantum number\") of the hadrons. The quark model underlies [\"flavor SU(3)\"](https:\/\/en.wikipedia.org\/wiki\/Flavour_\\(particle_physics\\) \"Flavour (particle physics)\"), or the [Eightfold Way](https:\/\/en.wikipedia.org\/wiki\/Eightfold_way_\\(physics\\) \"Eightfold way (physics)\"), the successful [classification scheme](https:\/\/en.wikipedia.org\/wiki\/Classification_scheme_\\(information_science\\) \"Classification scheme (information science)\") organizing the large number of lighter [hadrons](https:\/\/en.wikipedia.org\/wiki\/Hadron \"Hadron\") that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental [verification](https:\/\/en.wikipedia.org\/wiki\/Verification_and_validation \"Verification and validation\") beginning in the late 1960s and is a valid and effective classification of them to date. The model was independently proposed by physicists [Murray Gell-Mann](https:\/\/en.wikipedia.org\/wiki\/Murray_Gell-Mann \"Murray Gell-Mann\"),[\\[1\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-Gell-Man1964-1) who dubbed them \"quarks\" in a concise paper, and [George Zweig](https:\/\/en.wikipedia.org\/wiki\/George_Zweig \"George Zweig\"),[\\[2\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-Zweig1964a-2)[\\[3\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-Zweig1964b-3) who suggested \"aces\" in a longer manuscript. [André Petermann](https:\/\/en.wikipedia.org\/wiki\/Andr%C3%A9_Petermann \"André Petermann\") also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation.[\\[4\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-4)[\\[5\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-5) Today, the model has essentially been absorbed as a component of the established [quantum field theory](https:\/\/en.wikipedia.org\/wiki\/Quantum_field_theory \"Quantum field theory\") of strong and electroweak particle interactions, dubbed the [Standard Model](https:\/\/en.wikipedia.org\/wiki\/Standard_Model \"Standard Model\").\n\nHadrons are not really \"elementary\", and can be regarded as bound states of their \"valence quarks\" and antiquarks, which give rise to the [quantum numbers](https:\/\/en.wikipedia.org\/wiki\/Quantum_number \"Quantum number\") of the hadrons. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the [Poincaré symmetry](https:\/\/en.wikipedia.org\/wiki\/Poincar%C3%A9_symmetry \"Poincaré symmetry\")—*J**PC*, where *J*, *P* and *C* stand for the [total angular momentum](https:\/\/en.wikipedia.org\/wiki\/Total_angular_momentum \"Total angular momentum\"), [P-symmetry](https:\/\/en.wikipedia.org\/wiki\/P-symmetry \"P-symmetry\"), and [C-symmetry](https:\/\/en.wikipedia.org\/wiki\/C-symmetry \"C-symmetry\"), respectively.\n\nThe other set is the [flavor quantum numbers](https:\/\/en.wikipedia.org\/wiki\/Flavour_quantum_numbers \"Flavour quantum numbers\") such as the [isospin](https:\/\/en.wikipedia.org\/wiki\/Isospin \"Isospin\"), [strangeness](https:\/\/en.wikipedia.org\/wiki\/Strangeness \"Strangeness\"), [charm](https:\/\/en.wikipedia.org\/wiki\/Charm_\\(quantum_number\\) \"Charm (quantum number)\"), and so on. The strong interactions binding the quarks together are insensitive to these quantum numbers, so variation of them leads to systematic mass and coupling relationships among the hadrons in the same flavor multiplet.\n\nAll quarks are assigned a [baryon number](https:\/\/en.wikipedia.org\/wiki\/Baryon_number \"Baryon number\") of ⁠1\/3⁠. [Up](https:\/\/en.wikipedia.org\/wiki\/Up_quark \"Up quark\"), [charm](https:\/\/en.wikipedia.org\/wiki\/Charm_quark \"Charm quark\") and [top quarks](https:\/\/en.wikipedia.org\/wiki\/Top_quark \"Top quark\") have an [electric charge](https:\/\/en.wikipedia.org\/wiki\/Electric_charge \"Electric charge\") of +⁠2\/3⁠, while the [down](https:\/\/en.wikipedia.org\/wiki\/Down_quark \"Down quark\"), [strange](https:\/\/en.wikipedia.org\/wiki\/Strange_quark \"Strange quark\"), and [bottom quarks](https:\/\/en.wikipedia.org\/wiki\/Bottom_quark \"Bottom quark\") have an electric charge of −⁠1\/3⁠. Antiquarks have the opposite quantum numbers. Quarks are [spin-⁠1\/2⁠](https:\/\/en.wikipedia.org\/wiki\/Spin-1\/2 \"Spin-1\/2\") particles, and thus [fermions](https:\/\/en.wikipedia.org\/wiki\/Fermion \"Fermion\"). Each quark or antiquark obeys the Gell-Mann–Nishijima formula individually, so any additive assembly of them will as well.\n\n[Mesons](https:\/\/en.wikipedia.org\/wiki\/Meson \"Meson\") are made of a valence quark–antiquark pair (thus have a baryon number of 0), while [baryons](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\") are made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavors of quark (which form an approximate flavor [SU(3) symmetry](https:\/\/en.wikipedia.org\/wiki\/SU\\(3\\) \"SU(3)\")). There are generalizations to larger number of flavors.\n\nDeveloping classification schemes for [hadrons](https:\/\/en.wikipedia.org\/wiki\/Hadron \"Hadron\") became a timely 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](https:\/\/en.wikipedia.org\/wiki\/Wolfgang_Pauli \"Wolfgang Pauli\") to exclaim \"Had I foreseen that, I would have gone into botany.\" and [Enrico Fermi](https:\/\/en.wikipedia.org\/wiki\/Enrico_Fermi \"Enrico Fermi\") to advise his student [Leon Lederman](https:\/\/en.wikipedia.org\/wiki\/Leon_Lederman \"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 Alvarez](https:\/\/en.wikipedia.org\/wiki\/Luis_Walter_Alvarez \"Luis Walter Alvarez\"), who was at the forefront of many of these developments. Constructing hadrons as bound states of fewer constituents would thus organize the \"zoo\" at hand. Several early proposals, such as the ones by [Enrico Fermi](https:\/\/en.wikipedia.org\/wiki\/Enrico_Fermi \"Enrico Fermi\") and [Chen-Ning Yang](https:\/\/en.wikipedia.org\/wiki\/Chen-Ning_Yang \"Chen-Ning Yang\") (1949), and the [Sakata model](https:\/\/en.wikipedia.org\/wiki\/Sakata_model \"Sakata model\") (1956), ended up satisfactorily covering the mesons, but failed with baryons, and so were unable to explain all the data.\n\nThe [Gell-Mann–Nishijima formula](https:\/\/en.wikipedia.org\/wiki\/Gell-Mann%E2%80%93Nishijima_formula \"Gell-Mann–Nishijima formula\"), developed by [Murray Gell-Mann](https:\/\/en.wikipedia.org\/wiki\/Murray_Gell-Mann \"Murray Gell-Mann\") and [Kazuhiko Nishijima](https:\/\/en.wikipedia.org\/wiki\/Kazuhiko_Nishijima \"Kazuhiko Nishijima\"), led to the [Eightfold Way](https:\/\/en.wikipedia.org\/wiki\/Eightfold_way_\\(physics\\) \"Eightfold way (physics)\") classification, invented by Gell-Mann, with important independent contributions from [Yuval Ne'eman](https:\/\/en.wikipedia.org\/wiki\/Yuval_Ne%27eman \"Yuval Ne'eman\"), in 1961. The hadrons were organized into SU(3) representation multiplets, octets and decuplets, of roughly the same mass, due to the strong interactions; and smaller mass differences linked to the flavor quantum numbers, invisible to the strong interactions. The [Gell-Mann–Okubo mass formula](https:\/\/en.wikipedia.org\/wiki\/Gell-Mann%E2%80%93Okubo_mass_formula \"Gell-Mann–Okubo mass formula\") systematized the quantification of these small mass differences among members of a hadronic multiplet, controlled by the [explicit symmetry breaking](https:\/\/en.wikipedia.org\/wiki\/Explicit_symmetry_breaking \"Explicit symmetry breaking\") of SU(3).\n\nThe spin-⁠3\/2⁠ [Ω−  baryon](https:\/\/en.wikipedia.org\/wiki\/Omega_baryon \"Omega baryon\"), a member of the ground-state decuplet, was a crucial prediction of that classification. After it was discovered in an experiment at [Brookhaven National Laboratory](https:\/\/en.wikipedia.org\/wiki\/Brookhaven_National_Laboratory \"Brookhaven National Laboratory\"), Gell-Mann received a [Nobel Prize in Physics](https:\/\/en.wikipedia.org\/wiki\/Nobel_Prize_in_Physics \"Nobel Prize in Physics\") for his work on the Eightfold Way, in 1969.\n\nFinally, in 1964, Gell-Mann and [George Zweig](https:\/\/en.wikipedia.org\/wiki\/George_Zweig \"George Zweig\"), discerned independently what the Eightfold Way picture encodes: They posited three elementary fermionic constituents—the \"[up](https:\/\/en.wikipedia.org\/wiki\/Up_quark \"Up quark\")\", \"[down](https:\/\/en.wikipedia.org\/wiki\/Down_quark \"Down quark\")\", and \"[strange](https:\/\/en.wikipedia.org\/wiki\/Strange_quark \"Strange quark\")\" quarks—which are unobserved, and possibly unobservable in a free form. Simple pairwise or triplet combinations of these three constituents and their antiparticles underlie and elegantly encode the Eightfold Way classification, in an economical, tight structure, resulting in further simplicity. Hadronic mass differences were now linked to the different masses of the constituent quarks.\n\nIt would take about a decade for the unexpected nature—and physical reality—of these quarks to be appreciated more fully (See [Quarks](https:\/\/en.wikipedia.org\/wiki\/Quarks \"Quarks\")). Counter-intuitively, they cannot ever be observed in isolation ([color confinement](https:\/\/en.wikipedia.org\/wiki\/Color_confinement \"Color confinement\")), but instead always combine with other quarks to form full hadrons, which then furnish ample indirect information on the trapped quarks themselves. Conversely, the quarks serve in the definition of [quantum chromodynamics](https:\/\/en.wikipedia.org\/wiki\/Quantum_chromodynamics \"Quantum chromodynamics\"), the fundamental theory fully describing the strong interactions; and the Eightfold Way is now understood to be a consequence of the flavor symmetry structure of the lightest three of them.\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/c0\/Meson_nonet_-_spin_0.svg\/250px-Meson_nonet_-_spin_0.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:Meson_nonet_-_spin_0.svg)\n\n**Figure 2**: [Pseudoscalar mesons](https:\/\/en.wikipedia.org\/wiki\/Pseudoscalar_meson \"Pseudoscalar meson\") of spin-0 form a nonet\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/1\/13\/Meson_nonet_-_spin_1.svg\/250px-Meson_nonet_-_spin_1.svg.png)](https:\/\/en.wikipedia.org\/wiki\/File:Meson_nonet_-_spin_1.svg)\n\n**Figure 3**: [Vector mesons](https:\/\/en.wikipedia.org\/wiki\/Vector_mesons \"Vector mesons\") of spin-1 form a nonet\n\nThe Eightfold Way classification is named after the following fact: If we take three flavors of quarks, then the quarks lie in the [fundamental representation](https:\/\/en.wikipedia.org\/wiki\/Fundamental_representation \"Fundamental representation\"), **3** (called the triplet) of [flavor](https:\/\/en.wikipedia.org\/wiki\/Flavour_\\(particle_physics\\) \"Flavour (particle physics)\") [SU(3)](https:\/\/en.wikipedia.org\/wiki\/SU\\(3\\) \"SU(3)\"). The antiquarks lie in the complex conjugate representation **3**. The nine states (nonet) made out of a pair can be decomposed into the [trivial representation](https:\/\/en.wikipedia.org\/wiki\/Trivial_representation \"Trivial representation\"), **1** (called the singlet), and the [adjoint representation](https:\/\/en.wikipedia.org\/wiki\/Adjoint_representation_of_a_Lie_group \"Adjoint representation of a Lie group\"), **8** (called the octet). The notation for this decomposition is\n\n![{\\\\displaystyle \\\\mathbf {3} \\\\otimes \\\\mathbf {\\\\overline {3}} =\\\\mathbf {8} \\\\oplus \\\\mathbf {1} ~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/ac6f83cd866c815a8e296a97b3abd91cde4c78cc)\n\nFigure 1 shows the application of this decomposition to the mesons. If the flavor symmetry were exact (as in the limit that only the strong interactions operate, but the electroweak interactions are notionally switched off), then all nine mesons would have the same mass. However, the physical content of the full theory\\[*[clarification needed](https:\/\/en.wikipedia.org\/wiki\/Wikipedia:Please_clarify \"Wikipedia:Please clarify\")*\\] 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).\n\nN.B. Nevertheless, the mass splitting between the η and the η′ is larger than the quark model can accommodate, and this \"[η–η′ puzzle](https:\/\/en.wikipedia.org\/wiki\/QCD_vacuum#Eta_prime_meson \"QCD vacuum\")\" has its origin in topological peculiarities of the strong interaction vacuum, such as [instanton](https:\/\/en.wikipedia.org\/wiki\/Instanton \"Instanton\") configurations.\n\nMesons are hadrons with zero [baryon number](https:\/\/en.wikipedia.org\/wiki\/Baryon_number \"Baryon number\"). If the quark–antiquark pair are in an [orbital angular momentum](https:\/\/en.wikipedia.org\/wiki\/Angular_momentum_operator \"Angular momentum operator\") L state, and have [spin](https:\/\/en.wikipedia.org\/wiki\/Spin_\\(physics\\) \"Spin (physics)\") S, then\n\n- \\|*L* − *S*\\| ≤ *J* ≤ *L* + *S*, where *S* = 0 or 1,\n- *P* = (−1)*L*\\+1, where the 1 in the exponent arises from the [intrinsic parity](https:\/\/en.wikipedia.org\/wiki\/Intrinsic_parity \"Intrinsic parity\") of the quark–antiquark pair.\n- *C* = (−1)*L*\\+*S* for mesons which have no [flavor](https:\/\/en.wikipedia.org\/wiki\/Flavour_\\(particle_physics\\) \"Flavour (particle physics)\"). Flavored mesons have indefinite value of [*C*](https:\/\/en.wikipedia.org\/wiki\/C_parity \"C parity\").\n- For [isospin](https:\/\/en.wikipedia.org\/wiki\/Isospin \"Isospin\") *I* = 1 and 0 states, one can define a new [multiplicative quantum number](https:\/\/en.wikipedia.org\/wiki\/Multiplicative_quantum_number \"Multiplicative quantum number\") called the *[G-parity](https:\/\/en.wikipedia.org\/wiki\/G-parity \"G-parity\")* such that *G* = (−1)*I*\\+*L*\\+*S*.\n\nIf *P* = (−1)*J*, 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 thus called *exotic* (for example, the state *J**PC* = 0−−).\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/4\/4b\/Baryon_octet.png\/250px-Baryon_octet.png)](https:\/\/en.wikipedia.org\/wiki\/File:Baryon_octet.png)\n\n**Figure 4**. The *S* = ⁠1\/2⁠ ground state [baryon](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\") octet\n\n[![](https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/ec\/Baryon_decuplet.png\/250px-Baryon_decuplet.png)](https:\/\/en.wikipedia.org\/wiki\/File:Baryon_decuplet.png)\n\n**Figure 5**. The *S* = ⁠3\/2⁠ [baryon](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\") decuplet\n\nSince quarks are [fermions](https:\/\/en.wikipedia.org\/wiki\/Fermion \"Fermion\"), the [spin–statistics theorem](https:\/\/en.wikipedia.org\/wiki\/Spin%E2%80%93statistics_theorem \"Spin–statistics theorem\") implies that the [wavefunction](https:\/\/en.wikipedia.org\/wiki\/Wavefunction \"Wavefunction\") of a baryon must be antisymmetric under the exchange of any two quarks. This antisymmetric wavefunction is obtained by making it fully antisymmetric in color, discussed below, and symmetric in flavor, spin and space put together. With three flavors, the decomposition in flavor is ![{\\\\displaystyle \\\\mathbf {3} \\\\otimes \\\\mathbf {3} \\\\otimes \\\\mathbf {3} =\\\\mathbf {10} \\_{S}\\\\oplus \\\\mathbf {8} \\_{M}\\\\oplus \\\\mathbf {8} \\_{M}\\\\oplus \\\\mathbf {1} \\_{A}~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/efe21e8ee3332d4c573b43eea5321da19262e2c6) The decuplet is symmetric in flavor, 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.\n\nIt is sometimes useful to think of the [basis states](https:\/\/en.wikipedia.org\/wiki\/Quantum_state#Basis_states_of_one-particle_systems \"Quantum state\") of quarks as the six states of three flavors and two spins per flavor. This approximate symmetry is called spin-flavor [SU(6)](https:\/\/en.wikipedia.org\/wiki\/SU\\(6\\) \"SU(6)\"). In terms of this, the decomposition is ![{\\\\displaystyle \\\\mathbf {6} \\\\otimes \\\\mathbf {6} \\\\otimes \\\\mathbf {6} =\\\\mathbf {56} \\_{S}\\\\oplus \\\\mathbf {70} \\_{M}\\\\oplus \\\\mathbf {70} \\_{M}\\\\oplus \\\\mathbf {20} \\_{A}~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/613eb3fb4d716059f31551e9166f05abe035a79b)\n\nThe 56 states with symmetric combination of spin and flavour decompose under flavor [SU(3)](https:\/\/en.wikipedia.org\/wiki\/SU\\(3\\) \"SU(3)\") into ![{\\\\displaystyle \\\\mathbf {56} =\\\\mathbf {10} ^{\\\\frac {3}{2}}\\\\oplus \\\\mathbf {8} ^{\\\\frac {1}{2}}~,}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/6289d9cac1a1b9aceb282456deed0142207abff1) where the superscript denotes the spin, *S*, of the baryon. Since these states are symmetric in spin and flavor, 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.\n\nThe *S* = ⁠1\/2⁠ octet baryons are the two [nucleons](https:\/\/en.wikipedia.org\/wiki\/Nucleon \"Nucleon\") (p\\+  \n, n0  \n), the three [Sigmas](https:\/\/en.wikipedia.org\/wiki\/Sigma_baryon \"Sigma baryon\") (Σ\\+  \n, Σ0  \n, Σ−  \n), the two [Xis](https:\/\/en.wikipedia.org\/wiki\/Xi_baryon \"Xi baryon\") (Ξ0  \n, Ξ−  \n), and the [Lambda](https:\/\/en.wikipedia.org\/wiki\/Lambda_baryon \"Lambda baryon\") (Λ0  \n). The *S* = ⁠3\/2⁠ decuplet baryons are the four [Deltas](https:\/\/en.wikipedia.org\/wiki\/Delta_baryon \"Delta baryon\") (Δ\\++  \n, Δ\\+  \n, Δ0  \n, Δ−  \n), three [Sigmas](https:\/\/en.wikipedia.org\/wiki\/Sigma_baryon \"Sigma baryon\") (Σ∗+  \n, Σ∗0  \n, Σ∗−  \n), two [Xis](https:\/\/en.wikipedia.org\/wiki\/Xi_baryon \"Xi baryon\") (Ξ∗0  \n, Ξ∗−  \n), and the [Omega](https:\/\/en.wikipedia.org\/wiki\/Omega_particle \"Omega particle\") (Ω−  \n).\n\nFor example, the constituent quark model wavefunction for the proton is ![{\\\\displaystyle \\|{\\\\text{p}}\\_{\\\\uparrow }\\\\rangle ={\\\\frac {1}{\\\\sqrt {18}}}\\[2\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle +2\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\downarrow }\\\\rangle +2\\|{\\\\text{d}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{d}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }\\\\rangle -\\|{\\\\text{d}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{u}}\\_{\\\\downarrow }\\\\rangle -\\|{\\\\text{u}}\\_{\\\\downarrow }{\\\\text{u}}\\_{\\\\uparrow }{\\\\text{d}}\\_{\\\\uparrow }\\\\rangle \\]~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c5d84892af6c62784c12f0b691cd79d4d8584b3a)\n\nMixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other quantities that the model predicts successfully.\n\nThe group theory approach described above assumes that the quarks are eight components of a single particle, so the anti-symmetrization applies to all the quarks. A simpler approach is to consider the eight flavored quarks as eight separate, distinguishable, non-identical particles. Then the anti-symmetrization applies only to two identical quarks (like uu, for instance).[\\[6\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-JF1968-6)\n\nThen, the proton wavefunction can be written in a simpler form:\n\n![{\\\\displaystyle {\\\\text{p}}\\\\left({\\\\frac {1}{2}},{\\\\frac {1}{2}}\\\\right)={\\\\frac {{\\\\text{u}}{\\\\text{u}}{\\\\text{d}}}{\\\\sqrt {6}}}\\[2\\\\uparrow \\\\uparrow \\\\downarrow -\\\\uparrow \\\\downarrow \\\\uparrow -\\\\downarrow \\\\uparrow \\\\uparrow \\]}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/530602aa73765eab71fa2e8847f9f2764325d62c)\n\nand the\n\n![{\\\\displaystyle \\\\Delta ^{+}\\\\left({\\\\frac {3}{3}},{\\\\frac {3}{2}}\\\\right)={\\\\text{u}}{\\\\text{u}}{\\\\text{d}}\\[\\\\uparrow \\\\uparrow \\\\uparrow \\]~.}](https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/89c6b137d6e75df3c098948d8107f061ceafa1b8)\n\nIf quark–quark interactions are limited to two-body interactions, then all the successful quark model predictions, including sum rules for baryon masses and magnetic moments, can be derived.\n\nColor quantum numbers are the characteristic charges of the strong force, and are completely uninvolved in electroweak interactions. They were discovered as a consequence of the quark model classification, when it was appreciated that the spin *S* = ⁠3\/2⁠ baryon, the Δ\\++  \n, required three up quarks with parallel spins and vanishing orbital angular momentum. Therefore, it could not have an antisymmetric wavefunction, (required by the [Pauli exclusion principle](https:\/\/en.wikipedia.org\/wiki\/Pauli_exclusion_principle \"Pauli exclusion principle\")). [Oscar Greenberg](https:\/\/en.wikipedia.org\/wiki\/Oscar_Greenberg \"Oscar Greenberg\") noted this problem in 1964, suggesting that quarks should be [para-fermions](https:\/\/en.wikipedia.org\/wiki\/Para-fermion \"Para-fermion\").[\\[7\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-7)\n\nInstead, six months later, [Moo-Young Han](https:\/\/en.wikipedia.org\/wiki\/Moo-Young_Han \"Moo-Young Han\") and [Yoichiro Nambu](https:\/\/en.wikipedia.org\/wiki\/Yoichiro_Nambu \"Yoichiro Nambu\") suggested the existence of a hidden degree of freedom, they labeled as the group SU(3)' (but later called 'color). This led to three triplets of quarks whose wavefunction was anti-symmetric in the color degree of freedom. Flavor and color were intertwined in that model: they did not commute.[\\[8\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-8)\n\nThe modern concept of color completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [William Bardeen](https:\/\/en.wikipedia.org\/wiki\/William_A._Bardeen \"William A. Bardeen\"), [Harald Fritzsch](https:\/\/de.wikipedia.org\/wiki\/Harald_Fritzsch \"de:Harald Fritzsch\"), and [Murray Gell-Mann](https:\/\/en.wikipedia.org\/wiki\/Murray_Gell-Mann \"Murray Gell-Mann\").[\\[9\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-9)[\\[10\\]](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_note-10)\n\n## States outside the quark model\n\\[[edit](https:\/\/en.wikipedia.org\/w\/index.php?title=Quark_model&action=edit&section=5 \"Edit section: States outside the quark model\")\\]\n\nWhile the quark model is derivable from the theory of [quantum chromodynamics](https:\/\/en.wikipedia.org\/wiki\/Quantum_chromodynamics \"Quantum chromodynamics\"), the structure of hadrons is more complicated than this model allows. The full [quantum mechanical](https:\/\/en.wikipedia.org\/wiki\/Quantum_mechanics \"Quantum mechanics\") [wavefunction](https:\/\/en.wikipedia.org\/wiki\/Wavefunction \"Wavefunction\") of any hadron must include virtual quark pairs as well as virtual [gluons](https:\/\/en.wikipedia.org\/wiki\/Gluon \"Gluon\"), and allows for a variety of mixings. There may be hadrons which lie outside the quark model. Among these are the *[glueballs](https:\/\/en.wikipedia.org\/wiki\/Glueball \"Glueball\")* (which contain only valence gluons), *hybrids* (which contain valence quarks as well as gluons) and *[exotic hadrons](https:\/\/en.wikipedia.org\/wiki\/Exotic_hadron \"Exotic hadron\")* (such as [tetraquarks](https:\/\/en.wikipedia.org\/wiki\/Tetraquark \"Tetraquark\") or [pentaquarks](https:\/\/en.wikipedia.org\/wiki\/Pentaquark \"Pentaquark\")).\n\n- [Subatomic particles](https:\/\/en.wikipedia.org\/wiki\/Subatomic_particles \"Subatomic particles\")\n- [Hadrons](https:\/\/en.wikipedia.org\/wiki\/Hadron \"Hadron\"), [baryons](https:\/\/en.wikipedia.org\/wiki\/Baryon \"Baryon\"), [mesons](https:\/\/en.wikipedia.org\/wiki\/Meson \"Meson\") and [quarks](https:\/\/en.wikipedia.org\/wiki\/Quark \"Quark\")\n- [Exotic hadrons](https:\/\/en.wikipedia.org\/wiki\/Exotic_hadron \"Exotic hadron\"): [exotic mesons](https:\/\/en.wikipedia.org\/wiki\/Exotic_meson \"Exotic meson\") and [exotic baryons](https:\/\/en.wikipedia.org\/wiki\/Exotic_baryon \"Exotic baryon\")\n- [Quantum chromodynamics](https:\/\/en.wikipedia.org\/wiki\/Quantum_chromodynamics \"Quantum chromodynamics\"), [flavor](https:\/\/en.wikipedia.org\/wiki\/Flavour_\\(particle_physics\\) \"Flavour (particle physics)\"), the [QCD vacuum](https:\/\/en.wikipedia.org\/wiki\/QCD_vacuum \"QCD vacuum\")\n\n1. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-Gell-Man1964_1-0)**\n   [Gell-Mann, M.](https:\/\/en.wikipedia.org\/wiki\/Murray_Gell-Mann \"Murray Gell-Mann\") (4 January 1964). \"A Schematic Model of Baryons and Mesons\". *[Physics Letters](https:\/\/en.wikipedia.org\/wiki\/Physics_Letters \"Physics Letters\")*. **8** (3): 214–215\\. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1964PhL.....8..214G](https:\/\/ui.adsabs.harvard.edu\/abs\/1964PhL.....8..214G). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/S0031-9163(64)92001-3](https:\/\/doi.org\/10.1016%2FS0031-9163%2864%2992001-3).\n2. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-Zweig1964a_2-0)**\n   [Zweig, G.](https:\/\/en.wikipedia.org\/wiki\/George_Zweig \"George Zweig\") (17 January 1964). [An SU(3) Model for Strong Interaction Symmetry and its Breaking](https:\/\/cds.cern.ch\/record\/352337\/files\/CERN-TH-401.pdf) (PDF) (Report). CERN Report No.8182\/TH.401.\n3. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-Zweig1964b_3-0)**\n   [Zweig, G.](https:\/\/en.wikipedia.org\/wiki\/George_Zweig \"George Zweig\") (1964). [An SU(3) Model for Strong Interaction Symmetry and its Breaking: II](https:\/\/cds.cern.ch\/record\/570209\/files\/CERN-TH-412.pdf) (PDF) (Report). CERN Report No.8419\/TH.412.\n4. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-4)**\n   [Petermann, A.](https:\/\/en.wikipedia.org\/wiki\/Andr%C3%A9_Petermann \"André Petermann\") (1965). \"Propriétés de l'étrangeté et une formule de masse pour les mésons vectoriels\" \\[Strangeness properties and a mass formula for vector meson\\]. *[Nuclear Physics](https:\/\/en.wikipedia.org\/wiki\/Nuclear_Physics_\\(journal\\) \"Nuclear Physics (journal)\")*. **63** (2): 349–352\\. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1412\\.8681](https:\/\/arxiv.org\/abs\/1412.8681). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1965NucPh..63..349P](https:\/\/ui.adsabs.harvard.edu\/abs\/1965NucPh..63..349P). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/0029-5582(65)90348-2](https:\/\/doi.org\/10.1016%2F0029-5582%2865%2990348-2).\n5. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-5)**\n   Petrov, Vladimir A. (June 23–27, 2014). *Half a Century with QUARKS*. XXX-th International Workshop on High Energy Physics. [Protvino](https:\/\/en.wikipedia.org\/wiki\/Protvino \"Protvino\"), [Moscow Oblast](https:\/\/en.wikipedia.org\/wiki\/Moscow_Oblast \"Moscow Oblast\"), Russia. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[1412\\.8681](https:\/\/arxiv.org\/abs\/1412.8681).\n6. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-JF1968_6-0)**\n   Franklin, J. (1968). \"A Model of Baryons Made of Quarks with Hidden Spin\". *[Physical Review](https:\/\/en.wikipedia.org\/wiki\/Physical_Review \"Physical Review\")*. **172** (3): 1807–1817\\. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1968PhRv..172.1807F](https:\/\/ui.adsabs.harvard.edu\/abs\/1968PhRv..172.1807F). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1103\/PhysRev.172.1807](https:\/\/doi.org\/10.1103%2FPhysRev.172.1807).\n7. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-7)**\n   Greenberg, O.W. (1964). \"Spin and unitary-spin independence in a paraquark model of baryons and mesons\". *[Physical Review Letters](https:\/\/en.wikipedia.org\/wiki\/Physical_Review_Letters \"Physical Review Letters\")*. **13** (20): 598–602\\. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1964PhRvL..13..598G](https:\/\/ui.adsabs.harvard.edu\/abs\/1964PhRvL..13..598G). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1103\/PhysRevLett.13.598](https:\/\/doi.org\/10.1103%2FPhysRevLett.13.598).\n8. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-8)**\n   Han, M.Y.; Nambu, Y. (1965). [\"Three-triplet model with double SU(3) symmetry\"](https:\/\/digital.library.unt.edu\/ark:\/67531\/metadc1031342\/). *[Physical Review B](https:\/\/en.wikipedia.org\/wiki\/Physical_Review_B \"Physical Review B\")*. **139** (4B): 1006. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1965PhRv..139.1006H](https:\/\/ui.adsabs.harvard.edu\/abs\/1965PhRv..139.1006H). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1103\/PhysRev.139.B1006](https:\/\/doi.org\/10.1103%2FPhysRev.139.B1006).\n9. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-9)**\n   Bardeen, W.; Fritzsch, H.; Gell-Mann, M. (1973). [\"Light cone current algebra, *π*0 decay, and *e*\\+ *e*− annihilation\"](https:\/\/archive.org\/details\/scaleconformalsy0000unse\/page\/139). In Gatto, R. (ed.). *Scale and conformal symmetry in hadron physics*. [John Wiley & Sons](https:\/\/en.wikipedia.org\/wiki\/John_Wiley_%26_Sons \"John Wiley & Sons\"). p. [139](https:\/\/archive.org\/details\/scaleconformalsy0000unse\/page\/139). [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[hep-ph\/0211388](https:\/\/arxiv.org\/abs\/hep-ph\/0211388). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2002hep.ph...11388B](https:\/\/ui.adsabs.harvard.edu\/abs\/2002hep.ph...11388B). [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n   \n   [0-471-29292-3](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/0-471-29292-3 \"Special:BookSources\/0-471-29292-3\")\n   \n   .\n10. **[^](https:\/\/en.wikipedia.org\/wiki\/Quark_model#cite_ref-10)**\n    Fritzsch, H.; Gell-Mann, M.; Leutwyler, H. (1973). \"Advantages of the color octet gluon picture\". *[Physics Letters B](https:\/\/en.wikipedia.org\/wiki\/Physics_Letters_B \"Physics Letters B\")*. **47** (4): 365. [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[1973PhLB...47..365F](https:\/\/ui.adsabs.harvard.edu\/abs\/1973PhLB...47..365F). [CiteSeerX](https:\/\/en.wikipedia.org\/wiki\/CiteSeerX_\\(identifier\\) \"CiteSeerX (identifier)\") [10\\.1.1.453.4712](https:\/\/citeseerx.ist.psu.edu\/viewdoc\/summary?doi=10.1.1.453.4712). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/0370-2693(73)90625-4](https:\/\/doi.org\/10.1016%2F0370-2693%2873%2990625-4).\n\n- S. Eidelman *et al.* [Particle Data Group](https:\/\/en.wikipedia.org\/wiki\/Particle_Data_Group \"Particle Data Group\") (2004). [\"Review of Particle Physics\"](http:\/\/pdg.lbl.gov\/2004\/reviews\/quarkmodrpp.pdf) (PDF). *[Physics Letters B](https:\/\/en.wikipedia.org\/wiki\/Physics_Letters_B \"Physics Letters B\")*. **592** (1–4\\): 1. [arXiv](https:\/\/en.wikipedia.org\/wiki\/ArXiv_\\(identifier\\) \"ArXiv (identifier)\"):[astro-ph\/0406663](https:\/\/arxiv.org\/abs\/astro-ph\/0406663). [Bibcode](https:\/\/en.wikipedia.org\/wiki\/Bibcode_\\(identifier\\) \"Bibcode (identifier)\"):[2004PhLB..592....1P](https:\/\/ui.adsabs.harvard.edu\/abs\/2004PhLB..592....1P). [doi](https:\/\/en.wikipedia.org\/wiki\/Doi_\\(identifier\\) \"Doi (identifier)\"):[10\\.1016\/j.physletb.2004.06.001](https:\/\/doi.org\/10.1016%2Fj.physletb.2004.06.001). [S2CID](https:\/\/en.wikipedia.org\/wiki\/S2CID_\\(identifier\\) \"S2CID (identifier)\") [118588567](https:\/\/api.semanticscholar.org\/CorpusID:118588567).\n- Lichtenberg, D B (1970). *Unitary Symmetry and Elementary Particles*. Academic Press. [ISBN](https:\/\/en.wikipedia.org\/wiki\/ISBN_\\(identifier\\) \"ISBN (identifier)\")\n  \n  [978-1483242729](https:\/\/en.wikipedia.org\/wiki\/Special:BookSources\/978-1483242729 \"Special:BookSources\/978-1483242729\")\n  \n  .\n- Thomson, M A (2011), [Lecture notes](http:\/\/www.hep.phy.cam.ac.uk\/~thomson\/partIIIparticles\/handouts\/Handout_7_2011.pdf)\n- J.J.J. Kokkedee (1969). [*The quark model*](https:\/\/archive.org\/details\/quarkmodel0000kokk). [W. A. Benjamin](https:\/\/en.wikipedia.org\/wiki\/W._A._Benjamin \"W. A. Benjamin\"). [ASIN](https:\/\/en.wikipedia.org\/wiki\/ASIN_\\(identifier\\) \"ASIN (identifier)\") [B001RAVDIA](https:\/\/www.amazon.com\/dp\/B001RAVDIA).","meta_canonical":null}

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Boilerpipe Text	From Wikipedia, the free encyclopedia Figure 1 : The pseudoscalar meson nonet. Members of the original meson "octet" are shown in green, the singlet in magenta. Although these mesons are now grouped into a nonet, the Eightfold Way name derives from the patterns of eight for the mesons and baryons in the original classification scheme. In particle physics , the quark model is a classification scheme for hadrons in terms of their valence quarks —the quarks and antiquarks that give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)" , or the Eightfold Way , the successful classification scheme organizing the large number of lighter hadrons that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental verification beginning in the late 1960s and is a valid and effective classification of them to date. The model was independently proposed by physicists Murray Gell-Mann , [ 1 ] who dubbed them "quarks" in a concise paper, and George Zweig , [ 2 ] [ 3 ] who suggested "aces" in a longer manuscript. André Petermann also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation. [ 4 ] [ 5 ] Today, the model has essentially been absorbed as a component of the established quantum field theory of strong and electroweak particle interactions, dubbed the Standard Model . Hadrons are not really "elementary", and can be regarded as bound states of their "valence quarks" and antiquarks, which give rise to the quantum numbers of the hadrons. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the Poincaré symmetry — J PC , where J , P and C stand for the total angular momentum , P-symmetry , and C-symmetry , respectively. The other set is the flavor quantum numbers such as the isospin , strangeness , charm , and so on. The strong interactions binding the quarks together are insensitive to these quantum numbers, so variation of them leads to systematic mass and coupling relationships among the hadrons in the same flavor multiplet. All quarks are assigned a baryon number of ⁠ 1 / 3 ⁠ . Up , charm and top quarks have an electric charge of + ⁠ 2 / 3 ⁠ , while the down , strange , and bottom quarks have an electric charge of − ⁠ 1 / 3 ⁠ . Antiquarks have the opposite quantum numbers. Quarks are spin- ⁠ 1 / 2 ⁠ particles, and thus fermions . Each quark or antiquark obeys the Gell-Mann–Nishijima formula individually, so any additive assembly of them will as well. Mesons are made of a valence quark–antiquark pair (thus have a baryon number of 0), while baryons are made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavors of quark (which form an approximate flavor SU(3) symmetry ). There are generalizations to larger number of flavors. Developing classification schemes for hadrons became a timely 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 Alvarez , who was at the forefront of many of these developments. Constructing hadrons as bound states of fewer constituents would thus organize the "zoo" at hand. Several early proposals, such as the ones by Enrico Fermi and Chen-Ning Yang (1949), and the Sakata model (1956), ended up satisfactorily covering the mesons, but failed with baryons, and so were unable to explain all the data. The Gell-Mann–Nishijima formula , developed by Murray Gell-Mann and Kazuhiko Nishijima , led to the Eightfold Way classification, invented by Gell-Mann, with important independent contributions from Yuval Ne'eman , in 1961. The hadrons were organized into SU(3) representation multiplets, octets and decuplets, of roughly the same mass, due to the strong interactions; and smaller mass differences linked to the flavor quantum numbers, invisible to the strong interactions. The Gell-Mann–Okubo mass formula systematized the quantification of these small mass differences among members of a hadronic multiplet, controlled by the explicit symmetry breaking of SU(3). The spin- ⁠ 3 / 2 ⁠ Ω − baryon , a member of the ground-state decuplet, was a crucial prediction of that classification. After it was discovered in an experiment at Brookhaven National Laboratory , Gell-Mann received a Nobel Prize in Physics for his work on the Eightfold Way, in 1969. Finally, in 1964, Gell-Mann and George Zweig , discerned independently what the Eightfold Way picture encodes: They posited three elementary fermionic constituents—the " up ", " down ", and " strange " quarks—which are unobserved, and possibly unobservable in a free form. Simple pairwise or triplet combinations of these three constituents and their antiparticles underlie and elegantly encode the Eightfold Way classification, in an economical, tight structure, resulting in further simplicity. Hadronic mass differences were now linked to the different masses of the constituent quarks. It would take about a decade for the unexpected nature—and physical reality—of these quarks to be appreciated more fully (See Quarks ). Counter-intuitively, they cannot ever be observed in isolation ( color confinement ), but instead always combine with other quarks to form full hadrons, which then furnish ample indirect information on the trapped quarks themselves. Conversely, the quarks serve in the definition of quantum chromodynamics , the fundamental theory fully describing the strong interactions; and the Eightfold Way is now understood to be a consequence of the flavor symmetry structure of the lightest three of them. Figure 2 : Pseudoscalar mesons of spin-0 form a nonet Figure 3 : Vector mesons of spin-1 form a nonet The Eightfold Way classification is named after the following fact: If we take three flavors of quarks, then the quarks lie in the fundamental representation , 3 (called the triplet) of flavor SU(3) . The antiquarks lie in the complex conjugate representation 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 , 8 (called the octet). The notation for this decomposition is Figure 1 shows the application of this decomposition to the mesons. If the flavor symmetry were exact (as in the limit that only the strong interactions operate, but the electroweak interactions are notionally switched off), then all nine mesons would have the same mass. However, the physical content of the full theory [ clarification needed ] 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). N.B. Nevertheless, the mass splitting between the η and the η′ is larger than the quark model can accommodate, and this " η – η′ puzzle " has its origin in topological peculiarities of the strong interaction vacuum, such as instanton configurations. Mesons are hadrons with zero baryon number . If the quark–antiquark pair are in an orbital angular momentum L state, and have spin S , then \| L − S \| ≤ J ≤ L + S , where S = 0 or 1, P = (−1) L +1 , where the 1 in the exponent arises from the intrinsic parity of the quark–antiquark pair. C = (−1) L + S for mesons which have no flavor . Flavored mesons have indefinite value of C . For isospin I = 1 and 0 states, one can define a new multiplicative quantum number called the G-parity such that G = (−1) I + L + S . If P = (−1) J , 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 thus called exotic (for example, the state J PC = 0 −− ). Figure 4 . The S = ⁠ 1 / 2 ⁠ ground state baryon octet Figure 5 . The S = ⁠ 3 / 2 ⁠ baryon decuplet Since quarks are fermions , the spin–statistics theorem implies that the wavefunction of a baryon must be antisymmetric under the exchange of any two quarks. This antisymmetric wavefunction is obtained by making it fully antisymmetric in color, discussed below, and symmetric in flavor, spin and space put together. With three flavors, the decomposition in flavor is The decuplet is symmetric in flavor, 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. It is sometimes useful to think of the basis states of quarks as the six states of three flavors and two spins per flavor. This approximate symmetry is called spin-flavor SU(6) . In terms of this, the decomposition is The 56 states with symmetric combination of spin and flavour decompose under flavor SU(3) into where the superscript denotes the spin, S , of the baryon. Since these states are symmetric in spin and flavor, 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 = ⁠ 1 / 2 ⁠ octet baryons are the two nucleons ( p + , n 0 ), the three Sigmas ( Σ + , Σ 0 , Σ − ), the two Xis ( Ξ 0 , Ξ − ), and the Lambda ( Λ 0 ). The S = ⁠ 3 / 2 ⁠ decuplet baryons are the four Deltas ( Δ ++ , Δ + , Δ 0 , Δ − ), three Sigmas ( Σ ∗+ , Σ ∗0 , Σ ∗− ), two Xis ( Ξ ∗0 , Ξ ∗− ), and the Omega ( Ω − ). For example, the constituent quark model wavefunction for the proton is Mixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other quantities that the model predicts successfully. The group theory approach described above assumes that the quarks are eight components of a single particle, so the anti-symmetrization applies to all the quarks. A simpler approach is to consider the eight flavored quarks as eight separate, distinguishable, non-identical particles. Then the anti-symmetrization applies only to two identical quarks (like uu, for instance). [ 6 ] Then, the proton wavefunction can be written in a simpler form: and the If quark–quark interactions are limited to two-body interactions, then all the successful quark model predictions, including sum rules for baryon masses and magnetic moments, can be derived. Color quantum numbers are the characteristic charges of the strong force, and are completely uninvolved in electroweak interactions. They were discovered as a consequence of the quark model classification, when it was appreciated that the spin S = ⁠ 3 / 2 ⁠ baryon, the Δ ++ , required three up quarks with parallel spins and vanishing orbital angular momentum. Therefore, it could not have an antisymmetric wavefunction, (required by the Pauli exclusion principle ). Oscar Greenberg noted this problem in 1964, suggesting that quarks should be para-fermions . [ 7 ] Instead, six months later, Moo-Young Han and Yoichiro Nambu suggested the existence of a hidden degree of freedom, they labeled as the group SU(3)' (but later called 'color). This led to three triplets of quarks whose wavefunction was anti-symmetric in the color degree of freedom. Flavor and color were intertwined in that model: they did not commute. [ 8 ] The modern concept of color completely commuting with all other charges and providing the strong force charge was articulated in 1973, by William Bardeen , Harald Fritzsch , and Murray Gell-Mann . [ 9 ] [ 10 ] States outside the quark model [ edit ] While the quark model is derivable from the theory of quantum chromodynamics , the structure of hadrons is more complicated than this model allows. The full quantum mechanical wavefunction of any hadron must include virtual quark pairs as well as virtual gluons , and allows for a variety of mixings. There may be hadrons which lie outside the quark model. Among these are the glueballs (which contain only valence gluons), hybrids (which contain valence quarks as well as gluons) and exotic hadrons (such as tetraquarks or pentaquarks ). Subatomic particles Hadrons , baryons , mesons and quarks Exotic hadrons : exotic mesons and exotic baryons Quantum chromodynamics , flavor , the QCD vacuum ^ Gell-Mann, M. (4 January 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 . ^ Zweig, G. (17 January 1964). An SU(3) Model for Strong Interaction Symmetry and its Breaking (PDF) (Report). CERN Report No.8182/TH.401. ^ Zweig, G. (1964). An SU(3) Model for Strong Interaction Symmetry and its Breaking: II (PDF) (Report). CERN Report No.8419/TH.412. ^ Petermann, A. (1965). "Propriétés de l'étrangeté et une formule de masse pour les mésons vectoriels" [Strangeness properties and a mass formula for vector meson]. Nuclear Physics . 63 (2): 349– 352. arXiv : 1412.8681 . Bibcode : 1965NucPh..63..349P . doi : 10.1016/0029-5582(65)90348-2 . ^ Petrov, Vladimir A. (June 23–27, 2014). Half a Century with QUARKS . XXX-th International Workshop on High Energy Physics. Protvino , Moscow Oblast , Russia. arXiv : 1412.8681 . ^ Franklin, J. (1968). "A Model of Baryons Made of Quarks with Hidden Spin". Physical Review . 172 (3): 1807– 1817. Bibcode : 1968PhRv..172.1807F . doi : 10.1103/PhysRev.172.1807 . ^ Greenberg, O.W. (1964). "Spin and unitary-spin independence in a paraquark model of baryons and mesons". Physical Review Letters . 13 (20): 598– 602. Bibcode : 1964PhRvL..13..598G . doi : 10.1103/PhysRevLett.13.598 . ^ Han, M.Y.; Nambu, Y. (1965). "Three-triplet model with double SU(3) symmetry" . Physical Review B . 139 (4B): 1006. Bibcode : 1965PhRv..139.1006H . doi : 10.1103/PhysRev.139.B1006 . ^ Bardeen, W.; Fritzsch, H.; Gell-Mann, M. (1973). "Light cone current algebra, π 0 decay, and e + e − annihilation" . In Gatto, R. (ed.). Scale and conformal symmetry in hadron physics . John Wiley & Sons . p. 139 . arXiv : hep-ph/0211388 . Bibcode : 2002hep.ph...11388B . ISBN 0-471-29292-3 . ^ Fritzsch, H.; Gell-Mann, M.; Leutwyler, H. (1973). "Advantages of the color octet gluon picture". Physics Letters B . 47 (4): 365. Bibcode : 1973PhLB...47..365F . CiteSeerX 10.1.1.453.4712 . doi : 10.1016/0370-2693(73)90625-4 . S. Eidelman et al. Particle Data Group (2004). "Review of Particle Physics" (PDF) . Physics Letters B . 592 ( 1– 4): 1. arXiv : astro-ph/0406663 . Bibcode : 2004PhLB..592....1P . doi : 10.1016/j.physletb.2004.06.001 . S2CID 118588567 . Lichtenberg, D B (1970). Unitary Symmetry and Elementary Particles . Academic Press. ISBN 978-1483242729 . Thomson, M A (2011), Lecture notes J.J.J. Kokkedee (1969). The quark model . W. A. Benjamin . ASIN B001RAVDIA .
Markdown	[Jump to content](https://en.wikipedia.org/wiki/Quark_model#bodyContent) Main menu Main menu move to sidebar hide Navigation - [Main page](https://en.wikipedia.org/wiki/Main_Page "Visit the main page [z]") - [Contents](https://en.wikipedia.org/wiki/Wikipedia:Contents "Guides to browsing Wikipedia") - [Current events](https://en.wikipedia.org/wiki/Portal:Current_events "Articles related to current events") - [Random article](https://en.wikipedia.org/wiki/Special:Random "Visit a randomly selected article [x]") - [About Wikipedia](https://en.wikipedia.org/wiki/Wikipedia:About "Learn about Wikipedia and how it works") - [Contact us](https://en.wikipedia.org/wiki/Wikipedia:Contact_us "How to contact Wikipedia") Contribute - [Help](https://en.wikipedia.org/wiki/Help:Contents "Guidance on how to use and edit Wikipedia") - [Learn to edit](https://en.wikipedia.org/wiki/Help:Introduction "Learn how to edit Wikipedia") - [Community portal](https://en.wikipedia.org/wiki/Wikipedia:Community_portal "The hub for editors") - [Recent changes](https://en.wikipedia.org/wiki/Special:RecentChanges "A list of recent changes to Wikipedia [r]") - [Upload file](https://en.wikipedia.org/wiki/Wikipedia:File_upload_wizard "Add images or other media for use on Wikipedia") - [Special pages](https://en.wikipedia.org/wiki/Special:SpecialPages "A list of all special pages [q]") [![](https://en.wikipedia.org/static/images/icons/enwiki-25.svg) ![Wikipedia](https://en.wikipedia.org/static/images/mobile/copyright/wikipedia-wordmark-en-25.svg) ![The Free Encyclopedia](https://en.wikipedia.org/static/images/mobile/copyright/wikipedia-tagline-en-25.svg)](https://en.wikipedia.org/wiki/Main_Page) [Search](https://en.wikipedia.org/wiki/Special:Search "Search Wikipedia [f]") Appearance - [Donate](https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en) - [Create account](https://en.wikipedia.org/w/index.php?title=Special:CreateAccount&returnto=Quark+model "You are encouraged to create an account and log in; however, it is not mandatory") - [Log in](https://en.wikipedia.org/w/index.php?title=Special:UserLogin&returnto=Quark+model "You're encouraged to log in; however, it's not mandatory. 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[o]") ## Contents move to sidebar hide - [(Top)](https://en.wikipedia.org/wiki/Quark_model) - [1 History](https://en.wikipedia.org/wiki/Quark_model#History) - [2 Mesons](https://en.wikipedia.org/wiki/Quark_model#Mesons) - [3 Baryons](https://en.wikipedia.org/wiki/Quark_model#Baryons) Toggle Baryons subsection - [3\.1 Discovery of color](https://en.wikipedia.org/wiki/Quark_model#Discovery_of_color) - [4 States outside the quark model](https://en.wikipedia.org/wiki/Quark_model#States_outside_the_quark_model) - [5 See also](https://en.wikipedia.org/wiki/Quark_model#See_also) - [6 Notes](https://en.wikipedia.org/wiki/Quark_model#Notes) - [7 References](https://en.wikipedia.org/wiki/Quark_model#References) Toggle the table of contents # Quark model 15 languages - [العربية](https://ar.wikipedia.org/wiki/%D9%86%D9%85%D9%88%D8%B0%D8%AC_%D8%A7%D9%84%D9%83%D9%88%D8%A7%D8%B1%D9%83 "نموذج الكوارك – Arabic") - [Català](https://ca.wikipedia.org/wiki/Model_de_quarks "Model de quarks – Catalan") - [Español](https://es.wikipedia.org/wiki/Modelo_de_cuarks "Modelo de cuarks – Spanish") - [Euskara](https://eu.wikipedia.org/wiki/Quark_eredua "Quark eredua – Basque") - [فارسی](https://fa.wikipedia.org/wiki/%D9%85%D8%AF%D9%84_%DA%A9%D9%88%D8%A7%D8%B1%DA%A9 "مدل کوارک – Persian") - [Magyar](https://hu.wikipedia.org/wiki/Kvarkmodell "Kvarkmodell – Hungarian") - [Italiano](https://it.wikipedia.org/wiki/Modello_a_quark_costituenti "Modello a quark costituenti – Italian") - [日本語](https://ja.wikipedia.org/wiki/%E3%82%AF%E3%82%A9%E3%83%BC%E3%82%AF%E3%83%A2%E3%83%87%E3%83%AB "クォークモデル – Japanese") - [한국어](https://ko.wikipedia.org/wiki/%EC%BF%BC%ED%81%AC_%EB%AA%A8%ED%98%95 "쿼크 모형 – Korean") - [Русский](https://ru.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C "Кварковая модель – Russian") - [Slovenščina](https://sl.wikipedia.org/wiki/Kvarkovski_model "Kvarkovski model – Slovenian") - [Türkçe](https://tr.wikipedia.org/wiki/Kuark_modeli "Kuark modeli – Turkish") - [Українська](https://uk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B0_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C "Кваркова модель – Ukrainian") - [吴语](https://wuu.wikipedia.org/wiki/%E5%A4%B8%E5%85%8B%E6%A8%A1%E5%9E%8B "夸克模型 – Wu") - [中文](https://zh.wikipedia.org/wiki/%E5%A4%B8%E5%85%8B%E6%A8%A1%E5%9E%8B "夸克模型 – Chinese") [Edit links](https://www.wikidata.org/wiki/Special:EntityPage/Q1890674#sitelinks-wikipedia "Edit interlanguage links") - [Article](https://en.wikipedia.org/wiki/Quark_model "View the content page [c]") - [Talk](https://en.wikipedia.org/wiki/Talk:Quark_model "Discuss improvements to the content page [t]") English - [Read](https://en.wikipedia.org/wiki/Quark_model) - [Edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit "Edit this page [e]") - [View history](https://en.wikipedia.org/w/index.php?title=Quark_model&action=history "Past revisions of this page [h]") Tools Tools move to sidebar hide Actions - [Read](https://en.wikipedia.org/wiki/Quark_model) - [Edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit "Edit this page [e]") - [View history](https://en.wikipedia.org/w/index.php?title=Quark_model&action=history) General - 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[Printable version](https://en.wikipedia.org/w/index.php?title=Quark_model&printable=yes "Printable version of this page [p]") In other projects - [Wikidata item](https://www.wikidata.org/wiki/Special:EntityPage/Q1890674 "Structured data on this page hosted by Wikidata [g]") Appearance move to sidebar hide From Wikipedia, the free encyclopedia Classification scheme of hadrons [![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/8foldway.svg/250px-8foldway.svg.png)](https://en.wikipedia.org/wiki/File:8foldway.svg) Figure 1: The [pseudoscalar meson](https://en.wikipedia.org/wiki/Pseudoscalar_meson "Pseudoscalar meson") nonet. Members of the original meson "octet" are shown in green, the singlet in magenta. Although these mesons are now grouped into a nonet, the [Eightfold Way](https://en.wikipedia.org/wiki/Eightfold_way_\(physics\) "Eightfold way (physics)") name derives from the patterns of eight for the mesons and baryons in the original classification scheme. In [particle physics](https://en.wikipedia.org/wiki/Particle_physics "Particle physics"), the quark model is a classification scheme for [hadrons](https://en.wikipedia.org/wiki/Hadron "Hadron") in terms of their valence [quarks](https://en.wikipedia.org/wiki/Quark "Quark")—the quarks and antiquarks that give rise to the [quantum numbers](https://en.wikipedia.org/wiki/Quantum_number "Quantum number") of the hadrons. The quark model underlies ["flavor SU(3)"](https://en.wikipedia.org/wiki/Flavour_\(particle_physics\) "Flavour (particle physics)"), or the [Eightfold Way](https://en.wikipedia.org/wiki/Eightfold_way_\(physics\) "Eightfold way (physics)"), the successful [classification scheme](https://en.wikipedia.org/wiki/Classification_scheme_\(information_science\) "Classification scheme (information science)") organizing the large number of lighter [hadrons](https://en.wikipedia.org/wiki/Hadron "Hadron") that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental [verification](https://en.wikipedia.org/wiki/Verification_and_validation "Verification and validation") beginning in the late 1960s and is a valid and effective classification of them to date. The model was independently proposed by physicists [Murray Gell-Mann](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann"),[\[1\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-Gell-Man1964-1) who dubbed them "quarks" in a concise paper, and [George Zweig](https://en.wikipedia.org/wiki/George_Zweig "George Zweig"),[\[2\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-Zweig1964a-2)[\[3\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-Zweig1964b-3) who suggested "aces" in a longer manuscript. [André Petermann](https://en.wikipedia.org/wiki/Andr%C3%A9_Petermann "André Petermann") also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation.[\[4\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-4)[\[5\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-5) Today, the model has essentially been absorbed as a component of the established [quantum field theory](https://en.wikipedia.org/wiki/Quantum_field_theory "Quantum field theory") of strong and electroweak particle interactions, dubbed the [Standard Model](https://en.wikipedia.org/wiki/Standard_Model "Standard Model"). Hadrons are not really "elementary", and can be regarded as bound states of their "valence quarks" and antiquarks, which give rise to the [quantum numbers](https://en.wikipedia.org/wiki/Quantum_number "Quantum number") of the hadrons. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the [Poincaré symmetry](https://en.wikipedia.org/wiki/Poincar%C3%A9_symmetry "Poincaré symmetry")—JPC, where J, P and C stand for the [total angular momentum](https://en.wikipedia.org/wiki/Total_angular_momentum "Total angular momentum"), [P-symmetry](https://en.wikipedia.org/wiki/P-symmetry "P-symmetry"), and [C-symmetry](https://en.wikipedia.org/wiki/C-symmetry "C-symmetry"), respectively. The other set is the [flavor quantum numbers](https://en.wikipedia.org/wiki/Flavour_quantum_numbers "Flavour quantum numbers") such as the [isospin](https://en.wikipedia.org/wiki/Isospin "Isospin"), [strangeness](https://en.wikipedia.org/wiki/Strangeness "Strangeness"), [charm](https://en.wikipedia.org/wiki/Charm_\(quantum_number\) "Charm (quantum number)"), and so on. The strong interactions binding the quarks together are insensitive to these quantum numbers, so variation of them leads to systematic mass and coupling relationships among the hadrons in the same flavor multiplet. All quarks are assigned a [baryon number](https://en.wikipedia.org/wiki/Baryon_number "Baryon number") of ⁠1/3⁠. [Up](https://en.wikipedia.org/wiki/Up_quark "Up quark"), [charm](https://en.wikipedia.org/wiki/Charm_quark "Charm quark") and [top quarks](https://en.wikipedia.org/wiki/Top_quark "Top quark") have an [electric charge](https://en.wikipedia.org/wiki/Electric_charge "Electric charge") of +⁠2/3⁠, while the [down](https://en.wikipedia.org/wiki/Down_quark "Down quark"), [strange](https://en.wikipedia.org/wiki/Strange_quark "Strange quark"), and [bottom quarks](https://en.wikipedia.org/wiki/Bottom_quark "Bottom quark") have an electric charge of −⁠1/3⁠. Antiquarks have the opposite quantum numbers. Quarks are [spin-⁠1/2⁠](https://en.wikipedia.org/wiki/Spin-1/2 "Spin-1/2") particles, and thus [fermions](https://en.wikipedia.org/wiki/Fermion "Fermion"). Each quark or antiquark obeys the Gell-Mann–Nishijima formula individually, so any additive assembly of them will as well. [Mesons](https://en.wikipedia.org/wiki/Meson "Meson") are made of a valence quark–antiquark pair (thus have a baryon number of 0), while [baryons](https://en.wikipedia.org/wiki/Baryon "Baryon") are made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavors of quark (which form an approximate flavor [SU(3) symmetry](https://en.wikipedia.org/wiki/SU\(3\) "SU(3)")). There are generalizations to larger number of flavors. ## History \[[edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit&section=1 "Edit section: History")\] Developing classification schemes for [hadrons](https://en.wikipedia.org/wiki/Hadron "Hadron") became a timely 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](https://en.wikipedia.org/wiki/Wolfgang_Pauli "Wolfgang Pauli") to exclaim "Had I foreseen that, I would have gone into botany." and [Enrico Fermi](https://en.wikipedia.org/wiki/Enrico_Fermi "Enrico Fermi") to advise his student [Leon Lederman](https://en.wikipedia.org/wiki/Leon_Lederman "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 Alvarez](https://en.wikipedia.org/wiki/Luis_Walter_Alvarez "Luis Walter Alvarez"), who was at the forefront of many of these developments. Constructing hadrons as bound states of fewer constituents would thus organize the "zoo" at hand. Several early proposals, such as the ones by [Enrico Fermi](https://en.wikipedia.org/wiki/Enrico_Fermi "Enrico Fermi") and [Chen-Ning Yang](https://en.wikipedia.org/wiki/Chen-Ning_Yang "Chen-Ning Yang") (1949), and the [Sakata model](https://en.wikipedia.org/wiki/Sakata_model "Sakata model") (1956), ended up satisfactorily covering the mesons, but failed with baryons, and so were unable to explain all the data. The [Gell-Mann–Nishijima formula](https://en.wikipedia.org/wiki/Gell-Mann%E2%80%93Nishijima_formula "Gell-Mann–Nishijima formula"), developed by [Murray Gell-Mann](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann") and [Kazuhiko Nishijima](https://en.wikipedia.org/wiki/Kazuhiko_Nishijima "Kazuhiko Nishijima"), led to the [Eightfold Way](https://en.wikipedia.org/wiki/Eightfold_way_\(physics\) "Eightfold way (physics)") classification, invented by Gell-Mann, with important independent contributions from [Yuval Ne'eman](https://en.wikipedia.org/wiki/Yuval_Ne%27eman "Yuval Ne'eman"), in 1961. The hadrons were organized into SU(3) representation multiplets, octets and decuplets, of roughly the same mass, due to the strong interactions; and smaller mass differences linked to the flavor quantum numbers, invisible to the strong interactions. The [Gell-Mann–Okubo mass formula](https://en.wikipedia.org/wiki/Gell-Mann%E2%80%93Okubo_mass_formula "Gell-Mann–Okubo mass formula") systematized the quantification of these small mass differences among members of a hadronic multiplet, controlled by the [explicit symmetry breaking](https://en.wikipedia.org/wiki/Explicit_symmetry_breaking "Explicit symmetry breaking") of SU(3). The spin-⁠3/2⁠ [Ω− baryon](https://en.wikipedia.org/wiki/Omega_baryon "Omega baryon"), a member of the ground-state decuplet, was a crucial prediction of that classification. After it was discovered in an experiment at [Brookhaven National Laboratory](https://en.wikipedia.org/wiki/Brookhaven_National_Laboratory "Brookhaven National Laboratory"), Gell-Mann received a [Nobel Prize in Physics](https://en.wikipedia.org/wiki/Nobel_Prize_in_Physics "Nobel Prize in Physics") for his work on the Eightfold Way, in 1969. Finally, in 1964, Gell-Mann and [George Zweig](https://en.wikipedia.org/wiki/George_Zweig "George Zweig"), discerned independently what the Eightfold Way picture encodes: They posited three elementary fermionic constituents—the "[up](https://en.wikipedia.org/wiki/Up_quark "Up quark")", "[down](https://en.wikipedia.org/wiki/Down_quark "Down quark")", and "[strange](https://en.wikipedia.org/wiki/Strange_quark "Strange quark")" quarks—which are unobserved, and possibly unobservable in a free form. Simple pairwise or triplet combinations of these three constituents and their antiparticles underlie and elegantly encode the Eightfold Way classification, in an economical, tight structure, resulting in further simplicity. Hadronic mass differences were now linked to the different masses of the constituent quarks. It would take about a decade for the unexpected nature—and physical reality—of these quarks to be appreciated more fully (See [Quarks](https://en.wikipedia.org/wiki/Quarks "Quarks")). Counter-intuitively, they cannot ever be observed in isolation ([color confinement](https://en.wikipedia.org/wiki/Color_confinement "Color confinement")), but instead always combine with other quarks to form full hadrons, which then furnish ample indirect information on the trapped quarks themselves. Conversely, the quarks serve in the definition of [quantum chromodynamics](https://en.wikipedia.org/wiki/Quantum_chromodynamics "Quantum chromodynamics"), the fundamental theory fully describing the strong interactions; and the Eightfold Way is now understood to be a consequence of the flavor symmetry structure of the lightest three of them. ## Mesons \[[edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit&section=2 "Edit section: Mesons")\] See also: [Meson](https://en.wikipedia.org/wiki/Meson "Meson") and [List of mesons](https://en.wikipedia.org/wiki/List_of_mesons "List of mesons") [![](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Meson_nonet_-_spin_0.svg/250px-Meson_nonet_-_spin_0.svg.png)](https://en.wikipedia.org/wiki/File:Meson_nonet_-_spin_0.svg) Figure 2: [Pseudoscalar mesons](https://en.wikipedia.org/wiki/Pseudoscalar_meson "Pseudoscalar meson") of spin-0 form a nonet [![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/13/Meson_nonet_-_spin_1.svg/250px-Meson_nonet_-_spin_1.svg.png)](https://en.wikipedia.org/wiki/File:Meson_nonet_-_spin_1.svg) Figure 3: [Vector mesons](https://en.wikipedia.org/wiki/Vector_mesons "Vector mesons") of spin-1 form a nonet The Eightfold Way classification is named after the following fact: If we take three flavors of quarks, then the quarks lie in the [fundamental representation](https://en.wikipedia.org/wiki/Fundamental_representation "Fundamental representation"), 3 (called the triplet) of [flavor](https://en.wikipedia.org/wiki/Flavour_\(particle_physics\) "Flavour (particle physics)") [SU(3)](https://en.wikipedia.org/wiki/SU\(3\) "SU(3)"). The antiquarks lie in the complex conjugate representation 3. The nine states (nonet) made out of a pair can be decomposed into the [trivial representation](https://en.wikipedia.org/wiki/Trivial_representation "Trivial representation"), 1 (called the singlet), and the [adjoint representation](https://en.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_group "Adjoint representation of a Lie group"), 8 (called the octet). The notation for this decomposition is 3 ⊗ 3 ¯ \= 8 ⊕ 1 . {\\displaystyle \\mathbf {3} \\otimes \\mathbf {\\overline {3}} =\\mathbf {8} \\oplus \\mathbf {1} ~.} ![{\\displaystyle \\mathbf {3} \\otimes \\mathbf {\\overline {3}} =\\mathbf {8} \\oplus \\mathbf {1} ~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac6f83cd866c815a8e296a97b3abd91cde4c78cc) Figure 1 shows the application of this decomposition to the mesons. If the flavor symmetry were exact (as in the limit that only the strong interactions operate, but the electroweak interactions are notionally switched off), then all nine mesons would have the same mass. However, the physical content of the full theory\[[clarification needed](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify "Wikipedia:Please clarify")\] 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). N.B. Nevertheless, the mass splitting between the η and the η′ is larger than the quark model can accommodate, and this "[η–η′ puzzle](https://en.wikipedia.org/wiki/QCD_vacuum#Eta_prime_meson "QCD vacuum")" has its origin in topological peculiarities of the strong interaction vacuum, such as [instanton](https://en.wikipedia.org/wiki/Instanton "Instanton") configurations. Mesons are hadrons with zero [baryon number](https://en.wikipedia.org/wiki/Baryon_number "Baryon number"). If the quark–antiquark pair are in an [orbital angular momentum](https://en.wikipedia.org/wiki/Angular_momentum_operator "Angular momentum operator") L state, and have [spin](https://en.wikipedia.org/wiki/Spin_\(physics\) "Spin (physics)") S, then - \\|L − S\\| ≤ J ≤ L + S, where S = 0 or 1, - P = (−1)L\+1, where the 1 in the exponent arises from the [intrinsic parity](https://en.wikipedia.org/wiki/Intrinsic_parity "Intrinsic parity") of the quark–antiquark pair. - C = (−1)L\+S for mesons which have no [flavor](https://en.wikipedia.org/wiki/Flavour_\(particle_physics\) "Flavour (particle physics)"). Flavored mesons have indefinite value of [C](https://en.wikipedia.org/wiki/C_parity "C parity"). - For [isospin](https://en.wikipedia.org/wiki/Isospin "Isospin") I = 1 and 0 states, one can define a new [multiplicative quantum number](https://en.wikipedia.org/wiki/Multiplicative_quantum_number "Multiplicative quantum number") called the [G-parity](https://en.wikipedia.org/wiki/G-parity "G-parity") such that G = (−1)I\+L\+S. If P = (−1)J, 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 thus called exotic (for example, the state JPC = 0−−). ## Baryons \[[edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit&section=3 "Edit section: Baryons")\] Main article: [Baryon](https://en.wikipedia.org/wiki/Baryon "Baryon") See also: [List of baryons](https://en.wikipedia.org/wiki/List_of_baryons "List of baryons") [![](https://upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Baryon_octet.png/250px-Baryon_octet.png)](https://en.wikipedia.org/wiki/File:Baryon_octet.png) Figure 4. The S = ⁠1/2⁠ ground state [baryon](https://en.wikipedia.org/wiki/Baryon "Baryon") octet [![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Baryon_decuplet.png/250px-Baryon_decuplet.png)](https://en.wikipedia.org/wiki/File:Baryon_decuplet.png) Figure 5. The S = ⁠3/2⁠ [baryon](https://en.wikipedia.org/wiki/Baryon "Baryon") decuplet Since quarks are [fermions](https://en.wikipedia.org/wiki/Fermion "Fermion"), the [spin–statistics theorem](https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem "Spin–statistics theorem") implies that the [wavefunction](https://en.wikipedia.org/wiki/Wavefunction "Wavefunction") of a baryon must be antisymmetric under the exchange of any two quarks. This antisymmetric wavefunction is obtained by making it fully antisymmetric in color, discussed below, and symmetric in flavor, spin and space put together. With three flavors, the decomposition in flavor is 3 ⊗ 3 ⊗ 3 \= 10 S ⊕ 8 M ⊕ 8 M ⊕ 1 A . {\\displaystyle \\mathbf {3} \\otimes \\mathbf {3} \\otimes \\mathbf {3} =\\mathbf {10} \_{S}\\oplus \\mathbf {8} \_{M}\\oplus \\mathbf {8} \_{M}\\oplus \\mathbf {1} \_{A}~.} ![{\\displaystyle \\mathbf {3} \\otimes \\mathbf {3} \\otimes \\mathbf {3} =\\mathbf {10} \_{S}\\oplus \\mathbf {8} \_{M}\\oplus \\mathbf {8} \_{M}\\oplus \\mathbf {1} \_{A}~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efe21e8ee3332d4c573b43eea5321da19262e2c6) The decuplet is symmetric in flavor, 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. It is sometimes useful to think of the [basis states](https://en.wikipedia.org/wiki/Quantum_state#Basis_states_of_one-particle_systems "Quantum state") of quarks as the six states of three flavors and two spins per flavor. This approximate symmetry is called spin-flavor [SU(6)](https://en.wikipedia.org/wiki/SU\(6\) "SU(6)"). In terms of this, the decomposition is 6 ⊗ 6 ⊗ 6 \= 56 S ⊕ 70 M ⊕ 70 M ⊕ 20 A . {\\displaystyle \\mathbf {6} \\otimes \\mathbf {6} \\otimes \\mathbf {6} =\\mathbf {56} \_{S}\\oplus \\mathbf {70} \_{M}\\oplus \\mathbf {70} \_{M}\\oplus \\mathbf {20} \_{A}~.} ![{\\displaystyle \\mathbf {6} \\otimes \\mathbf {6} \\otimes \\mathbf {6} =\\mathbf {56} \_{S}\\oplus \\mathbf {70} \_{M}\\oplus \\mathbf {70} \_{M}\\oplus \\mathbf {20} \_{A}~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/613eb3fb4d716059f31551e9166f05abe035a79b) The 56 states with symmetric combination of spin and flavour decompose under flavor [SU(3)](https://en.wikipedia.org/wiki/SU\(3\) "SU(3)") into 56 \= 10 3 2 ⊕ 8 1 2 , {\\displaystyle \\mathbf {56} =\\mathbf {10} ^{\\frac {3}{2}}\\oplus \\mathbf {8} ^{\\frac {1}{2}}~,} ![{\\displaystyle \\mathbf {56} =\\mathbf {10} ^{\\frac {3}{2}}\\oplus \\mathbf {8} ^{\\frac {1}{2}}~,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6289d9cac1a1b9aceb282456deed0142207abff1) where the superscript denotes the spin, S, of the baryon. Since these states are symmetric in spin and flavor, 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 = ⁠1/2⁠ octet baryons are the two [nucleons](https://en.wikipedia.org/wiki/Nucleon "Nucleon") (p\+ , n0 ), the three [Sigmas](https://en.wikipedia.org/wiki/Sigma_baryon "Sigma baryon") (Σ\+ , Σ0 , Σ− ), the two [Xis](https://en.wikipedia.org/wiki/Xi_baryon "Xi baryon") (Ξ0 , Ξ− ), and the [Lambda](https://en.wikipedia.org/wiki/Lambda_baryon "Lambda baryon") (Λ0 ). The S = ⁠3/2⁠ decuplet baryons are the four [Deltas](https://en.wikipedia.org/wiki/Delta_baryon "Delta baryon") (Δ\++ , Δ\+ , Δ0 , Δ− ), three [Sigmas](https://en.wikipedia.org/wiki/Sigma_baryon "Sigma baryon") (Σ∗+ , Σ∗0 , Σ∗− ), two [Xis](https://en.wikipedia.org/wiki/Xi_baryon "Xi baryon") (Ξ∗0 , Ξ∗− ), and the [Omega](https://en.wikipedia.org/wiki/Omega_particle "Omega particle") (Ω− ). For example, the constituent quark model wavefunction for the proton is \\| p ↑ ⟩ \= 1 18 \[ 2 \\| u ↑ d ↓ u ↑ ⟩ \+ 2 \\| u ↑ u ↑ d ↓ ⟩ \+ 2 \\| d ↓ u ↑ u ↑ ⟩ − \\| u ↑ u ↓ d ↑ ⟩ − \\| u ↑ d ↑ u ↓ ⟩ − \\| u ↓ d ↑ u ↑ ⟩ − \\| d ↑ u ↓ u ↑ ⟩ − \\| d ↑ u ↑ u ↓ ⟩ − \\| u ↓ u ↑ d ↑ ⟩ \] . {\\displaystyle \\|{\\text{p}}\_{\\uparrow }\\rangle ={\\frac {1}{\\sqrt {18}}}\[2\\|{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }\\rangle +2\\|{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\downarrow }\\rangle +2\\|{\\text{d}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }\\rangle -\\|{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }{\\text{d}}\_{\\uparrow }\\rangle -\\|{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }\\rangle -\\|{\\text{u}}\_{\\downarrow }{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }\\rangle -\\|{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }\\rangle -\\|{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }\\rangle -\\|{\\text{u}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\uparrow }\\rangle \]~.} ![{\\displaystyle \\|{\\text{p}}\_{\\uparrow }\\rangle ={\\frac {1}{\\sqrt {18}}}\[2\\|{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }\\rangle +2\\|{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\downarrow }\\rangle +2\\|{\\text{d}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }\\rangle -\\|{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }{\\text{d}}\_{\\uparrow }\\rangle -\\|{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }\\rangle -\\|{\\text{u}}\_{\\downarrow }{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }\\rangle -\\|{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }\\rangle -\\|{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }\\rangle -\\|{\\text{u}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\uparrow }\\rangle \]~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c5d84892af6c62784c12f0b691cd79d4d8584b3a) Mixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other quantities that the model predicts successfully. The group theory approach described above assumes that the quarks are eight components of a single particle, so the anti-symmetrization applies to all the quarks. A simpler approach is to consider the eight flavored quarks as eight separate, distinguishable, non-identical particles. Then the anti-symmetrization applies only to two identical quarks (like uu, for instance).[\[6\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-JF1968-6) Then, the proton wavefunction can be written in a simpler form: p ( 1 2 , 1 2 ) \= u u d 6 \[ 2 ↑↑↓ − ↑↓↑ − ↓↑↑ \] {\\displaystyle {\\text{p}}\\left({\\frac {1}{2}},{\\frac {1}{2}}\\right)={\\frac {{\\text{u}}{\\text{u}}{\\text{d}}}{\\sqrt {6}}}\[2\\uparrow \\uparrow \\downarrow -\\uparrow \\downarrow \\uparrow -\\downarrow \\uparrow \\uparrow \]} ![{\\displaystyle {\\text{p}}\\left({\\frac {1}{2}},{\\frac {1}{2}}\\right)={\\frac {{\\text{u}}{\\text{u}}{\\text{d}}}{\\sqrt {6}}}\[2\\uparrow \\uparrow \\downarrow -\\uparrow \\downarrow \\uparrow -\\downarrow \\uparrow \\uparrow \]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/530602aa73765eab71fa2e8847f9f2764325d62c) and the Δ \+ ( 3 3 , 3 2 ) \= u u d \[ ↑↑↑ \] . {\\displaystyle \\Delta ^{+}\\left({\\frac {3}{3}},{\\frac {3}{2}}\\right)={\\text{u}}{\\text{u}}{\\text{d}}\[\\uparrow \\uparrow \\uparrow \]~.} ![{\\displaystyle \\Delta ^{+}\\left({\\frac {3}{3}},{\\frac {3}{2}}\\right)={\\text{u}}{\\text{u}}{\\text{d}}\[\\uparrow \\uparrow \\uparrow \]~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/89c6b137d6e75df3c098948d8107f061ceafa1b8) If quark–quark interactions are limited to two-body interactions, then all the successful quark model predictions, including sum rules for baryon masses and magnetic moments, can be derived. ### Discovery of color \[[edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit&section=4 "Edit section: Discovery of color")\] Main article: [Color charge](https://en.wikipedia.org/wiki/Color_charge "Color charge") Color quantum numbers are the characteristic charges of the strong force, and are completely uninvolved in electroweak interactions. They were discovered as a consequence of the quark model classification, when it was appreciated that the spin S = ⁠3/2⁠ baryon, the Δ\++ , required three up quarks with parallel spins and vanishing orbital angular momentum. Therefore, it could not have an antisymmetric wavefunction, (required by the [Pauli exclusion principle](https://en.wikipedia.org/wiki/Pauli_exclusion_principle "Pauli exclusion principle")). [Oscar Greenberg](https://en.wikipedia.org/wiki/Oscar_Greenberg "Oscar Greenberg") noted this problem in 1964, suggesting that quarks should be [para-fermions](https://en.wikipedia.org/wiki/Para-fermion "Para-fermion").[\[7\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-7) Instead, six months later, [Moo-Young Han](https://en.wikipedia.org/wiki/Moo-Young_Han "Moo-Young Han") and [Yoichiro Nambu](https://en.wikipedia.org/wiki/Yoichiro_Nambu "Yoichiro Nambu") suggested the existence of a hidden degree of freedom, they labeled as the group SU(3)' (but later called 'color). This led to three triplets of quarks whose wavefunction was anti-symmetric in the color degree of freedom. Flavor and color were intertwined in that model: they did not commute.[\[8\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-8) The modern concept of color completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [William Bardeen](https://en.wikipedia.org/wiki/William_A._Bardeen "William A. Bardeen"), [Harald Fritzsch](https://de.wikipedia.org/wiki/Harald_Fritzsch "de:Harald Fritzsch"), and [Murray Gell-Mann](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann").[\[9\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-9)[\[10\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-10) ## States outside the quark model \[[edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit&section=5 "Edit section: States outside the quark model")\] While the quark model is derivable from the theory of [quantum chromodynamics](https://en.wikipedia.org/wiki/Quantum_chromodynamics "Quantum chromodynamics"), the structure of hadrons is more complicated than this model allows. The full [quantum mechanical](https://en.wikipedia.org/wiki/Quantum_mechanics "Quantum mechanics") [wavefunction](https://en.wikipedia.org/wiki/Wavefunction "Wavefunction") of any hadron must include virtual quark pairs as well as virtual [gluons](https://en.wikipedia.org/wiki/Gluon "Gluon"), and allows for a variety of mixings. There may be hadrons which lie outside the quark model. Among these are the [glueballs](https://en.wikipedia.org/wiki/Glueball "Glueball") (which contain only valence gluons), hybrids (which contain valence quarks as well as gluons) and [exotic hadrons](https://en.wikipedia.org/wiki/Exotic_hadron "Exotic hadron") (such as [tetraquarks](https://en.wikipedia.org/wiki/Tetraquark "Tetraquark") or [pentaquarks](https://en.wikipedia.org/wiki/Pentaquark "Pentaquark")). ## See also \[[edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit&section=6 "Edit section: See also")\] - [Subatomic particles](https://en.wikipedia.org/wiki/Subatomic_particles "Subatomic particles") - [Hadrons](https://en.wikipedia.org/wiki/Hadron "Hadron"), [baryons](https://en.wikipedia.org/wiki/Baryon "Baryon"), [mesons](https://en.wikipedia.org/wiki/Meson "Meson") and [quarks](https://en.wikipedia.org/wiki/Quark "Quark") - [Exotic hadrons](https://en.wikipedia.org/wiki/Exotic_hadron "Exotic hadron"): [exotic mesons](https://en.wikipedia.org/wiki/Exotic_meson "Exotic meson") and [exotic baryons](https://en.wikipedia.org/wiki/Exotic_baryon "Exotic baryon") - [Quantum chromodynamics](https://en.wikipedia.org/wiki/Quantum_chromodynamics "Quantum chromodynamics"), [flavor](https://en.wikipedia.org/wiki/Flavour_\(particle_physics\) "Flavour (particle physics)"), the [QCD vacuum](https://en.wikipedia.org/wiki/QCD_vacuum "QCD vacuum") ## Notes \[[edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit&section=7 "Edit section: Notes")\] 1. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-Gell-Man1964_1-0) [Gell-Mann, M.](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann") (4 January 1964). "A Schematic Model of Baryons and Mesons". [Physics Letters](https://en.wikipedia.org/wiki/Physics_Letters "Physics Letters"). 8 (3): 214–215\. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1964PhL.....8..214G](https://ui.adsabs.harvard.edu/abs/1964PhL.....8..214G). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/S0031-9163(64)92001-3](https://doi.org/10.1016%2FS0031-9163%2864%2992001-3). 2. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-Zweig1964a_2-0) [Zweig, G.](https://en.wikipedia.org/wiki/George_Zweig "George Zweig") (17 January 1964). [An SU(3) Model for Strong Interaction Symmetry and its Breaking](https://cds.cern.ch/record/352337/files/CERN-TH-401.pdf) (PDF) (Report). CERN Report No.8182/TH.401. 3. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-Zweig1964b_3-0) [Zweig, G.](https://en.wikipedia.org/wiki/George_Zweig "George Zweig") (1964). [An SU(3) Model for Strong Interaction Symmetry and its Breaking: II](https://cds.cern.ch/record/570209/files/CERN-TH-412.pdf) (PDF) (Report). CERN Report No.8419/TH.412. 4. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-4) [Petermann, A.](https://en.wikipedia.org/wiki/Andr%C3%A9_Petermann "André Petermann") (1965). "Propriétés de l'étrangeté et une formule de masse pour les mésons vectoriels" \[Strangeness properties and a mass formula for vector meson\]. [Nuclear Physics](https://en.wikipedia.org/wiki/Nuclear_Physics_\(journal\) "Nuclear Physics (journal)"). 63 (2): 349–352\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1412\.8681](https://arxiv.org/abs/1412.8681). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1965NucPh..63..349P](https://ui.adsabs.harvard.edu/abs/1965NucPh..63..349P). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/0029-5582(65)90348-2](https://doi.org/10.1016%2F0029-5582%2865%2990348-2). 5. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-5) Petrov, Vladimir A. (June 23–27, 2014). Half a Century with QUARKS. XXX-th International Workshop on High Energy Physics. [Protvino](https://en.wikipedia.org/wiki/Protvino "Protvino"), [Moscow Oblast](https://en.wikipedia.org/wiki/Moscow_Oblast "Moscow Oblast"), Russia. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1412\.8681](https://arxiv.org/abs/1412.8681). 6. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-JF1968_6-0) Franklin, J. (1968). "A Model of Baryons Made of Quarks with Hidden Spin". [Physical Review](https://en.wikipedia.org/wiki/Physical_Review "Physical Review"). 172 (3): 1807–1817\. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1968PhRv..172.1807F](https://ui.adsabs.harvard.edu/abs/1968PhRv..172.1807F). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1103/PhysRev.172.1807](https://doi.org/10.1103%2FPhysRev.172.1807). 7. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-7) Greenberg, O.W. (1964). "Spin and unitary-spin independence in a paraquark model of baryons and mesons". [Physical Review Letters](https://en.wikipedia.org/wiki/Physical_Review_Letters "Physical Review Letters"). 13 (20): 598–602\. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1964PhRvL..13..598G](https://ui.adsabs.harvard.edu/abs/1964PhRvL..13..598G). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1103/PhysRevLett.13.598](https://doi.org/10.1103%2FPhysRevLett.13.598). 8. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-8) Han, M.Y.; Nambu, Y. (1965). ["Three-triplet model with double SU(3) symmetry"](https://digital.library.unt.edu/ark:/67531/metadc1031342/). [Physical Review B](https://en.wikipedia.org/wiki/Physical_Review_B "Physical Review B"). 139 (4B): 1006. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1965PhRv..139.1006H](https://ui.adsabs.harvard.edu/abs/1965PhRv..139.1006H). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1103/PhysRev.139.B1006](https://doi.org/10.1103%2FPhysRev.139.B1006). 9. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-9) Bardeen, W.; Fritzsch, H.; Gell-Mann, M. (1973). ["Light cone current algebra, π0 decay, and e\+ e− annihilation"](https://archive.org/details/scaleconformalsy0000unse/page/139). In Gatto, R. (ed.). Scale and conformal symmetry in hadron physics. [John Wiley & Sons](https://en.wikipedia.org/wiki/John_Wiley_%26_Sons "John Wiley & Sons"). p. [139](https://archive.org/details/scaleconformalsy0000unse/page/139). [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-ph/0211388](https://arxiv.org/abs/hep-ph/0211388). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2002hep.ph...11388B](https://ui.adsabs.harvard.edu/abs/2002hep.ph...11388B). [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [0-471-29292-3](https://en.wikipedia.org/wiki/Special:BookSources/0-471-29292-3 "Special:BookSources/0-471-29292-3") . 10. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-10) Fritzsch, H.; Gell-Mann, M.; Leutwyler, H. (1973). "Advantages of the color octet gluon picture". [Physics Letters B](https://en.wikipedia.org/wiki/Physics_Letters_B "Physics Letters B"). 47 (4): 365. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1973PhLB...47..365F](https://ui.adsabs.harvard.edu/abs/1973PhLB...47..365F). [CiteSeerX](https://en.wikipedia.org/wiki/CiteSeerX_\(identifier\) "CiteSeerX (identifier)") [10\.1.1.453.4712](https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.453.4712). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/0370-2693(73)90625-4](https://doi.org/10.1016%2F0370-2693%2873%2990625-4). ## References \[[edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit&section=8 "Edit section: References")\] - S. Eidelman et al. [Particle Data Group](https://en.wikipedia.org/wiki/Particle_Data_Group "Particle Data Group") (2004). ["Review of Particle Physics"](http://pdg.lbl.gov/2004/reviews/quarkmodrpp.pdf) (PDF). [Physics Letters B](https://en.wikipedia.org/wiki/Physics_Letters_B "Physics Letters B"). 592 (1–4\): 1. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[astro-ph/0406663](https://arxiv.org/abs/astro-ph/0406663). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2004PhLB..592....1P](https://ui.adsabs.harvard.edu/abs/2004PhLB..592....1P). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/j.physletb.2004.06.001](https://doi.org/10.1016%2Fj.physletb.2004.06.001). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [118588567](https://api.semanticscholar.org/CorpusID:118588567). - Lichtenberg, D B (1970). Unitary Symmetry and Elementary Particles. Academic Press. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-1483242729](https://en.wikipedia.org/wiki/Special:BookSources/978-1483242729 "Special:BookSources/978-1483242729") . - Thomson, M A (2011), [Lecture notes](http://www.hep.phy.cam.ac.uk/~thomson/partIIIparticles/handouts/Handout_7_2011.pdf) - J.J.J. Kokkedee (1969). [The quark model](https://archive.org/details/quarkmodel0000kokk). [W. A. Benjamin](https://en.wikipedia.org/wiki/W._A._Benjamin "W. A. Benjamin"). [ASIN](https://en.wikipedia.org/wiki/ASIN_\(identifier\) "ASIN (identifier)") [B001RAVDIA](https://www.amazon.com/dp/B001RAVDIA). \| [v](https://en.wikipedia.org/wiki/Template:Particles "Template:Particles") [t](https://en.wikipedia.org/wiki/Template_talk:Particles "Template talk:Particles") [e](https://en.wikipedia.org/wiki/Special:EditPage/Template:Particles "Special:EditPage/Template:Particles")[Particles in physics](https://en.wikipedia.org/wiki/Particle_physics "Particle physics") \| \| \|---\|---\| \| [Elementary](https://en.wikipedia.org/wiki/Elementary_particle "Elementary particle") \| \| \| \| \| \| [Fermions](https://en.wikipedia.org/wiki/Fermion "Fermion") \| \| \| \| \| \| [Quarks](https://en.wikipedia.org/wiki/Quark "Quark") \| [Up (quark](https://en.wikipedia.org/wiki/Up_quark "Up quark") [antiquark)](https://en.wikipedia.org/wiki/Up_antiquark "Up antiquark") [Down (quark](https://en.wikipedia.org/wiki/Down_quark "Down quark") [antiquark)](https://en.wikipedia.org/wiki/Down_antiquark "Down antiquark") [Charm (quark](https://en.wikipedia.org/wiki/Charm_quark "Charm quark") [antiquark)](https://en.wikipedia.org/wiki/Charm_antiquark "Charm antiquark") [Strange (quark](https://en.wikipedia.org/wiki/Strange_quark "Strange quark") [antiquark)](https://en.wikipedia.org/wiki/Strange_antiquark "Strange antiquark") [Top (quark](https://en.wikipedia.org/wiki/Top_quark "Top quark") [antiquark)](https://en.wikipedia.org/wiki/Top_antiquark "Top antiquark") [Bottom (quark](https://en.wikipedia.org/wiki/Bottom_quark "Bottom quark") [antiquark)](https://en.wikipedia.org/wiki/Bottom_antiquark "Bottom antiquark") \| \| [Leptons](https://en.wikipedia.org/wiki/Lepton "Lepton") \| [Electron](https://en.wikipedia.org/wiki/Electron "Electron") [Positron](https://en.wikipedia.org/wiki/Positron "Positron") [Muon](https://en.wikipedia.org/wiki/Muon "Muon") [Antimuon](https://en.wikipedia.org/wiki/Muon "Muon") [Tau](https://en.wikipedia.org/wiki/Tau_\(particle\) "Tau (particle)") [Antitau](https://en.wikipedia.org/wiki/Tau_\(particle\) "Tau (particle)") [Neutrino](https://en.wikipedia.org/wiki/Neutrino "Neutrino") [Electron neutrino](https://en.wikipedia.org/wiki/Electron_neutrino "Electron neutrino") [Electron antineutrino](https://en.wikipedia.org/wiki/Neutrino#Antineutrinos "Neutrino") [Muon neutrino](https://en.wikipedia.org/wiki/Muon_neutrino "Muon neutrino") [Muon antineutrino](https://en.wikipedia.org/wiki/Neutrino#Antineutrinos "Neutrino") [Tau neutrino](https://en.wikipedia.org/wiki/Tau_neutrino "Tau neutrino") [Tau antineutrino](https://en.wikipedia.org/wiki/Neutrino#Antineutrinos "Neutrino") \| \| [Bosons](https://en.wikipedia.org/wiki/Boson "Boson") \| \| \| \| \| \| [Gauge](https://en.wikipedia.org/wiki/Gauge_boson "Gauge boson") \| [Photon](https://en.wikipedia.org/wiki/Photon "Photon") [Gluon](https://en.wikipedia.org/wiki/Gluon "Gluon") [W and Z bosons](https://en.wikipedia.org/wiki/W_and_Z_bosons "W and Z bosons") \| \| [Scalar](https://en.wikipedia.org/wiki/Scalar_boson "Scalar boson") \| [Higgs boson](https://en.wikipedia.org/wiki/Higgs_boson "Higgs boson") \| \| [Ghost fields](https://en.wikipedia.org/wiki/Ghost_\(physics\) "Ghost (physics)") \| [Faddeev–Popov ghosts](https://en.wikipedia.org/wiki/Faddeev%E2%80%93Popov_ghost "Faddeev–Popov ghost") \| \| [Hypothetical](https://en.wikipedia.org/wiki/List_of_hypothetical_particles "List of hypothetical particles") \| \| \| \| \| \| [Superpartners](https://en.wikipedia.org/wiki/Superpartner "Superpartner") \| \| \| \| \| \| [Gauginos](https://en.wikipedia.org/wiki/Gaugino "Gaugino") \| [Gluino](https://en.wikipedia.org/wiki/Gluino "Gluino") [Gravitino](https://en.wikipedia.org/wiki/Gravitino "Gravitino") [Photino](https://en.wikipedia.org/wiki/Photino "Photino") \| \| Others \| [Axino](https://en.wikipedia.org/wiki/Axino "Axino") [Chargino](https://en.wikipedia.org/wiki/Chargino "Chargino") [Higgsino](https://en.wikipedia.org/wiki/Higgsino "Higgsino") [Neutralino](https://en.wikipedia.org/wiki/Neutralino "Neutralino") [Sfermion](https://en.wikipedia.org/wiki/Sfermion "Sfermion") ([Stop squark](https://en.wikipedia.org/wiki/Stop_squark "Stop squark")) \| \| Others \| [Axion](https://en.wikipedia.org/wiki/Axion "Axion") [Curvaton](https://en.wikipedia.org/wiki/Curvaton "Curvaton") [Dilaton](https://en.wikipedia.org/wiki/Dilaton "Dilaton") [Dual graviton](https://en.wikipedia.org/wiki/Dual_graviton "Dual graviton") [Graviphoton](https://en.wikipedia.org/wiki/Graviphoton "Graviphoton") [Graviton](https://en.wikipedia.org/wiki/Graviton "Graviton") [Inflaton](https://en.wikipedia.org/wiki/Inflaton "Inflaton") [Leptoquark](https://en.wikipedia.org/wiki/Leptoquark "Leptoquark") [Magnetic monopole](https://en.wikipedia.org/wiki/Magnetic_monopole "Magnetic monopole") [Majoron](https://en.wikipedia.org/wiki/Majoron "Majoron") [Majorana fermion](https://en.wikipedia.org/wiki/Majorana_fermion "Majorana fermion") [Dark photon](https://en.wikipedia.org/wiki/Dark_photon "Dark photon") [Preon](https://en.wikipedia.org/wiki/Preon "Preon") [Sterile neutrino](https://en.wikipedia.org/wiki/Sterile_neutrino "Sterile neutrino") [Tachyon](https://en.wikipedia.org/wiki/Tachyon "Tachyon") [W′ and Z′ bosons](https://en.wikipedia.org/wiki/W%E2%80%B2_and_Z%E2%80%B2_bosons "W′ and Z′ bosons") [X and Y bosons](https://en.wikipedia.org/wiki/X_and_Y_bosons "X and Y bosons") \| \| [Composite](https://en.wikipedia.org/wiki/Bound_state "Bound state") \| \| \| \| \| \| [Hadrons](https://en.wikipedia.org/wiki/Hadron "Hadron") \| \| \| \| \| \| [Baryons](https://en.wikipedia.org/wiki/Baryon "Baryon") \| [Nucleon](https://en.wikipedia.org/wiki/Nucleon "Nucleon") [Proton](https://en.wikipedia.org/wiki/Proton "Proton") [Antiproton](https://en.wikipedia.org/wiki/Antiproton "Antiproton") [Neutron](https://en.wikipedia.org/wiki/Neutron "Neutron") [Antineutron](https://en.wikipedia.org/wiki/Antineutron "Antineutron") [Delta baryon](https://en.wikipedia.org/wiki/Delta_baryon "Delta baryon") [Lambda baryon](https://en.wikipedia.org/wiki/Lambda_baryon "Lambda baryon") [Sigma baryon](https://en.wikipedia.org/wiki/Sigma_baryon "Sigma baryon") [Xi baryon](https://en.wikipedia.org/wiki/Xi_baryon "Xi baryon") [Omega baryon](https://en.wikipedia.org/wiki/Omega_baryon "Omega baryon") \| \| [Mesons](https://en.wikipedia.org/wiki/Meson "Meson") \| [Pion](https://en.wikipedia.org/wiki/Pion "Pion") [Rho meson](https://en.wikipedia.org/wiki/Rho_meson "Rho meson") [Eta and eta prime mesons](https://en.wikipedia.org/wiki/Eta_meson "Eta meson") [Bottom eta meson](https://en.wikipedia.org/wiki/Bottom_eta_meson "Bottom eta meson") [Phi meson](https://en.wikipedia.org/wiki/Phi_meson "Phi meson") [J/psi meson](https://en.wikipedia.org/wiki/J/psi_meson "J/psi meson") [Omega meson](https://en.wikipedia.org/wiki/Omega_meson "Omega meson") [Upsilon meson](https://en.wikipedia.org/wiki/Upsilon_meson "Upsilon meson") [Kaon](https://en.wikipedia.org/wiki/Kaon "Kaon") [B meson](https://en.wikipedia.org/wiki/B_meson "B meson") [D meson](https://en.wikipedia.org/wiki/D_meson "D meson") [Quarkonium](https://en.wikipedia.org/wiki/Quarkonium "Quarkonium") \| \| [Exotic hadrons](https://en.wikipedia.org/wiki/Exotic_hadron "Exotic hadron") \| [Tetraquark](https://en.wikipedia.org/wiki/Tetraquark "Tetraquark") ([Double-charm tetraquark](https://en.wikipedia.org/wiki/Double-charm_tetraquark "Double-charm tetraquark")) [Pentaquark](https://en.wikipedia.org/wiki/Pentaquark "Pentaquark") \| \| Others \| [Atomic nuclei](https://en.wikipedia.org/wiki/Atomic_nucleus "Atomic nucleus") [Atoms](https://en.wikipedia.org/wiki/Atom "Atom") [Exotic atoms](https://en.wikipedia.org/wiki/Exotic_atom "Exotic atom") [Positronium](https://en.wikipedia.org/wiki/Positronium "Positronium") [Muonium](https://en.wikipedia.org/wiki/Muonium "Muonium") [Tauonium](https://en.wikipedia.org/wiki/Tauonium "Tauonium") [Onia](https://en.wikipedia.org/wiki/Onium "Onium") [Pionium](https://en.wikipedia.org/wiki/Pionium "Pionium") [Protonium](https://en.wikipedia.org/wiki/Protonium "Protonium") [Antihydrogen](https://en.wikipedia.org/wiki/Antihydrogen "Antihydrogen") [Superatoms](https://en.wikipedia.org/wiki/Superatom "Superatom") [Molecules](https://en.wikipedia.org/wiki/Molecule "Molecule") \| \| [Hypothetical](https://en.wikipedia.org/wiki/List_of_hypothetical_particles "List of hypothetical particles") \| \| \| \| \| \| \| \| \| Baryons \| [Hexaquark](https://en.wikipedia.org/wiki/Hexaquark "Hexaquark") [Heptaquark](https://en.wikipedia.org/wiki/Heptaquark "Heptaquark") [Skyrmion](https://en.wikipedia.org/wiki/Skyrmion "Skyrmion") \| \| Mesons \| [Glueball](https://en.wikipedia.org/wiki/Glueball "Glueball") [Theta meson](https://en.wikipedia.org/wiki/Theta_meson "Theta meson") [T meson](https://en.wikipedia.org/wiki/T_meson "T meson") \| \| Others \| [Mesonic molecule](https://en.wikipedia.org/wiki/Mesonic_molecule "Mesonic molecule") [Pomeron](https://en.wikipedia.org/wiki/Pomeron "Pomeron") [Diquark](https://en.wikipedia.org/wiki/Diquark "Diquark") [R-hadron](https://en.wikipedia.org/wiki/R-hadron "R-hadron") \| \| [Quasiparticles](https://en.wikipedia.org/wiki/Quasiparticle "Quasiparticle") \| [Anyon](https://en.wikipedia.org/wiki/Anyon "Anyon") [Davydov soliton](https://en.wikipedia.org/wiki/Davydov_soliton "Davydov soliton") [Dropleton](https://en.wikipedia.org/wiki/Dropleton "Dropleton") [Exciton](https://en.wikipedia.org/wiki/Exciton "Exciton") [Fracton](https://en.wikipedia.org/wiki/Fracton_\(subdimensional_particle\) "Fracton (subdimensional particle)") [Hole](https://en.wikipedia.org/wiki/Electron_hole "Electron hole") [Magnon](https://en.wikipedia.org/wiki/Magnon "Magnon") [Phonon](https://en.wikipedia.org/wiki/Phonon "Phonon") [Plasmaron](https://en.wikipedia.org/wiki/Plasmaron "Plasmaron") [Plasmon](https://en.wikipedia.org/wiki/Plasmon "Plasmon") [Polariton](https://en.wikipedia.org/wiki/Polariton "Polariton") [Polaron](https://en.wikipedia.org/wiki/Polaron "Polaron") [Roton](https://en.wikipedia.org/wiki/Roton "Roton") [Trion](https://en.wikipedia.org/wiki/Trion_\(physics\) "Trion (physics)") \| \| Lists \| [Baryons](https://en.wikipedia.org/wiki/List_of_baryons "List of baryons") [Mesons](https://en.wikipedia.org/wiki/List_of_mesons "List of mesons") [Particles](https://en.wikipedia.org/wiki/List_of_particles "List of particles") [Quasiparticles](https://en.wikipedia.org/wiki/List_of_quasiparticles "List of quasiparticles") [Timeline of particle discoveries](https://en.wikipedia.org/wiki/Timeline_of_particle_discoveries "Timeline of particle discoveries") \| \| Related \| [History of subatomic physics](https://en.wikipedia.org/wiki/History_of_subatomic_physics "History of subatomic physics") [timeline](https://en.wikipedia.org/wiki/Timeline_of_atomic_and_subatomic_physics "Timeline of atomic and subatomic physics") [Standard Model](https://en.wikipedia.org/wiki/Standard_Model "Standard Model") [mathematical formulation](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model "Mathematical formulation of the Standard Model") [Subatomic particles](https://en.wikipedia.org/wiki/Subatomic_particle "Subatomic particle") [Particles](https://en.wikipedia.org/wiki/Particle "Particle") [Antiparticles](https://en.wikipedia.org/wiki/Antiparticle "Antiparticle") [Nuclear physics](https://en.wikipedia.org/wiki/Nuclear_physics "Nuclear physics") [Eightfold way](https://en.wikipedia.org/wiki/Eightfold_way_\(physics\) "Eightfold way (physics)") [Quark model]() [Exotic matter](https://en.wikipedia.org/wiki/Exotic_matter "Exotic matter") [Massless particle](https://en.wikipedia.org/wiki/Massless_particle "Massless particle") [Relativistic particle](https://en.wikipedia.org/wiki/Relativistic_particle "Relativistic particle") [Virtual particle](https://en.wikipedia.org/wiki/Virtual_particle "Virtual particle") [Wave–particle duality](https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality "Wave–particle duality") [Particle chauvinism](https://en.wikipedia.org/wiki/Particle_chauvinism "Particle chauvinism") \| \| [![](https://upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/20px-Symbol_portal_class.svg.png)](https://en.wikipedia.org/wiki/File:Symbol_portal_class.svg "Portal") [Physics portal](https://en.wikipedia.org/wiki/Portal:Physics "Portal:Physics") \| \| \| [v](https://en.wikipedia.org/wiki/Template:Standard_model_of_physics "Template:Standard model of physics") [t](https://en.wikipedia.org/wiki/Template_talk:Standard_model_of_physics "Template talk:Standard model of physics") [e](https://en.wikipedia.org/wiki/Special:EditPage/Template:Standard_model_of_physics "Special:EditPage/Template:Standard model of physics")[Standard Model](https://en.wikipedia.org/wiki/Standard_Model "Standard Model") \| \| \| \|---\|---\|---\| \| Background \| [Particle physics](https://en.wikipedia.org/wiki/Particle_physics "Particle physics") [Fermions](https://en.wikipedia.org/wiki/Fermion "Fermion") [Gauge boson](https://en.wikipedia.org/wiki/Gauge_boson "Gauge boson") [Higgs boson](https://en.wikipedia.org/wiki/Higgs_boson "Higgs boson") [Quantum field theory](https://en.wikipedia.org/wiki/Quantum_field_theory "Quantum field theory") [Gauge theory](https://en.wikipedia.org/wiki/Gauge_theory "Gauge theory") [Strong interaction](https://en.wikipedia.org/wiki/Strong_interaction "Strong interaction") [Color charge](https://en.wikipedia.org/wiki/Color_charge "Color charge") [Quantum chromodynamics](https://en.wikipedia.org/wiki/Quantum_chromodynamics "Quantum chromodynamics") [Quark model]() [Electroweak interaction](https://en.wikipedia.org/wiki/Electroweak_interaction "Electroweak interaction") [Weak interaction](https://en.wikipedia.org/wiki/Weak_interaction "Weak interaction") [Quantum electrodynamics](https://en.wikipedia.org/wiki/Quantum_electrodynamics "Quantum electrodynamics") [Fermi's interaction](https://en.wikipedia.org/wiki/Fermi%27s_interaction "Fermi's interaction") [Weak hypercharge](https://en.wikipedia.org/wiki/Weak_hypercharge "Weak hypercharge") [Weak isospin](https://en.wikipedia.org/wiki/Weak_isospin "Weak isospin") \| ![](https://upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/250px-Standard_Model_of_Elementary_Particles.svg.png) \| \| Constituents \| [CKM matrix](https://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix "Cabibbo–Kobayashi–Maskawa matrix") [Spontaneous symmetry breaking](https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking "Spontaneous symmetry breaking") [Higgs mechanism](https://en.wikipedia.org/wiki/Higgs_mechanism "Higgs mechanism") [Mathematical formulation of the Standard Model](https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model "Mathematical formulation of the Standard Model") \| \| \| [Beyond the Standard Model](https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model "Physics beyond the Standard Model") \| \| \| \| \| \| \| \| Evidence \| [Hierarchy problem](https://en.wikipedia.org/wiki/Hierarchy_problem "Hierarchy problem") [Dark matter](https://en.wikipedia.org/wiki/Dark_matter "Dark matter") [Cosmological constant](https://en.wikipedia.org/wiki/Cosmological_constant "Cosmological constant") [problem](https://en.wikipedia.org/wiki/Cosmological_constant_problem "Cosmological constant problem") [Strong CP problem](https://en.wikipedia.org/wiki/CP_violation "CP violation") [Neutrino oscillation](https://en.wikipedia.org/wiki/Neutrino_oscillation "Neutrino oscillation") \| \| \| Theories \| [Technicolor](https://en.wikipedia.org/wiki/Technicolor_\(physics\) "Technicolor (physics)") [Kaluza–Klein theory](https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory "Kaluza–Klein theory") [Grand Unified Theory](https://en.wikipedia.org/wiki/Grand_Unified_Theory "Grand Unified Theory") [Theory of everything](https://en.wikipedia.org/wiki/Theory_of_everything "Theory of everything") \| \| \| [Supersymmetry](https://en.wikipedia.org/wiki/Supersymmetry "Supersymmetry") \| [MSSM](https://en.wikipedia.org/wiki/Minimal_Supersymmetric_Standard_Model "Minimal Supersymmetric Standard Model") [NMSSM](https://en.wikipedia.org/wiki/Next-to-Minimal_Supersymmetric_Standard_Model "Next-to-Minimal Supersymmetric Standard Model") [Split supersymmetry](https://en.wikipedia.org/wiki/Split_supersymmetry "Split supersymmetry") [Supergravity](https://en.wikipedia.org/wiki/Supergravity "Supergravity") \| \| \| [Quantum gravity](https://en.wikipedia.org/wiki/Quantum_gravity "Quantum gravity") \| [String theory](https://en.wikipedia.org/wiki/String_theory "String theory") [Superstring theory](https://en.wikipedia.org/wiki/Superstring_theory "Superstring theory") [Loop quantum gravity](https://en.wikipedia.org/wiki/Loop_quantum_gravity "Loop quantum gravity") [Causal dynamical triangulation](https://en.wikipedia.org/wiki/Causal_dynamical_triangulation "Causal dynamical triangulation") [Canonical quantum gravity](https://en.wikipedia.org/wiki/Canonical_quantum_gravity "Canonical quantum gravity") [Superfluid vacuum theory](https://en.wikipedia.org/wiki/Superfluid_vacuum_theory "Superfluid vacuum theory") [Twistor theory](https://en.wikipedia.org/wiki/Twistor_theory "Twistor theory") \| \| \| Experiments \| [Gran Sasso](https://en.wikipedia.org/wiki/Laboratori_Nazionali_del_Gran_Sasso "Laboratori Nazionali del Gran Sasso") [INO](https://en.wikipedia.org/wiki/India-based_Neutrino_Observatory "India-based Neutrino Observatory") [LHC](https://en.wikipedia.org/wiki/Large_Hadron_Collider "Large Hadron Collider") [SNO](https://en.wikipedia.org/wiki/Sudbury_Neutrino_Observatory "Sudbury Neutrino Observatory") [Super-K](https://en.wikipedia.org/wiki/Super-Kamiokande "Super-Kamiokande") [Tevatron](https://en.wikipedia.org/wiki/Tevatron "Tevatron") \| \| \| ![](https://upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/20px-Symbol_category_class.svg.png) [Category](https://en.wikipedia.org/wiki/Category:Standard_Model "Category:Standard Model") [![](https://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png)](https://en.wikipedia.org/wiki/File:Commons-logo.svg "Commons page") [Commons](https://commons.wikimedia.org/wiki/Category:Standard_Model_\(physics\) "commons:Category:Standard Model (physics)") \| \| \| ![](https://en.wikipedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=1) Retrieved from 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Readable Markdown	From Wikipedia, the free encyclopedia [![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/8foldway.svg/250px-8foldway.svg.png)](https://en.wikipedia.org/wiki/File:8foldway.svg) Figure 1: The [pseudoscalar meson](https://en.wikipedia.org/wiki/Pseudoscalar_meson "Pseudoscalar meson") nonet. Members of the original meson "octet" are shown in green, the singlet in magenta. Although these mesons are now grouped into a nonet, the [Eightfold Way](https://en.wikipedia.org/wiki/Eightfold_way_\(physics\) "Eightfold way (physics)") name derives from the patterns of eight for the mesons and baryons in the original classification scheme. In [particle physics](https://en.wikipedia.org/wiki/Particle_physics "Particle physics"), the quark model is a classification scheme for [hadrons](https://en.wikipedia.org/wiki/Hadron "Hadron") in terms of their valence [quarks](https://en.wikipedia.org/wiki/Quark "Quark")—the quarks and antiquarks that give rise to the [quantum numbers](https://en.wikipedia.org/wiki/Quantum_number "Quantum number") of the hadrons. The quark model underlies ["flavor SU(3)"](https://en.wikipedia.org/wiki/Flavour_\(particle_physics\) "Flavour (particle physics)"), or the [Eightfold Way](https://en.wikipedia.org/wiki/Eightfold_way_\(physics\) "Eightfold way (physics)"), the successful [classification scheme](https://en.wikipedia.org/wiki/Classification_scheme_\(information_science\) "Classification scheme (information science)") organizing the large number of lighter [hadrons](https://en.wikipedia.org/wiki/Hadron "Hadron") that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental [verification](https://en.wikipedia.org/wiki/Verification_and_validation "Verification and validation") beginning in the late 1960s and is a valid and effective classification of them to date. The model was independently proposed by physicists [Murray Gell-Mann](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann"),[\[1\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-Gell-Man1964-1) who dubbed them "quarks" in a concise paper, and [George Zweig](https://en.wikipedia.org/wiki/George_Zweig "George Zweig"),[\[2\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-Zweig1964a-2)[\[3\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-Zweig1964b-3) who suggested "aces" in a longer manuscript. [André Petermann](https://en.wikipedia.org/wiki/Andr%C3%A9_Petermann "André Petermann") also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation.[\[4\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-4)[\[5\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-5) Today, the model has essentially been absorbed as a component of the established [quantum field theory](https://en.wikipedia.org/wiki/Quantum_field_theory "Quantum field theory") of strong and electroweak particle interactions, dubbed the [Standard Model](https://en.wikipedia.org/wiki/Standard_Model "Standard Model"). Hadrons are not really "elementary", and can be regarded as bound states of their "valence quarks" and antiquarks, which give rise to the [quantum numbers](https://en.wikipedia.org/wiki/Quantum_number "Quantum number") of the hadrons. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the [Poincaré symmetry](https://en.wikipedia.org/wiki/Poincar%C3%A9_symmetry "Poincaré symmetry")—JPC, where J, P and C stand for the [total angular momentum](https://en.wikipedia.org/wiki/Total_angular_momentum "Total angular momentum"), [P-symmetry](https://en.wikipedia.org/wiki/P-symmetry "P-symmetry"), and [C-symmetry](https://en.wikipedia.org/wiki/C-symmetry "C-symmetry"), respectively. The other set is the [flavor quantum numbers](https://en.wikipedia.org/wiki/Flavour_quantum_numbers "Flavour quantum numbers") such as the [isospin](https://en.wikipedia.org/wiki/Isospin "Isospin"), [strangeness](https://en.wikipedia.org/wiki/Strangeness "Strangeness"), [charm](https://en.wikipedia.org/wiki/Charm_\(quantum_number\) "Charm (quantum number)"), and so on. The strong interactions binding the quarks together are insensitive to these quantum numbers, so variation of them leads to systematic mass and coupling relationships among the hadrons in the same flavor multiplet. All quarks are assigned a [baryon number](https://en.wikipedia.org/wiki/Baryon_number "Baryon number") of ⁠1/3⁠. [Up](https://en.wikipedia.org/wiki/Up_quark "Up quark"), [charm](https://en.wikipedia.org/wiki/Charm_quark "Charm quark") and [top quarks](https://en.wikipedia.org/wiki/Top_quark "Top quark") have an [electric charge](https://en.wikipedia.org/wiki/Electric_charge "Electric charge") of +⁠2/3⁠, while the [down](https://en.wikipedia.org/wiki/Down_quark "Down quark"), [strange](https://en.wikipedia.org/wiki/Strange_quark "Strange quark"), and [bottom quarks](https://en.wikipedia.org/wiki/Bottom_quark "Bottom quark") have an electric charge of −⁠1/3⁠. Antiquarks have the opposite quantum numbers. Quarks are [spin-⁠1/2⁠](https://en.wikipedia.org/wiki/Spin-1/2 "Spin-1/2") particles, and thus [fermions](https://en.wikipedia.org/wiki/Fermion "Fermion"). Each quark or antiquark obeys the Gell-Mann–Nishijima formula individually, so any additive assembly of them will as well. [Mesons](https://en.wikipedia.org/wiki/Meson "Meson") are made of a valence quark–antiquark pair (thus have a baryon number of 0), while [baryons](https://en.wikipedia.org/wiki/Baryon "Baryon") are made of three quarks (thus have a baryon number of 1). This article discusses the quark model for the up, down, and strange flavors of quark (which form an approximate flavor [SU(3) symmetry](https://en.wikipedia.org/wiki/SU\(3\) "SU(3)")). There are generalizations to larger number of flavors. Developing classification schemes for [hadrons](https://en.wikipedia.org/wiki/Hadron "Hadron") became a timely 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](https://en.wikipedia.org/wiki/Wolfgang_Pauli "Wolfgang Pauli") to exclaim "Had I foreseen that, I would have gone into botany." and [Enrico Fermi](https://en.wikipedia.org/wiki/Enrico_Fermi "Enrico Fermi") to advise his student [Leon Lederman](https://en.wikipedia.org/wiki/Leon_Lederman "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 Alvarez](https://en.wikipedia.org/wiki/Luis_Walter_Alvarez "Luis Walter Alvarez"), who was at the forefront of many of these developments. Constructing hadrons as bound states of fewer constituents would thus organize the "zoo" at hand. Several early proposals, such as the ones by [Enrico Fermi](https://en.wikipedia.org/wiki/Enrico_Fermi "Enrico Fermi") and [Chen-Ning Yang](https://en.wikipedia.org/wiki/Chen-Ning_Yang "Chen-Ning Yang") (1949), and the [Sakata model](https://en.wikipedia.org/wiki/Sakata_model "Sakata model") (1956), ended up satisfactorily covering the mesons, but failed with baryons, and so were unable to explain all the data. The [Gell-Mann–Nishijima formula](https://en.wikipedia.org/wiki/Gell-Mann%E2%80%93Nishijima_formula "Gell-Mann–Nishijima formula"), developed by [Murray Gell-Mann](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann") and [Kazuhiko Nishijima](https://en.wikipedia.org/wiki/Kazuhiko_Nishijima "Kazuhiko Nishijima"), led to the [Eightfold Way](https://en.wikipedia.org/wiki/Eightfold_way_\(physics\) "Eightfold way (physics)") classification, invented by Gell-Mann, with important independent contributions from [Yuval Ne'eman](https://en.wikipedia.org/wiki/Yuval_Ne%27eman "Yuval Ne'eman"), in 1961. The hadrons were organized into SU(3) representation multiplets, octets and decuplets, of roughly the same mass, due to the strong interactions; and smaller mass differences linked to the flavor quantum numbers, invisible to the strong interactions. The [Gell-Mann–Okubo mass formula](https://en.wikipedia.org/wiki/Gell-Mann%E2%80%93Okubo_mass_formula "Gell-Mann–Okubo mass formula") systematized the quantification of these small mass differences among members of a hadronic multiplet, controlled by the [explicit symmetry breaking](https://en.wikipedia.org/wiki/Explicit_symmetry_breaking "Explicit symmetry breaking") of SU(3). The spin-⁠3/2⁠ [Ω− baryon](https://en.wikipedia.org/wiki/Omega_baryon "Omega baryon"), a member of the ground-state decuplet, was a crucial prediction of that classification. After it was discovered in an experiment at [Brookhaven National Laboratory](https://en.wikipedia.org/wiki/Brookhaven_National_Laboratory "Brookhaven National Laboratory"), Gell-Mann received a [Nobel Prize in Physics](https://en.wikipedia.org/wiki/Nobel_Prize_in_Physics "Nobel Prize in Physics") for his work on the Eightfold Way, in 1969. Finally, in 1964, Gell-Mann and [George Zweig](https://en.wikipedia.org/wiki/George_Zweig "George Zweig"), discerned independently what the Eightfold Way picture encodes: They posited three elementary fermionic constituents—the "[up](https://en.wikipedia.org/wiki/Up_quark "Up quark")", "[down](https://en.wikipedia.org/wiki/Down_quark "Down quark")", and "[strange](https://en.wikipedia.org/wiki/Strange_quark "Strange quark")" quarks—which are unobserved, and possibly unobservable in a free form. Simple pairwise or triplet combinations of these three constituents and their antiparticles underlie and elegantly encode the Eightfold Way classification, in an economical, tight structure, resulting in further simplicity. Hadronic mass differences were now linked to the different masses of the constituent quarks. It would take about a decade for the unexpected nature—and physical reality—of these quarks to be appreciated more fully (See [Quarks](https://en.wikipedia.org/wiki/Quarks "Quarks")). Counter-intuitively, they cannot ever be observed in isolation ([color confinement](https://en.wikipedia.org/wiki/Color_confinement "Color confinement")), but instead always combine with other quarks to form full hadrons, which then furnish ample indirect information on the trapped quarks themselves. Conversely, the quarks serve in the definition of [quantum chromodynamics](https://en.wikipedia.org/wiki/Quantum_chromodynamics "Quantum chromodynamics"), the fundamental theory fully describing the strong interactions; and the Eightfold Way is now understood to be a consequence of the flavor symmetry structure of the lightest three of them. [![](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Meson_nonet_-_spin_0.svg/250px-Meson_nonet_-_spin_0.svg.png)](https://en.wikipedia.org/wiki/File:Meson_nonet_-_spin_0.svg) Figure 2: [Pseudoscalar mesons](https://en.wikipedia.org/wiki/Pseudoscalar_meson "Pseudoscalar meson") of spin-0 form a nonet [![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/13/Meson_nonet_-_spin_1.svg/250px-Meson_nonet_-_spin_1.svg.png)](https://en.wikipedia.org/wiki/File:Meson_nonet_-_spin_1.svg) Figure 3: [Vector mesons](https://en.wikipedia.org/wiki/Vector_mesons "Vector mesons") of spin-1 form a nonet The Eightfold Way classification is named after the following fact: If we take three flavors of quarks, then the quarks lie in the [fundamental representation](https://en.wikipedia.org/wiki/Fundamental_representation "Fundamental representation"), 3 (called the triplet) of [flavor](https://en.wikipedia.org/wiki/Flavour_\(particle_physics\) "Flavour (particle physics)") [SU(3)](https://en.wikipedia.org/wiki/SU\(3\) "SU(3)"). The antiquarks lie in the complex conjugate representation 3. The nine states (nonet) made out of a pair can be decomposed into the [trivial representation](https://en.wikipedia.org/wiki/Trivial_representation "Trivial representation"), 1 (called the singlet), and the [adjoint representation](https://en.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_group "Adjoint representation of a Lie group"), 8 (called the octet). The notation for this decomposition is ![{\\displaystyle \\mathbf {3} \\otimes \\mathbf {\\overline {3}} =\\mathbf {8} \\oplus \\mathbf {1} ~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac6f83cd866c815a8e296a97b3abd91cde4c78cc) Figure 1 shows the application of this decomposition to the mesons. If the flavor symmetry were exact (as in the limit that only the strong interactions operate, but the electroweak interactions are notionally switched off), then all nine mesons would have the same mass. However, the physical content of the full theory\[[clarification needed](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify "Wikipedia:Please clarify")\] 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). N.B. Nevertheless, the mass splitting between the η and the η′ is larger than the quark model can accommodate, and this "[η–η′ puzzle](https://en.wikipedia.org/wiki/QCD_vacuum#Eta_prime_meson "QCD vacuum")" has its origin in topological peculiarities of the strong interaction vacuum, such as [instanton](https://en.wikipedia.org/wiki/Instanton "Instanton") configurations. Mesons are hadrons with zero [baryon number](https://en.wikipedia.org/wiki/Baryon_number "Baryon number"). If the quark–antiquark pair are in an [orbital angular momentum](https://en.wikipedia.org/wiki/Angular_momentum_operator "Angular momentum operator") L state, and have [spin](https://en.wikipedia.org/wiki/Spin_\(physics\) "Spin (physics)") S, then - \\|L − S\\| ≤ J ≤ L + S, where S = 0 or 1, - P = (−1)L\+1, where the 1 in the exponent arises from the [intrinsic parity](https://en.wikipedia.org/wiki/Intrinsic_parity "Intrinsic parity") of the quark–antiquark pair. - C = (−1)L\+S for mesons which have no [flavor](https://en.wikipedia.org/wiki/Flavour_\(particle_physics\) "Flavour (particle physics)"). Flavored mesons have indefinite value of [C](https://en.wikipedia.org/wiki/C_parity "C parity"). - For [isospin](https://en.wikipedia.org/wiki/Isospin "Isospin") I = 1 and 0 states, one can define a new [multiplicative quantum number](https://en.wikipedia.org/wiki/Multiplicative_quantum_number "Multiplicative quantum number") called the [G-parity](https://en.wikipedia.org/wiki/G-parity "G-parity") such that G = (−1)I\+L\+S. If P = (−1)J, 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 thus called exotic (for example, the state JPC = 0−−). [![](https://upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Baryon_octet.png/250px-Baryon_octet.png)](https://en.wikipedia.org/wiki/File:Baryon_octet.png) Figure 4. The S = ⁠1/2⁠ ground state [baryon](https://en.wikipedia.org/wiki/Baryon "Baryon") octet [![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Baryon_decuplet.png/250px-Baryon_decuplet.png)](https://en.wikipedia.org/wiki/File:Baryon_decuplet.png) Figure 5. The S = ⁠3/2⁠ [baryon](https://en.wikipedia.org/wiki/Baryon "Baryon") decuplet Since quarks are [fermions](https://en.wikipedia.org/wiki/Fermion "Fermion"), the [spin–statistics theorem](https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem "Spin–statistics theorem") implies that the [wavefunction](https://en.wikipedia.org/wiki/Wavefunction "Wavefunction") of a baryon must be antisymmetric under the exchange of any two quarks. This antisymmetric wavefunction is obtained by making it fully antisymmetric in color, discussed below, and symmetric in flavor, spin and space put together. With three flavors, the decomposition in flavor is ![{\\displaystyle \\mathbf {3} \\otimes \\mathbf {3} \\otimes \\mathbf {3} =\\mathbf {10} \_{S}\\oplus \\mathbf {8} \_{M}\\oplus \\mathbf {8} \_{M}\\oplus \\mathbf {1} \_{A}~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efe21e8ee3332d4c573b43eea5321da19262e2c6) The decuplet is symmetric in flavor, 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. It is sometimes useful to think of the [basis states](https://en.wikipedia.org/wiki/Quantum_state#Basis_states_of_one-particle_systems "Quantum state") of quarks as the six states of three flavors and two spins per flavor. This approximate symmetry is called spin-flavor [SU(6)](https://en.wikipedia.org/wiki/SU\(6\) "SU(6)"). In terms of this, the decomposition is ![{\\displaystyle \\mathbf {6} \\otimes \\mathbf {6} \\otimes \\mathbf {6} =\\mathbf {56} \_{S}\\oplus \\mathbf {70} \_{M}\\oplus \\mathbf {70} \_{M}\\oplus \\mathbf {20} \_{A}~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/613eb3fb4d716059f31551e9166f05abe035a79b) The 56 states with symmetric combination of spin and flavour decompose under flavor [SU(3)](https://en.wikipedia.org/wiki/SU\(3\) "SU(3)") into ![{\\displaystyle \\mathbf {56} =\\mathbf {10} ^{\\frac {3}{2}}\\oplus \\mathbf {8} ^{\\frac {1}{2}}~,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6289d9cac1a1b9aceb282456deed0142207abff1) where the superscript denotes the spin, S, of the baryon. Since these states are symmetric in spin and flavor, 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 = ⁠1/2⁠ octet baryons are the two [nucleons](https://en.wikipedia.org/wiki/Nucleon "Nucleon") (p\+ , n0 ), the three [Sigmas](https://en.wikipedia.org/wiki/Sigma_baryon "Sigma baryon") (Σ\+ , Σ0 , Σ− ), the two [Xis](https://en.wikipedia.org/wiki/Xi_baryon "Xi baryon") (Ξ0 , Ξ− ), and the [Lambda](https://en.wikipedia.org/wiki/Lambda_baryon "Lambda baryon") (Λ0 ). The S = ⁠3/2⁠ decuplet baryons are the four [Deltas](https://en.wikipedia.org/wiki/Delta_baryon "Delta baryon") (Δ\++ , Δ\+ , Δ0 , Δ− ), three [Sigmas](https://en.wikipedia.org/wiki/Sigma_baryon "Sigma baryon") (Σ∗+ , Σ∗0 , Σ∗− ), two [Xis](https://en.wikipedia.org/wiki/Xi_baryon "Xi baryon") (Ξ∗0 , Ξ∗− ), and the [Omega](https://en.wikipedia.org/wiki/Omega_particle "Omega particle") (Ω− ). For example, the constituent quark model wavefunction for the proton is ![{\\displaystyle \\|{\\text{p}}\_{\\uparrow }\\rangle ={\\frac {1}{\\sqrt {18}}}\[2\\|{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }\\rangle +2\\|{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\downarrow }\\rangle +2\\|{\\text{d}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }\\rangle -\\|{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }{\\text{d}}\_{\\uparrow }\\rangle -\\|{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }\\rangle -\\|{\\text{u}}\_{\\downarrow }{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }\\rangle -\\|{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }\\rangle -\\|{\\text{d}}\_{\\uparrow }{\\text{u}}\_{\\uparrow }{\\text{u}}\_{\\downarrow }\\rangle -\\|{\\text{u}}\_{\\downarrow }{\\text{u}}\_{\\uparrow }{\\text{d}}\_{\\uparrow }\\rangle \]~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c5d84892af6c62784c12f0b691cd79d4d8584b3a) Mixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other quantities that the model predicts successfully. The group theory approach described above assumes that the quarks are eight components of a single particle, so the anti-symmetrization applies to all the quarks. A simpler approach is to consider the eight flavored quarks as eight separate, distinguishable, non-identical particles. Then the anti-symmetrization applies only to two identical quarks (like uu, for instance).[\[6\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-JF1968-6) Then, the proton wavefunction can be written in a simpler form: ![{\\displaystyle {\\text{p}}\\left({\\frac {1}{2}},{\\frac {1}{2}}\\right)={\\frac {{\\text{u}}{\\text{u}}{\\text{d}}}{\\sqrt {6}}}\[2\\uparrow \\uparrow \\downarrow -\\uparrow \\downarrow \\uparrow -\\downarrow \\uparrow \\uparrow \]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/530602aa73765eab71fa2e8847f9f2764325d62c) and the ![{\\displaystyle \\Delta ^{+}\\left({\\frac {3}{3}},{\\frac {3}{2}}\\right)={\\text{u}}{\\text{u}}{\\text{d}}\[\\uparrow \\uparrow \\uparrow \]~.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/89c6b137d6e75df3c098948d8107f061ceafa1b8) If quark–quark interactions are limited to two-body interactions, then all the successful quark model predictions, including sum rules for baryon masses and magnetic moments, can be derived. Color quantum numbers are the characteristic charges of the strong force, and are completely uninvolved in electroweak interactions. They were discovered as a consequence of the quark model classification, when it was appreciated that the spin S = ⁠3/2⁠ baryon, the Δ\++ , required three up quarks with parallel spins and vanishing orbital angular momentum. Therefore, it could not have an antisymmetric wavefunction, (required by the [Pauli exclusion principle](https://en.wikipedia.org/wiki/Pauli_exclusion_principle "Pauli exclusion principle")). [Oscar Greenberg](https://en.wikipedia.org/wiki/Oscar_Greenberg "Oscar Greenberg") noted this problem in 1964, suggesting that quarks should be [para-fermions](https://en.wikipedia.org/wiki/Para-fermion "Para-fermion").[\[7\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-7) Instead, six months later, [Moo-Young Han](https://en.wikipedia.org/wiki/Moo-Young_Han "Moo-Young Han") and [Yoichiro Nambu](https://en.wikipedia.org/wiki/Yoichiro_Nambu "Yoichiro Nambu") suggested the existence of a hidden degree of freedom, they labeled as the group SU(3)' (but later called 'color). This led to three triplets of quarks whose wavefunction was anti-symmetric in the color degree of freedom. Flavor and color were intertwined in that model: they did not commute.[\[8\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-8) The modern concept of color completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [William Bardeen](https://en.wikipedia.org/wiki/William_A._Bardeen "William A. Bardeen"), [Harald Fritzsch](https://de.wikipedia.org/wiki/Harald_Fritzsch "de:Harald Fritzsch"), and [Murray Gell-Mann](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann").[\[9\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-9)[\[10\]](https://en.wikipedia.org/wiki/Quark_model#cite_note-10) ## States outside the quark model \[[edit](https://en.wikipedia.org/w/index.php?title=Quark_model&action=edit&section=5 "Edit section: States outside the quark model")\] While the quark model is derivable from the theory of [quantum chromodynamics](https://en.wikipedia.org/wiki/Quantum_chromodynamics "Quantum chromodynamics"), the structure of hadrons is more complicated than this model allows. The full [quantum mechanical](https://en.wikipedia.org/wiki/Quantum_mechanics "Quantum mechanics") [wavefunction](https://en.wikipedia.org/wiki/Wavefunction "Wavefunction") of any hadron must include virtual quark pairs as well as virtual [gluons](https://en.wikipedia.org/wiki/Gluon "Gluon"), and allows for a variety of mixings. There may be hadrons which lie outside the quark model. Among these are the [glueballs](https://en.wikipedia.org/wiki/Glueball "Glueball") (which contain only valence gluons), hybrids (which contain valence quarks as well as gluons) and [exotic hadrons](https://en.wikipedia.org/wiki/Exotic_hadron "Exotic hadron") (such as [tetraquarks](https://en.wikipedia.org/wiki/Tetraquark "Tetraquark") or [pentaquarks](https://en.wikipedia.org/wiki/Pentaquark "Pentaquark")). - [Subatomic particles](https://en.wikipedia.org/wiki/Subatomic_particles "Subatomic particles") - [Hadrons](https://en.wikipedia.org/wiki/Hadron "Hadron"), [baryons](https://en.wikipedia.org/wiki/Baryon "Baryon"), [mesons](https://en.wikipedia.org/wiki/Meson "Meson") and [quarks](https://en.wikipedia.org/wiki/Quark "Quark") - [Exotic hadrons](https://en.wikipedia.org/wiki/Exotic_hadron "Exotic hadron"): [exotic mesons](https://en.wikipedia.org/wiki/Exotic_meson "Exotic meson") and [exotic baryons](https://en.wikipedia.org/wiki/Exotic_baryon "Exotic baryon") - [Quantum chromodynamics](https://en.wikipedia.org/wiki/Quantum_chromodynamics "Quantum chromodynamics"), [flavor](https://en.wikipedia.org/wiki/Flavour_\(particle_physics\) "Flavour (particle physics)"), the [QCD vacuum](https://en.wikipedia.org/wiki/QCD_vacuum "QCD vacuum") 1. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-Gell-Man1964_1-0) [Gell-Mann, M.](https://en.wikipedia.org/wiki/Murray_Gell-Mann "Murray Gell-Mann") (4 January 1964). "A Schematic Model of Baryons and Mesons". [Physics Letters](https://en.wikipedia.org/wiki/Physics_Letters "Physics Letters"). 8 (3): 214–215\. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1964PhL.....8..214G](https://ui.adsabs.harvard.edu/abs/1964PhL.....8..214G). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/S0031-9163(64)92001-3](https://doi.org/10.1016%2FS0031-9163%2864%2992001-3). 2. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-Zweig1964a_2-0) [Zweig, G.](https://en.wikipedia.org/wiki/George_Zweig "George Zweig") (17 January 1964). [An SU(3) Model for Strong Interaction Symmetry and its Breaking](https://cds.cern.ch/record/352337/files/CERN-TH-401.pdf) (PDF) (Report). CERN Report No.8182/TH.401. 3. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-Zweig1964b_3-0) [Zweig, G.](https://en.wikipedia.org/wiki/George_Zweig "George Zweig") (1964). [An SU(3) Model for Strong Interaction Symmetry and its Breaking: II](https://cds.cern.ch/record/570209/files/CERN-TH-412.pdf) (PDF) (Report). CERN Report No.8419/TH.412. 4. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-4) [Petermann, A.](https://en.wikipedia.org/wiki/Andr%C3%A9_Petermann "André Petermann") (1965). "Propriétés de l'étrangeté et une formule de masse pour les mésons vectoriels" \[Strangeness properties and a mass formula for vector meson\]. [Nuclear Physics](https://en.wikipedia.org/wiki/Nuclear_Physics_\(journal\) "Nuclear Physics (journal)"). 63 (2): 349–352\. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1412\.8681](https://arxiv.org/abs/1412.8681). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1965NucPh..63..349P](https://ui.adsabs.harvard.edu/abs/1965NucPh..63..349P). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/0029-5582(65)90348-2](https://doi.org/10.1016%2F0029-5582%2865%2990348-2). 5. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-5) Petrov, Vladimir A. (June 23–27, 2014). Half a Century with QUARKS. XXX-th International Workshop on High Energy Physics. [Protvino](https://en.wikipedia.org/wiki/Protvino "Protvino"), [Moscow Oblast](https://en.wikipedia.org/wiki/Moscow_Oblast "Moscow Oblast"), Russia. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[1412\.8681](https://arxiv.org/abs/1412.8681). 6. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-JF1968_6-0) Franklin, J. (1968). "A Model of Baryons Made of Quarks with Hidden Spin". [Physical Review](https://en.wikipedia.org/wiki/Physical_Review "Physical Review"). 172 (3): 1807–1817\. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1968PhRv..172.1807F](https://ui.adsabs.harvard.edu/abs/1968PhRv..172.1807F). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1103/PhysRev.172.1807](https://doi.org/10.1103%2FPhysRev.172.1807). 7. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-7) Greenberg, O.W. (1964). "Spin and unitary-spin independence in a paraquark model of baryons and mesons". [Physical Review Letters](https://en.wikipedia.org/wiki/Physical_Review_Letters "Physical Review Letters"). 13 (20): 598–602\. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1964PhRvL..13..598G](https://ui.adsabs.harvard.edu/abs/1964PhRvL..13..598G). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1103/PhysRevLett.13.598](https://doi.org/10.1103%2FPhysRevLett.13.598). 8. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-8) Han, M.Y.; Nambu, Y. (1965). ["Three-triplet model with double SU(3) symmetry"](https://digital.library.unt.edu/ark:/67531/metadc1031342/). [Physical Review B](https://en.wikipedia.org/wiki/Physical_Review_B "Physical Review B"). 139 (4B): 1006. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1965PhRv..139.1006H](https://ui.adsabs.harvard.edu/abs/1965PhRv..139.1006H). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1103/PhysRev.139.B1006](https://doi.org/10.1103%2FPhysRev.139.B1006). 9. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-9) Bardeen, W.; Fritzsch, H.; Gell-Mann, M. (1973). ["Light cone current algebra, π0 decay, and e\+ e− annihilation"](https://archive.org/details/scaleconformalsy0000unse/page/139). In Gatto, R. (ed.). Scale and conformal symmetry in hadron physics. [John Wiley & Sons](https://en.wikipedia.org/wiki/John_Wiley_%26_Sons "John Wiley & Sons"). p. [139](https://archive.org/details/scaleconformalsy0000unse/page/139). [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[hep-ph/0211388](https://arxiv.org/abs/hep-ph/0211388). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2002hep.ph...11388B](https://ui.adsabs.harvard.edu/abs/2002hep.ph...11388B). [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [0-471-29292-3](https://en.wikipedia.org/wiki/Special:BookSources/0-471-29292-3 "Special:BookSources/0-471-29292-3") . 10. [^](https://en.wikipedia.org/wiki/Quark_model#cite_ref-10) Fritzsch, H.; Gell-Mann, M.; Leutwyler, H. (1973). "Advantages of the color octet gluon picture". [Physics Letters B](https://en.wikipedia.org/wiki/Physics_Letters_B "Physics Letters B"). 47 (4): 365. [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[1973PhLB...47..365F](https://ui.adsabs.harvard.edu/abs/1973PhLB...47..365F). [CiteSeerX](https://en.wikipedia.org/wiki/CiteSeerX_\(identifier\) "CiteSeerX (identifier)") [10\.1.1.453.4712](https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.453.4712). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/0370-2693(73)90625-4](https://doi.org/10.1016%2F0370-2693%2873%2990625-4). - S. Eidelman et al. [Particle Data Group](https://en.wikipedia.org/wiki/Particle_Data_Group "Particle Data Group") (2004). ["Review of Particle Physics"](http://pdg.lbl.gov/2004/reviews/quarkmodrpp.pdf) (PDF). [Physics Letters B](https://en.wikipedia.org/wiki/Physics_Letters_B "Physics Letters B"). 592 (1–4\): 1. [arXiv](https://en.wikipedia.org/wiki/ArXiv_\(identifier\) "ArXiv (identifier)"):[astro-ph/0406663](https://arxiv.org/abs/astro-ph/0406663). [Bibcode](https://en.wikipedia.org/wiki/Bibcode_\(identifier\) "Bibcode (identifier)"):[2004PhLB..592....1P](https://ui.adsabs.harvard.edu/abs/2004PhLB..592....1P). [doi](https://en.wikipedia.org/wiki/Doi_\(identifier\) "Doi (identifier)"):[10\.1016/j.physletb.2004.06.001](https://doi.org/10.1016%2Fj.physletb.2004.06.001). [S2CID](https://en.wikipedia.org/wiki/S2CID_\(identifier\) "S2CID (identifier)") [118588567](https://api.semanticscholar.org/CorpusID:118588567). - Lichtenberg, D B (1970). Unitary Symmetry and Elementary Particles. Academic Press. [ISBN](https://en.wikipedia.org/wiki/ISBN_\(identifier\) "ISBN (identifier)") [978-1483242729](https://en.wikipedia.org/wiki/Special:BookSources/978-1483242729 "Special:BookSources/978-1483242729") . - Thomson, M A (2011), [Lecture notes](http://www.hep.phy.cam.ac.uk/~thomson/partIIIparticles/handouts/Handout_7_2011.pdf) - J.J.J. Kokkedee (1969). [The quark model](https://archive.org/details/quarkmodel0000kokk). [W. A. Benjamin](https://en.wikipedia.org/wiki/W._A._Benjamin "W. A. Benjamin"). [ASIN](https://en.wikipedia.org/wiki/ASIN_\(identifier\) "ASIN (identifier)") [B001RAVDIA](https://www.amazon.com/dp/B001RAVDIA).
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