A widely accepted theory of strong nuclear force in which quarks are bound together by gluons; proposed in 1973; also known as QCD. Quarks interact because of a colour quantity on each in a way analogous to the interaction between charged particles because of the charge on each particle.
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). QCD is a quantum field theory of a special kind called a non-abelian gauge theory.
QCD enjoys two peculiar properties:
asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD. Quark matter: the equations of QCD predict that a sea of quarks and gluons should be formed at high temperature and density.‹The template Unsolved has been proposed for deletion here.›
Terminology
The word quark was coined by Murray Gell-Mann in its present sense, the word having been taken from the phrase "Three quarks for Muster Mark" in Finnegans Wake by James Joyce.
The three kinds of charge in QCD (as opposed to one in Quantum electrodynamics or QED) are usually referred to as "color charge" by loose analogy to the three kinds of color (red, green and blue) perceived by humans. Since the theory of electric charge is dubbed "electrodynamics", the Greek word "chroma" Χρώμα (meaning color) is applied to the theory of color charge, "chromodynamics".
Lagrangian
The gauge invariant QCD Lagrangian is
where is the quark field, are the Dirac matrices, are the 8 gauge fields, and are related to the Gell-Mann matrices.History
With the invention of bubble chambers and spark chambers in the 1950s, experimental particle physics discovered a large and ever-growing number of particles called hadrons. Gell-Mann and George Zweig went on to propose in 1963 that the structure of the groups could be explained by the existence of three flavors of smaller particles inside the hadrons: the quarks.
At this stage, one particle, the Δ++ remained mysterious; in the quark model, it is composed of three up quarks with parallel spins. Greenberg independently resolved the problem by proposing that quarks possess an additional SU(3) gauge degree of freedom, later called color charge. Han and Nambu noted that quarks would interact via an octet of vector gauge bosons: the gluons.
Since free quark searches consistently failed to turn up any evidence for the new particles, it was then believed that quarks were merely convenient mathematical constructs, not real particles. Richard Feynman argued that high energy experiments showed quarks to be real: he called them partons (since they were parts of hadrons).
Although the study of the strong interaction remained daunting, the discovery of asymptotic freedom by David Gross, David Politzer and Frank Wilczek allowed people to make precise predictions of the results of many high energy experiments using the techniques of perturbation theory.
The other side of asymptotic freedom is confinement. Since the force between color charges does not decrease with distance, it is believed that quarks and gluons can never be liberated from hadrons. Other aspects of non-perturbative QCD are the exploration of phases of quark matter, including the quark-gluon plasma.
The theory
Some definitions
Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations.
QCD is a gauge theory of the SU(3) gauge group obtained by taking the color charge to define a local symmetry.
Since the strong interaction does not discriminate between different flavors of quark, QCD has approximate flavor symmetry, which is broken by the differing masses of the quarks.
There are additional global symmetries whose definitions require the notion of chirality, discrimination between left and right-handed.
The symmetry groups
The color group SU(3) corresponds to the local symmetry whose gauging gives rise to QCD. If one considers a version of QCD with Nf flavors of massless quarks, then there is a global (chiral) flavor symmetry group . The chiral symmetry is spontaneously broken by the QCD vacuum to the vector (L+R) SUV(Nf) with the formation of a chiral condensate. The vector symmetry, UB(1) corresponds to the baryon number of quarks and is an exact symmetry.
Cautionary note
In many applications of QCD one can ignore the heavy flavors of quark (charm, bottom and top). In QCD the color group belongs to a local symmetry and hence is gauged. The Eightfold way is based on the flavor group and ignores the local symmetry which gives QCD.
The fields
Quarks are massive spin-1/2 fermions which carry a color charge whose gauging is the content of QCD. Quarks are represented by Dirac fields in the fundamental representation 3 of the gauge group SU(3). They carry global quantum numbers including the baryon number, which is 1/3 for each quark, hypercharge and one of the flavor quantum numbers.
Gluons are spin-1 bosons which also carry color charges, since they lie in the adjoint representation 8 of SU(3).
Every quark has its own antiquark. The charge of each antiquark is exactly the opposite of the corresponding quark.
The dynamics
According to the rules of quantum field theory, and the associated Feynman diagrams, the above theory gives rise to three basic interactions: a quark may emit (or absorb) a gluon, a gluon may emit (or absorb) a gluon, and two gluons may directly interact.
Methods
Further analysis of the content of the theory is complicated.
Perturbative QCD
This approach is based on asymptotic freedom, which allows perturbation theory to be used accurately in experiments performed at very high energies.
Lattice QCD
Among non-perturbative approaches to QCD, the most well established one is lattice QCD.
1/N expansion
A well-known approximation scheme, the 1/N expansion, starts from the premise that the number of colors is infinite, and makes a series of corrections to account for the fact that it is not.
Effective theories
For specific problems some theories may be written down which seem to give qualitatively correct results. Among the best such effective models one should now count chiral perturbation theory (which expands around light quark masses near zero) and heavy quark effective theory (which expands around heavy quark mass near infinity).
Experimental tests
The notion of quark flavours was prompted by the necessity of explaining the properties of hadrons during the development of the quark model.
The first evidence for quarks as real constiutent elements of hadrons was obtained in deep inelastic scattering experiments at SLAC.
Good quantitative tests of perturbative QCD are
the running of the QCD coupling as deduced from many observations scaling violation in polarized and unpolarized deep inelastic scattering vector boson production at colliders (this includes the Drell-Yan process) jet cross sections in colliders event shape observables at the LEP heavy-quark production in collidersQuantitative tests of non-perturbative QCD are fewer, because the predictions are harder to make. The whole subject of quark matter and the quark-gluon plasma is a non-perturbative test bed for QCD which still remains to be properly exploited.
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