- Quark model
In

physics , the**quark model**is a classification scheme forhadron s in terms of their**valence quarks**, i.e., thequark s (and antiquarks) which give rise to thequantum number s of the hadrons. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from thePoincaré symmetry —**J**(where^{PC}(m)**J**is theangular momentum ,**P**, theintrinsic parity , and**C**thecharge conjugation parity). The remainder are flavour quantum numbers such as theisospin ,**I**. When three flavours of quarks are taken into account, the quark model is also known as the eightfold way, after the meson octet of the figure below (with an allusion to the eightfold way of buddhism).The quark model uses the standard assignment of quantum numbers to quarks — spin 1/2,

baryon number 1/3,electric charge 2/3 for the u quark and -1/3 for the d and s. Antiquarks have the opposite quantum numbers.Meson s are made of a valence quark-antiquark pair, and hence have baryon number zero.Baryon s are made of three quarks and hence have unit baryon number. This article discusses the quark model forSU(3) flavour, which involves the u, d and s quarks. There are generalizations to larger number of flavours.**History**Developing classification schemes for

hadron s became a burning question after new experimental techniques uncovered so many of them that it became clear that they could not all be elementary. These discoveries ledWolfgang Pauli to exclaim "Had I foreseen that, I would have gone into botany" (sometimes quoted as saying toLeon Lederman : "Young man, if I could remember the names of these particles, I would have been a botanist"), but brought a Nobel prize for the experimental particle physicistLuis Alvarez who was at the forefront of many of these developments. Several early proposals, such as the one byShoichi Sakata , were unable to explain all the data. A version developed byMoo-Young Han andYoichiro Nambu was also eventually found untenable. The quark model in its modern form was developed byMurray Gell-Mann andKazuhiko Nishijima . The model received important contributions fromYuval Ne'eman andGeorge Zweig . The spin 3/2 Ω^{-}baryon, a member of the ground state decuplet, was a prediction of the model, which was eventually discovered in an experiment atBrookhaven National Laboratory . Gell-Mann received a Nobel prize for his work on the quark model.**Mesons**The

**eightfold way**classification is named after the following fact. If we take three flavours of quarks, then the quarks lie in thefundamental representation ,**3**(called the triplet) of flavourSU(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 theadjoint representation ,**8**(called the octet). The notation for this decomposition is:$mathbf\{3\}otimes\; mathbf\{3\}^*\; =\; mathbf\{8\}\; oplus\; mathbf\{1\}$.Figure 1 shows the application of this decomposition to the mesons. If the flavour symmetry were exact, then all nine mesons would have the same mass. The physical content of the theory includes consideration of the symmetry breaking induced by the quark mass differences, and considerations of mixing between various multiplets (such as the octet and the singlet). The splitting between the η and the η' is larger than the quark model can accommodate — a fact called the η-η' puzzle. This is resolved byinstanton s (see the article on theQCD vacuum ).Mesons are hadrons with zero

baryon number . If the quark-antiquark pair are in anorbital angular momentum **L**state, and have spin**S**, then

***|L-S| ≤ J ≤ L+S**, where**S = 0**or 1.

***P = (-1)**, where the "1" in the exponent arises from the intrinsic parity of the antiquark.^{L+1}

***C = (-1)**for mesons which have no flavour. Flavoured mesons have indefinite value of^{L+S}**C**.

*Forisospin **I = 1**and 0 states, one can define a newmultiplicative quantum number calledsuch thatG parity **G = (-1)**.Clearly, if^{I+L+S}**P = (-1)**, (called "natural parity states") then^{J}**S = 1**, and hence**PC = 1**. All other quantum numbers are called**exotic**, as is the state**0**. A^{--}List of mesons is available.**Baryons**Since quarks are

fermion s, thespin-statistics theorem implies that thewavefunction of a baryon must be antisymmetric under exchange of quarks. This antisymmetric wavefunction is obtained by making it fully antisymmetric in colour and symmetric in flavour, spin and space put together. With three flavours, the decomposition in flavour is:$mathbf\{3\}otimesmathbf\{3\}otimesmathbf\{3\}=mathbf\{10\}\_Soplusmathbf\{8\}\_Moplusmathbf\{8\}\_Moplusmathbf\{1\}\_A$.The decuplet is symmetric in flavour, the singlet antisymmetric and the two octets have mixed symmetry. The space and spin parts of the states are thereby fixed once the orbital angular momentum is given.It is sometimes useful to think of the basis states of quarks as the six states of three flavours and two spins per flavour. This approximate symmetry is called spin-flavour

SU(6) . In terms of this, the decomposition is::$mathbf\{6\}otimesmathbf\{6\}otimesmathbf\{6\}=mathbf\{56\}\_Soplusmathbf\{70\}\_Moplusmathbf\{70\}\_Moplusmathbf\{20\}\_A$The 56 states with symmetric combination of spin and flavour decompose under flavour

SU(3) into::$mathbf\{56\}=mathbf\{10\}^frac\{3\}\{2\}oplusmathbf\{8\}^frac\{1\}\{2\}$where the superscript denotes the spin,

**S**, of the baryon. Since these states are symmetric in spin and flavour, they should also be symmetric in space — a condition that is easily satisfied by making the orbital angular momentum**L=0**. These are the ground state baryons. The**S=1/2****octet baryons**are**n, p, Σ**. The^{0,±}, Ξ^{0,-}, Λ**S=3/2****decuplet baryons**are**Δ**. Mixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other questions that the model deals with.^{0,±,++}, Σ^{0,±}, Ξ^{0,-}, Ω^{-}**The discovery of colour**Colour quantum numbers have been used from the beginning. However, colour was discovered as a consequence of this classification when it was realized that the spin

**S=3/2**baryon, the Δ^{++}required three u quarks with parallel spins and vanishing orbital angular momentum, and therefore could not have an antisymmetric wavefunction unless there was a hidden quantum number (due to thePauli exclusion principle ).Oscar Greenberg noted this problem, and suggested in a [*http://prola.aps.org/abstract/PRL/v13/i20/p598_1 paper written in 1964*] that quarks should bepara-fermion s. Six months laterMoo-Young Han andYoichiro Nambu suggested the existence of [*http://prola.aps.org/abstract/PR/v139/i4B/pB1006_1 three triplets of quarks*] to solve this problem. The concept of colour was definitely established in the 1973 article written jointly by William Bardeen,Harald Fritzsch andMurray Gell-Mann ,which appeared in the proceedings of a conference inFrascati (ISBN 0-471-29292-3).**tates outside the quark model**Now that the quark model is understood to be derivable from

quantum chromodynamics , one understands that the structure of hadrons is more complicated than is revealed in this model. The fullwavefunction of any hadron must include virtual quark pairs as well as virtual gluons. Also, 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(such as the tetraquark mesons which contain two quark-antiquark pairs as valence particles, or themultiquark states pentaquark baryon which contains four quarks and an antiquark in the valence). These may be**exotic**, in that the quantum numbers cannot be found in the quark models (such as mesons with**P=(-1)**and^{J}**PC=-1**), or normal. For more on these states see the article onexotic hadron s.**ee also***

Subatomic particles

*Hadron s,baryon s,meson s andquark s

*Exotic hadron s:exotic meson s andexotic baryon s

*Quantum chromodynamics , flavour, theQCD vacuum **References and external links***"Lie algebras in particle physics"; Howard Georgi. ISBN 0-7382-0233-9

*"The quark model"; J.J.J. Kokkedee.

* [*http://pdg.lbl.gov/2004/reviews/quarkmodrpp.pdf Particle data group: the quark model*] ; S. Eidelman et al, "Physics Letters B 592", 2004, p 1

* [*http://35.9.69.219/home/modules/pdf_modules/m282.pdf MISN-0-282: "SU(3) and the quark model"*] (PDF file) by J. Richard Christman for [*http://www.physnet.org Project PHYSNET*] .

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**quark model**— kvarkinis modelis statusas T sritis fizika atitikmenys: angl. quark model vok. Quarkmodell, n rus. кварковая модель, f; модель кварков, f pranc. modèle des quarks, m … Fizikos terminų žodynas**quark model**— Physics. a scheme that explains the quantum numbers of all the baryons and mesons by assuming that baryons are composed of three quarks and mesons of a quark and an antiquark, with different combinations of quark and antiquark flavors giving… … Universalium**quark model**— Physics. a scheme that explains the quantum numbers of all the baryons and mesons by assuming that baryons are composed of three quarks and mesons of a quark and an antiquark, with different combinations of quark and antiquark flavors giving… … Useful english dictionary**Quark**— In physics, a quark (IPAEng|kwɔrk, IPAEng|kwɑːk or IPAEng|kwɑːrk) is a type of subatomic particle. [cite web |title=Fundamental Particles |publisher=Oxford Physics |url=http://www.physics.ox.ac.uk/documents/pUS/dIS/fundam.htm |accessdate=2008 06… … Wikipedia**quark**— /kwawrk, kwahrk/, n. Physics. any of the hypothetical particles with spin 1/2, baryon number 1/3, and electric charge 1/3 or 2/3 that, together with their antiparticles, are believed to constitute all the elementary particles classed as baryons… … Universalium**Quark–gluon plasma**— A QGP is formed at the collision point of two relativistically accelerated gold ions in the center of the STAR detector at the relativistic heavy ion collider at the Brookhaven national laboratory. A quark–gluon plasma … Wikipedia**Quark**— Pour les articles homonymes, voir Quark (homonymie). Quarks Propriétés générales Classification Fermions Composition Élémentaire Propriétés physiques Masse … Wikipédia en Français**Quark Express**— QuarkXPress Entwickler: Quark Inc. Aktuelle Version: 8.02 (Mac), 8.02 (Win) (Januar 2009) Betriebssystem: Mac OS X (10.4.x, 10.5.x), Windows XP, Windows Vista … Deutsch Wikipedia**Quark XPress**— QuarkXPress Entwickler: Quark Inc. Aktuelle Version: 8.02 (Mac), 8.02 (Win) (Januar 2009) Betriebssystem: Mac OS X (10.4.x, 10.5.x), Windows XP, Windows Vista … Deutsch Wikipedia**Quark Xpress**— QuarkXPress Entwickler: Quark Inc. Aktuelle Version: 8.02 (Mac), 8.02 (Win) (Januar 2009) Betriebssystem: Mac OS X (10.4.x, 10.5.x), Windows XP, Windows Vista … Deutsch Wikipedia