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QCD enjoys two peculiar properties:
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". HISTORY With the invention of s. At this stage, one particle, the Δ++ remained mysterious; in the quark model, it is composed of three up quarks with parallel spins. However, since quarks are s. 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. proposed that certain relations should then hold in Deep Inelastic Scattering of Electron s and protons, which were spectacularly verified in experiments at SLAC in 1969 . 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 (quantum Mechanics) . Evidence of Gluon s was discovered in Three Jet Event s at PETRA in 1979. These experiments became more and more precise, culminating in the verification of Perturbative QCD at the level of a few percent at the LEP in CERN . 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 . This aspect of the theory is verified within Lattice QCD computations, but is not mathematically proven. One of the ''Millennium Prizes'' announced by the Clay Mathematics Institute requires a claimant to produce such a proof. 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. These can be
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. If the Spin of a particle has a positive Projection on its direction of motion then it is called left-handed; otherwise, it is right-handed.
The symmetry groups The color group SU(3) corresponds to the local symmetry whose gauging gives rise to QCD. The electric charge labels a representation of the local symmetry group U(1) which is gauged to give group. 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) with the formation of a Chiral Condensate . The vector symmetry, corresponds to the baryon number of quarks and is an exact symmetry. The axial symmetry is exact in the classical theory, but broken in the quantum theory, an occurrence called an Anomaly . Gluon field configurations called Instanton s are closely related to this anomaly. Cautionary note In many applications of QCD one can ignore the heavy flavors of quark (charm, bottom and top). In this case the effective flavor group is often SU(3), which should not be confused with the color group. In QCD the color group belongs to a local symmetry and hence is gauged. The flavor group is not gauged. The Eightfold way is based on the flavor group and ignores the local symmetry which gives QCD. The fields '' Quark s'' are massive spin-1/2 Fermion s which carry a Color Charge whose gauging is the content of QCD. Quarks are represented by Dirac Field s in the Fundamental Representation 3 of the Gauge Group SU(3) . They also carry electric charge (either -1/3 or 2/3) and participate in Weak Interactions as part of isospin doublets. They carry global quantum numbers including the Baryon Number , which is 1/3 for each quark, Hypercharge and one of the Flavor Quantum Numbers . '' Gluon s'' are spin-1 Boson s which also carry Color Charge s, since they lie in the Adjoint Representation 8 of SU(3) . They have no electric charge, do not participate in the weak interactions, and have no flavor. They lie in the Singlet Representation '''1''' of all these symmetry groups. Every quark has its own antiquark. The charge of each antiquark is exactly the opposite of the corresponding quark. QCD The Lagrangian of QCD (with color, flavor and spin indices suppressed) looks exactly like that of QED : : where F denotes the gluon field tensor, ψ the quark field and D the covariant derivative. Part of its content lies in the Feynman Rules which state that all processes which occur in the theory can be resolved into the elementary interactions (called vertices): ''qqg'', ''ggg'' and ''gggg''. A quark may emit (or absorb) a gluon, a gluon may emit (or absorb) a gluon, and two gluons may directly interact. In QED, only the first kind of vertex occurs, since photons have no charge. METHODS Further analysis of the content of the theory is complicated. Various techniques have been developed to work with QCD. Some of them are discussed briefly below. Perturbative QCD This approach is based on asymptotic freedom, which allows Perturbation Theory to be used accurately in experiments performed at very high energies. Although limited in scope, this approach has resulted in the most precise tests of QCD to date. Lattice QCD Among non-perturbative approaches to QCD, the most well established one is Lattice QCD . This approach uses a discrete set of space-time points (called the lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation which is then carried out on Supercomputers . While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means. 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. Until now it has been the source of qualitative insight rather than a method for quantitative predictions. Modern variants include the AdS/CFT approach. Effective theories For specific problems some theories may be written down which seem to give qualitatively correct results. In the best of cases, these may then be obtained as systematic expansions in some parameter of the QCD Lagrangian. 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). Other less accurate models are the Nambu-Jona-Lasinio Model and the Chiral Model . EXPERIMENTAL TESTS The notion of quark Flavours was prompted by the necessity of explaining the properties of Hadron s during the development of the Quark Model . The notion of colour was necessiated by the puzzle of the Δ++. This has been dealt with in the section on The History Of QCD . The first evidence for Quark s as real constiutent elements of Hadron s was obtained in Deep Inelastic Scattering experiments at SLAC . The first evidence for gluons came in Three Jet Event s at PETRA . Good quantitative tests of perturbative QCD are
Quantitative tests of non-perturbative QCD are fewer, because the predictions are harder to make. The best is probably the s of hadrons and their Weak Matrix Elements are promising candidates for future quantitative tests. 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. SEE ALSO
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