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Encyclopedia > Quark model

In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, i.e., the 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 Poincare symmetryJPC(m) (where J is the angular momentum, P, the intrinsic parity, and C the charge conjugation parity). The remainder are flavour quantum numbers such as the isospin, 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). This is a discussion of a present category of science. ... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... The six flavours of quarks and their most likely decay modes. ... Quantum numbers describe values of conserved quantity in the dynamics of the quantum system. ... Poincare symmetry is the full symmetry of special relativity and includes translations (ie, displacements) in time and space (these form the Abelian Lie group of translations on space-time) rotations in space (this forms the non-Abelian Lie group of 3-dimensional rotations) boosts, ie, transformations connecting two uniformly moving... This gyroscope remains upright while spinning due to its angular momentum. ... In physics, in particular quantum mechanics, the intrinsic parity is a phase factor that arises as an eigenvalue of the parity operation (a reflection about the origin). ... C-symmetry means the symmetry of physical laws over a charge-inversion transformation. ... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... Isospin (isotopic spin, isobaric spin) is a physical quantity which is mathematically analogous to spin. ... In physics, the Eightfold Way is a term coined by American physicist Murray Gell-Mann for a theory for organizing microscopical particles like quarks and hadrons. ... The Dharma wheel, often used to represent the Noble Eightfold Path The Noble Eightfold Path (Pāli: Ariyo aṭṭhaṅgiko maggo; Sanskrit: Ārya ṣṭāṅga mārgaḥ; Chinese: 八正道, Bāzhèngdào; Japanese: 八正道, Hasshōdō, Thai: อริยมรรคแปด, Ariya Mugg Paad, Mongolian qutuɣtan-u naiman gesigün-ü mör) is, in...


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. Mesons are made of a valence quark-antiquark pair, and hence have baryon number zero. Baryons are made of three quarks and hence have unit baryon number. This article discusses the quark model for SU(3) flavour, which involves the u, d and s quarks. There are generalizations to larger number of flavours. In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... In particle physics, the baryon number is an approximate conserved quantum number. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Mesons of spin 1 form a nonet In particle physics, a meson is a strongly interacting boson, that is, it is a hadron with integral spin. ... Combinations of three u, d or s-quarks with a total spin of 3/2 form the so-called baryon decuplet. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ...

Figure 1: The pseudoscalar meson nonet. Members of the octet are shown in green, the singlet in magenta. The name eightfold way derives from this classification.
Figure 1: The pseudoscalar meson nonet. Members of the octet are shown in green, the singlet in magenta. The name eightfold way derives from this classification.

Contents

Picture of the pseudoscalar meson nonet. ... Picture of the pseudoscalar meson nonet. ...

History

Developing classification schemes for hadrons became a burning question after new experimental techniques uncovered so many of them that it became clear that they could not all be elementary. These discoveries led Enrico Fermi to exclaim "Had I foreseen that, I would have gone into botany" (sometimes quoted as saying to Leon 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 physicist Luis Alvarez who was at the forefront of many of these developments. Several early proposals, such as the one by Shoichi Sakata, were unable to explain all the data. A version developed by Moo-Young Han and Yoichiro Nambu was also eventually found untenable. The quark model in its modern form was developed by Murray Gell-Mann and Kazuhiko Nishijima. The model received important contributions from Yuval Ne'eman and George Zweig. The spin S=3/2, Ω- baryon, a member of the ground state decuplet, was a prediction of the model, which was eventually discovered in an experiment at Brookhaven National Laboratory. Gell-Mann received a Nobel prize for his work on the quark model. Image File history File links Mergefrom. ... In physics, the Eightfold Way is a term coined by American physicist Murray Gell-Mann for a theory for organizing microscopical particles like quarks and hadrons. ... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... Enrico Fermi (September 29, 1901 – November 28, 1954) was an Italian physicist most noted for his work on the development of the first nuclear reactor, and for his contributions to the development of quantum theory, particle physics and statistical mechanics. ... Leon Max Lederman (born July 15, 1922) is an American experimental physicist who was awarded the Nobel Prize in Physics in 1988 for his work on neutrinos. ... Portrait of Luis Alvarez Luis Walter Alvarez (June 13, 1911 – September 1, 1988) of San Francisco, California, USA, was a famed physicist of Spanish descent, who worked at the University of California, Berkeley. ... Dr. Moo-Young Han (1934- ) is a professor of physics at Duke University. ... Yoichiro Nambu (1921–) is a Japanese-born American physicist. ... Murray Gell-Mann (born September 15, 1929 in Manhattan, New York City, USA) is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. ... Yuval Neeman (May 14, 1925 – April 26, 2006), was an Israeli physicist and politician. ... George Zweig was originally trained as a particle physicist under Richard Feynman and later turned his attention to neurobiology. ... ≠ Aerial view of Brookhaven National Laboratory. ...


Mesons

See also: Meson.
Mesons of spin 0 form a nonet
Mesons of spin 0 form a nonet
Mesons of spin 1 form a nonet
Mesons of spin 1 form a nonet

The eightfold way classification is named after the following fact. If we take three flavours of quarks, then the quarks lie in the fundamental representation, 3 (called the triplet) of flavour 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 Mesons of spin 1 form a nonet In particle physics, a meson is a strongly interacting boson, that is, it is a hadron with integral spin. ... Image File history File links Download high resolution version (909x655, 69 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): List of particles List of mesons ... Image File history File links Download high resolution version (909x655, 69 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): List of particles List of mesons ... Image File history File links Download high-resolution version (1000x721, 79 KB) Noneto mesônico de spin 1. ... Image File history File links Download high-resolution version (1000x721, 79 KB) Noneto mesônico de spin 1. ... In mathematics, a fundamental representation is a representation of a mathematical structure, such as a group, that satisfies the following condition: All other irreducible representations of the group can be found in the tensor products of the fundamental representation with many copies of itself. ... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... In mathematics, in particular group representation theory, a group representation of the group G is called a trivial representation if (i) it is defined on a one-dimensional vector space V over a field K and (ii) all elements g of G act on V as the identity mapping. ... In mathematics, the adjoint representation (or adjoint action) of a Lie group G is the natural representation of G on its own Lie algebra. ...

3 ⊗ 3*  =  8 + 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 by instantons (see the article on the QCD vacuum). This article or section is in need of attention from an expert on the subject. ... The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). ...


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 In particle physics, the baryon number is an approximate conserved quantum number. ... The Azimuthal quantum number (or orbital angular momentum quantum number) l is a quantum number for an atomic orbital which determines its orbital angular momentum. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ...

  • |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 antiquark.
  • C = (-1)L+S for mesons which have no flavour. Flavoured mesons have indefinite value of C.
  • For isospin I = 1 and 0 states, one can define a new multiplicative quantum number called G parity such that G = (-1)I+L+S.

Clearly, if P = (-1)J, (called natural parity states) then S = 1, and hence PC = 1. All other quantum numbers are called exotic, as is the state 0--. A List of mesons is available. Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... Isospin (isotopic spin, isobaric spin) is a physical quantity which is mathematically analogous to spin. ... In quantum field theory, multiplicative quantum numbers are conserved quantum numbers of a special kind. ... In theoretical physics, G-parity is a multiplicative quantum number that results from the generalization of C-parity to multiplets of particles. ... A list of mesons. ...

Baryons

Figure 2. The S=1/2 ground state baryon octet
Figure 2. The S=1/2 ground state baryon octet
Figure 3. The S=3/2 baryon decuplet
Figure 3. 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 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 File links The following pages link to this file: Eightfold way (physics) Quark model Categories: GFDL images ... File links The following pages link to this file: Eightfold way (physics) Quark model Categories: GFDL images ... Created using LaTeX. See talk page for more information. ... Created using LaTeX. See talk page for more information. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... The spin-statistics theorem in quantum mechanics relates the spin of a particle to the statistics obeyed by that particle. ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ...

3 ⊗ 3 ⊗ 3 = 10S + 8M + 8M + 1A.

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 A quantum state is any possible state in which a quantum mechanical system can be. ... In mathematics, the special unitary group of degree n, denoted SU(n), is the group of n×n unitary matrices with unit determinant. ...

6 ⊗ 6 ⊗ 6 = 56S + 70M + 70M + 20A.

The 56 states with symmetric combination of spin and flavour decompose under flavour SU(3) into In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ...

56 = 103/2 + 81/2

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, Σ0,±, Ξ0,-, Λ. The S=3/2 decuplet baryons are Δ0,±,++, Σ0,±, Ξ0,-, Ω-. Mixing of baryons, mass splittings within and between multiplets, and magnetic moments are some of the other questions that the model deals with.


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 the Pauli exclusion principle). Oscar Greenberg noted this problem, and suggested in a paper written in 1964 that quarks should be para-fermions. Six months later Moo-Young Han and Yoichiro Nambu suggested the existence of 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 and Murray Gell-Mann, which appeared in the proceedings of a conference in Frascati (ISBN 0-471-29292-3). The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... Oscar Wallace Greenberg is an American physicist and professor at University of Maryland, College Park. ... In quantum mechanics, despite what many textbooks and articles erronously claim, the Bose-Einstein and Fermi-Dirac statistics (and Maxwell-Boltzmann statistics) are not the only alternatives. ... Dr. Moo-Young Han (1934- ) is a professor of physics at Duke University. ... Yoichiro Nambu (1921–) is a Japanese-born American physicist. ... Murray Gell-Mann (born September 15, 1929 in Manhattan, New York City, USA) is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...


States 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 full wavefunction 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 multiquark states (such as the tetraquark mesons which contain two quark-antiquark pairs as valence particles, or the 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)J and PC=-1), or normal. For more on these states see the article on exotic hadrons. Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ... A pentaquark is a subatomic particle consisting of a group of five quarks (compared to three quarks in normal baryons and two in mesons), or more specifically four quarks and one anti-quark. ... A regular meson made from a quark (q) and antiquark (q-bar) with spins s2 and s1 respectively and having an overall angular momentum L Exotic hadrons are subatomic particles made of quarks (and possibly gluons), but which do not fit into the usual schema of hadrons. ...


See also

Helium atom (not to scale) Showing two protons (red), two neutrons (green) and a probability cloud (gray) of two electrons (yellow). ... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... Combinations of three u, d or s-quarks with a total spin of 3/2 form the so-called baryon decuplet. ... Mesons of spin 1 form a nonet In particle physics, a meson is a strongly interacting boson, that is, it is a hadron with integral spin. ... The six flavours of quarks and their most likely decay modes. ... A regular meson made from a quark (q) and antiquark (q-bar) with spins s2 and s1 respectively and having an overall angular momentum L Exotic hadrons are subatomic particles made of quarks (and possibly gluons), but which do not fit into the usual schema of hadrons. ... Identities and classification of possible tetraquark mesons. ... Ordinary baryons are bound states of 3 quarks. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). ...

References and external links


  Results from FactBites:
 
Quark - MSN Encarta (1524 words)
Unlike other elementary particles, quarks have electric charges that are a fraction of the standard charge—that is, the charge (e) of one proton.
A particle containing the charm quark, the second-generation partner of the strange quark, was discovered at the Stanford Linear Accelerator and at the Brookhaven National Laboratory in Brookhaven, New York, in 1974.
The long-awaited discovery of the top quark filled a hole in the standard model, a theory that physicists had developed to explain particles and their interactions.
Quark - Printer-friendly - MSN Encarta (1524 words)
Quarks never occur alone; they always are found in combination with other quarks in larger particles of matter.
The up and down quarks belong to the first generation, the charm and strange belong to the second generation, and the top and bottom belong to the third generation.
The color charges of the quarks in a baryon are all different and add up to 0, or white, making the baryon “colorless.” The color charges of the quark and antiquark in a meson are complementary and also add up to 0 (white), making the meson colorless.
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