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In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, i. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Particle physics, a hadron ( from the ἁδρός hadrós, " stout, thick " ( e. , the quarks (and antiquarks) which give rise to the quantum numbers of the hadrons. In Physics, a quark (kwɔrk kwɑːk or kwɑːrk is a type of Subatomic particle. Quantum numbers describe values of conserved numbers in the dynamics of the Quantum system. These quantum numbers are labels identifying the hadrons, and are of two kinds. One set comes from the Poincare symmetry — JPC(m) (where J is the angular momentum, P, the intrinsic parity, and C the charge conjugation parity). In Physics and Mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. In Physics, C-symmetry means the symmetry of physical laws under a charge -conjugation transformation. The remainder are flavour quantum numbers such as the isospin, I. In Particle physics, flavour or flavor (see spelling differences) is a Quantum number of Elementary particles related to their In Physics, and specifically Particle physics, isospin ( isotopic spin, isobaric spin) is a Quantum number related to the 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). In Physics, the Eightfold Way is a term coined by American Physicist Murray Gell-Mann for a theory organizing subatomic Baryons

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. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin In Particle physics, the baryon number is an approximate conserved Quantum number of a system Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Antiquarks have the opposite quantum numbers. Mesons are made of a valence quark-antiquark pair, and hence have baryon number zero. In Particle physics, a meson is a strongly interacting Boson &mdashthat is a Hadron with integer spin. Baryons are made of three quarks and hence have unit baryon number. Baryons are the family of Subatomic particles with a Baryon number of 1 This article discusses the quark model for SU(3) flavour, which involves the u, d and s quarks. Special Unit 2In Mathematics, the special unitary group of degree n, denoted SU( n) is the group of n × n There are generalizations to larger number of flavours.

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

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. In Particle physics, a hadron ( from the ἁδρός hadrós, " stout, thick " ( These discoveries led Wolfgang Pauli 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. Leon Max Lederman (born July 15, 1922) is an American Experimental physicist and Nobel Prize in Physics laureate for Luis W Alvarez (June 13 1911 San Francisco California &ndash September 1 1988 was an American physicist and Inventor, who spent nearly 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. Dr Moo-Young Han (born 1934 is a professor of physics at Duke University. is a Japan -born American Physicist, currently a Professor at the University of Chicago. The quark model in its modern form was developed by Murray Gell-Mann and Kazuhiko Nishijima. Murray Gell-Mann (born September 15, 1929) is an American Physicist who received the 1969 Nobel Prize in physics for his work The model received important contributions from Yuval Ne'eman and George Zweig. Yuval Ne'eman (יובל נאמן born 14 May 1925, died 26 April 2006) was an Israeli Soldier, physicist George Zweig (born 1937 in Moscow Russia into a Jewish family was originally trained as a Particle physicist under Richard Feynman and later turned his attention 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. Brookhaven National Laboratory ( BNL) is a United States national laboratory located in Upton New York on Long Island, and was formally established Gell-Mann received a Nobel prize for his work on the quark model.

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. In Particle physics, a meson is a strongly interacting Boson &mdashthat is a Hadron with integer spin. If we take three flavours of quarks, then the quarks lie in the fundamental representation, 3 (called the triplet) of flavour SU(3). In Representation theory of Lie groups and Lie algebras a fundamental representation is an irreducible finite-dimensional representation of a semisimple In Particle physics, flavour or flavor (see spelling differences) is a Quantum number of Elementary particles related to their Special Unit 2In Mathematics, the special unitary group of degree n, denoted SU( n) is the group of n × n 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). In the mathematical field of Representation theory, a trivial representation is a representation ( V, &phi) of a group In Mathematics, the adjoint representation (or adjoint action) of a Lie group G is the natural representation of G on its 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 by instantons (see the article on the QCD vacuum). An instanton or pseudoparticle is a notion appearing in theoretical and Mathematical physics. The QCD vacuum is the Vacuum state of Quantum chromodynamics (QCD

Mesons are hadrons with zero baryon number. In Particle physics, the baryon number is an approximate conserved Quantum number of a system If the quark-antiquark pair are in an orbital angular momentum L state, and have spin S, then

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. This is a list of known and predicted Mesons. Mesons are made of Quarks and as such are part of the Subatomic particle family called the Hadrons

Baryons

See also: Baryon
Figure 2. The S=1/2 ground state baryon octet
Figure 2. Baryons are the family of Subatomic particles with a Baryon number of 1 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. In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. The spin-statistics theorem in Quantum mechanics relates the spin of a particle to the statistics obeyed by that particle A wave function or wavefunction is a mathematical tool used in Quantum mechanics to describe any physical system 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}\otimes\mathbf{3}\otimes\mathbf{3}=\mathbf{10}_S\oplus\mathbf{8}_M\oplus\mathbf{8}_M\oplus\mathbf{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. In Quantum physics, a quantum state is a mathematical object that fully describes a quantum system. This approximate symmetry is called spin-flavour SU(6). Special Unit 2In Mathematics, the special unitary group of degree n, denoted SU( n) is the group of n × n In terms of this, the decomposition is

\mathbf{6}\otimes\mathbf{6}\otimes\mathbf{6}=\mathbf{56}_S\oplus\mathbf{70}_M\oplus\mathbf{70}_M\oplus\mathbf{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}\oplus\mathbf{8}^\frac{1}{2}

where the superscript denotes the spin, S, of the baryon. Special Unit 2In Mathematics, the special unitary group of degree n, denoted SU( n) is the group of n × n 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). The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925 Oscar Greenberg noted this problem, and suggested in a paper written in 1964 that quarks should be para-fermions. Oscar Wallace Greenberg is an American Physicist and professor at University of Maryland College Park. In Quantum mechanics and Statistical mechanics, parastatistics is one of several alternatives to the better known Particle statistics models ( Six months later Moo-Young Han and Yoichiro Nambu suggested the existence of three triplets of quarks to solve this problem. Dr Moo-Young Han (born 1934 is a professor of physics at Duke University. is a Japan -born American Physicist, currently a Professor at the University of Chicago. 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). Murray Gell-Mann (born September 15, 1929) is an American Physicist who received the 1969 Nobel Prize in physics for his work Frascati is a town and commune in the Province of Rome in the Latium region of central Italy.

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. Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the The full wavefunction of any hadron must include virtual quark pairs as well as virtual gluons. A wave function or wavefunction is a mathematical tool used in Quantum mechanics to describe any physical system 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). A pentaquark is an hypothetical subatomic particle consisting of a group of five Quarks (compared to three quarks in normal Baryons and two in Mesons, or 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. Exotic Hadrons are Subatomic particles made of Quarks (and possibly Gluons) but which do not fit into the usual schema of hadrons

See also

References and external links

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