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{{Standard model of particle physics|cTopic=quantum phromodynamics}}
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In [[theoretical physics]], '''quantum chromodynamics''' ('''QCD''') is a theory of [[strong interaction]]s, a [[fundamental force]] describing the interactions between [[quark]]s and [[gluon]]s which make up [[hadron]]s such as the [[proton]], [[neutron]] and [[pion]]. QCD is a type of [[quantum field theory]] called a [[non-abelian gauge theory]] with symmetry group [[special unitary group|SU(3)]]. The QCD analog of electric charge is a property called 'color'. Gluons are the [[force carrier]] of the theory, like photons are for the electromagnetic force [[quantum electrodynamics]]. The theory is an important part of the [[Standard Model]] of [[particle physics]]. A huge body of [[Quantum chromodynamics#Experimental tests|experimental evidence for QCD]] has been gathered over the years.
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QCD enjoys two peculiar properties:
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*'''[[Color confinement|Confinement]]''', which means that the force between quarks does not diminish as they are separated. Because of this, when you do split the quark the energy is enough to create another quark thus creating another quark pair; they are forever bound into hadrons such as the [[proton]] and the [[neutron]] or the pion and kaon. 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]].
*'''[[Asymptotic freedom]]''', which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark-gluon plasma. This prediction of QCD was first discovered in the early 1970s by [[David Politzer]] and by [[Frank Wilczek]] and [[David Gross]]. For this work they were awarded the 2004 [[Nobel Prize in Physics]].


There is no known phase-transition line separating these two properties; confinement is dominant in low-energy scales but, as energy increases, asymptotic freedom becomes dominant.
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==Terminology==
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The word ''quark'' was coined by American physicist [[Murray Gell-Mann]] (b. 1929) in its present sense. It originally comes from the phrase "Three quarks for Muster Mark" in ''[[Finnegans Wake]]'' by [[James Joyce]]. On June 27, 1978, Gell-Mann wrote a private letter to the editor of the Oxford English Dictionary, in which he related that he had been influenced by Joyce's words: "The allusion to three quarks seemed perfect." (Originally, only three quarks had been discovered.) Gell-Mann, however, wanted to pronounce the word with (ô) not (ä), as Joyce seemed to indicate by rhyming words in the vicinity such as ''Mark''. Gell-Mann got around that "by supposing that one ingredient of the line 'Three quarks for Muster Mark' was a cry of 'Three quarts for Mister . . . ' heard in H.C. Earwicker's pub," a plausible suggestion given the complex punning in Joyce's novel.<ref>
{{cite book
| last = Gell-Mann
| first = Murray
| authorlink =Murray Gell-Mann
| title = The Quark and the Jaguar
| publisher = [[Owl Books]]
| year = 1995
| isbn = 978-0-8050-7253-2
}}</ref>


The three kinds of [[Charge (physics)|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) [[color vision|perceived by humans]]. Other than this nomenclature, the quantum parameter "color" is completely unrelated to the everyday, familiar phenomenon of color.  
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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".
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With the invention of [[bubble chamber]]s and [[spark chamber]]s in the 1950s, experimental [[particle physics]] discovered a large and ever-growing number of particles called [[hadron]]s. It seemed that such a large number of particles could not all be [[fundamental particles|fundamental]]. First, the particles were classified by [[Charge (physics)|charge]] and [[isospin]] by [[Eugene Wigner]] and [[Werner Heisenberg]]; then, in 1953, according to [[Strangeness (particle physics)|strangeness]] by [[Murray Gell-Mann]] and [[Kazuhiko Nishijima]]. To gain greater insight, the hadrons were sorted into groups having similar properties and masses using the ''[[eightfold way (physics)|eightfold way]]'', invented in 1961 by Gell-Mann and [[Yuval Ne'eman]]. Gell-Mann and [[George Zweig]], correcting an earlier approach of [[Shoichi Sakata]], went on to propose in 1963 that the structure of the groups could be explained by the existence of three [[flavour (particle physics)|flavor]]s of smaller particles inside the hadrons: the [[quark]]s.
 
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Perhaps the first remark that quarks should possess an additional quantum number was made<ref>
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{{cite arxiv
|eprint=0904.0343
|author1=Fyodor Tkachov
|title=A contribution to the history of quarks: Boris Struminsky's 1965 JINR publication
|class=physics.hist-ph
|year=2009
}}</ref> as a short footnote in the preprint of [[Boris Struminsky]]<ref name="struminsky">B. V. Struminsky, Magnetic moments of barions in the quark model. [[JINR]]-Preprint P-1939, Dubna, Russia. Submitted on January 7, 1965.</ref> in connection with Ω<sup>-</sup> [[Omega baryon|hyperon]] composed of three [[strange quark]]s with parallel spins (this situation was peculiar, because since quarks are [[fermion]]s, such combination is forbidden by the [[Pauli exclusion principle]]): {{Quotation|Three identical quarks cannot form an antisymmetric S-state. In order to realize an antisymmetric orbital S-state, it is necessary for the quark to have an additional quantum number.|B. V. Struminsky|Magnetic moments of barions in the quark model|[[JINR]]-Preprint P-1939, Dubna, Submitted on January 7, 1965}} Boris Struminsky was a PhD student of [[Nikolay Bogolyubov]]. The problem considered in this preprint was suggested by Nikolay Bogolyubov, who advised Boris Struminsky in this research.<ref name="struminsky" /> In the beginning of 1965, [[Nikolay Bogolyubov]], [[Boris Struminsky]] and [[Albert Tavkhelidze]] wrote a preprint with a more detailed discussion of the additional quark quantum degree of freedom.<ref>[[Nikolay Bogolyubov|N. Bogolubov]], B. Struminsky, A. Tavkhelidze. On composite models in the theory of elementary particles. [[JINR]] Preprint D-1968, [[Dubna]] 1965.</ref> This work was also presented by Albert Tavchelidze without obtaining consent of his collaborators for doing so at an international conference in [[Trieste]] ([[Italy]]), in May 1965.<ref>A. Tavkhelidze. Proc. Seminar on High Energy Physics and Elementary Particles, Trieste, 1965, Vienna IAEA, 1965, p. 763.</ref><ref>V. A. Matveev and A. N. Tavkhelidze (INR, RAS, Moscow) [http://www.inr.ru/quantum.html The quantum number color, colored quarks and QCD] (Dedicated to the 40th Anniversary of the Discovery of the Quantum Number Color). Report presented at the 99th Session of the JINR Scientific Council, Dubna, 19–20 January 2006.</ref>


A similar mysterious situation was with the [[Delta baryon|Δ<sup>++</sup> baryon]]; in the quark model, it is composed of three [[up quark]]s with parallel spins. In 1965, [[Moo-Young Han]] with [[Yoichiro Nambu]] and [[Oscar W. Greenberg]] independently resolved the problem by proposing that quarks possess an additional [[special unitary group|'''SU'''(3)]] [[gauge theory|gauge]] [[degrees of freedom (physics and chemistry)|degree of freedom]], later called color charge. Han and Nambu noted that quarks might interact via an octet of vector [[gauge boson]]s: the [[gluon]]s.
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Since free quark searches consistently failed to turn up any evidence for the new particles, and because an elementary particle back then was ''defined'' as a particle which could be separated and isolated, Gell-Mann often said that quarks were merely convenient mathematical constructs, not real particles. The meaning of this statement was usually clear in context: He meant quarks are confined, but he also was implying that the strong interactions could probably not be fully described by quantum field theory.
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[[Richard Feynman]] argued that high energy experiments showed quarks are real particles: he called them ''partons'' (since they were parts of hadrons). By particles, Feynman meant objects which travel along paths, elementary particles in a field theory.
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The difference between Feynman's and Gell-Mann's approaches reflected a deep split in the theoretical physics community. Feynman thought the quarks have a distribution of position or momentum, like any other particle, and he (correctly) believed that the diffusion of parton momentum explained [[pomeron|diffractive scattering]]. Although Gell-Mann believed that certain quark charges could be localized, he was open to the possibility that the quarks themselves could not be localized because space and time break down. This was the more radical approach of [[S-matrix theory]].
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[[James Daniel Bjorken|James Bjorken]] proposed that pointlike partons would imply certain relations should hold in [[deep inelastic scattering]] of [[electron]]s and protons, which were spectacularly verified in experiments at [[SLAC]] in 1969. This led physicists to abandon the S-matrix approach for the strong interactions.
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The discovery of [[asymptotic freedom]] in the strong interactions by [[David Gross]], [[David Politzer]] and [[Frank Wilczek]] allowed physicists to make precise predictions of the results of many high energy experiments using the quantum field theory technique of [[perturbation theory (quantum mechanics)|perturbation theory]]. Evidence of gluons 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]].
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The other side of asymptotic freedom is [[Color confinement|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 Prize Problems]] 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 [[QCD matter|quark matter]], including the [[quark-gluon plasma]].
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The relation between the short-distance particle limit and the confining long-distance limit is one of the topics recently explored using [[string theory]], the modern form of S-matrix theory.<ref>
== Tiffany Jewellery Nz like Westchester ==
{{cite journal
|author=J. Polchinski, M. Strassler
|year=2002
|title=Hard Scattering and Gauge/String duality
|journal=[[Physical Review Letters]]
|volume=88 |page=31601
|doi=10.1103/PhysRevLett.88.031601
|pmid=11801052
|issue=3
|arxiv = hep-th/0109174 |bibcode = 2002PhRvL..88c1601P }}</ref><ref>
{{cite journal
|last1=Brower | first1=Richard C.
|last2=Mathur | first2=Samir D.
|author3=Chung-I Tan
|title=Glueball Spectrum for QCD from AdS Supergravity Duality
|year=2000
|doi=10.1016/S0550-3213(00)00435-1
|journal=Nuclear Physics B
|volume=587
|pages=249–276
  |arxiv=hep-th/0003115
|bibcode = 2000NuPhB.587..249B }}</ref>


==Theory==
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{{unsolved|physics|QCD in the non-[[perturbation theory (quantum mechanics)|perturbative]] regime:
 
*'''[[Color confinement|Confinement]]''': the equations of QCD remain unsolved at [[energy scale]]s relevant for describing [[atomic nucleus|atomic nuclei]]. How does QCD give rise to the physics of nuclei and nuclear constituents?
  <li>[http://tu.linuxaudiosystems.com/node/6#comment-60784221 http://tu.linuxaudiosystems.com/node/6#comment-60784221]</li>
*'''[[QCD matter|Quark matter]]''': the equations of QCD predict that a [[quark–gluon plasma|plasma (or soup) of quarks and gluons]] should be formed at high temperature and density. What are the properties of this [[phase of matter]]?}}
 
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===Some definitions===
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Every field theory of [[particle physics]] is based on certain symmetries of nature whose existence is deduced from observations. These can be
*[[Local symmetry|local symmetries]], that is the symmetry acts independently at each point in [[space-time]]. Each such symmetry is the basis of a [[gauge theory]] and requires the introduction of its own [[gauge boson]]s.
*[[Global symmetry|global symmetries]], which are symmetries whose operations must be simultaneously applied to all points of space-time.


QCD is a gauge theory of the [[special unitary group|'''SU'''(3)]] gauge group obtained by taking the [[color charge]] to define a local symmetry.
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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.
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There are additional global symmetries whose definitions require the notion of [[chirality (physics)|chirality]], discrimination between left and right-handed. If the [[spin (physics)|spin]] of a particle has a positive [[projection (linear algebra)|projection]] on its direction of motion then it is called left-handed; otherwise, it is right-handed.  Chirality and handedness are not the same, but become approximately equivalent at high energies.
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*'''Chiral''' symmetries involve independent transformations of these two types of particle.
 
*'''Vector''' symmetries (also called diagonal symmetries) mean the same transformation is applied on the two chiralities.
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*'''Axial''' symmetries are those in which one transformation is applied on left-handed particles and the inverse on the right-handed particles.
 
 
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===Additional remarks: duality===
 
As mentioned, ''asymptotic freedom'' means that at large energy –  this corresponds also to ''short distances'' – there is practically no interaction between the particles. This is in contrast – more precisely one would say ''[[Dualism|dual]]'' - to what one is used to, since usually one connects the absence of interactions with ''large''&nbsp;distances. However, as already mentioned in the original paper of Franz Wegner,<ref>F. Wegner, ''Duality in Generalized Ising Models and Phase Transitions without Local Order Parameter'', J. Math. Phys. '''12''' (1971) 2259-2272.
  <li>[http://www.histoirepassion.eu/spip.php?article7/ http://www.histoirepassion.eu/spip.php?article7/]</li>
:Reprinted in [[Claudio Rebbi]] (ed.), ''Lattice Gauge Theories and Monte Carlo Simulations'', World Scientific, Singapore (1983), p. 60-73. Abstract: [http://www.tphys.uni-heidelberg.de/~wegner/Abstracts.html#12]</ref> a solid state theorist who introduced 1971 simple gauge invariant lattice models, the high-temperature behaviour of the ''original model'', e.g. the strong decay of correlations at large distances, corresponds to the low-temperature behaviour of the (usually ordered!) ''dual model'', namely the asymptotic decay of non-trivial correlations, e.g. short-range deviations from almost perfect arrangements, for short distances. Here, in contrast to Wegner, we have only the dual model, which is that one described in this article.<ref>Perhaps one can guess that in the "original" model mainly the quarks would fluctuate, whereas in the present one, the "dual" model, mainly the gluons do.</ref>
 
 
</ul>
===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 [[Quantum electrodynamics|QED]]: this is an [[abelian group]]. If one considers a version of QCD with ''N<sub>f</sub>'' flavors of massless quarks, then there is a global ([[chirality (physics)|chiral]]) flavor symmetry group '''SU'''<sub>L</sub>(''N<sub>f</sub>'') &times; '''SU'''<sub>R</sub>(''N<sub>f</sub>'') &times; '''U'''<sub>B</sub>(1) &times; '''U'''<sub>A</sub>(1). The chiral symmetry is [[spontaneous symmetry breaking|spontaneously broken]] by the [[QCD vacuum]] to the vector (L+R) '''SU'''<sub>V</sub>(''N<sub>f</sub>'')  with the formation of a [[chiral condensate]]. The vector symmetry, '''U'''<sub>B</sub>(1) corresponds to the baryon number of quarks and is an exact symmetry. The axial symmetry '''U'''<sub>A</sub>(1) is exact in the classical theory, but broken in the quantum theory, an occurrence called an [[anomaly (physics)|anomaly]]. Gluon field configurations called [[instanton]]s are closely related to this anomaly.
 
There are two different types of '''SU'''(3) symmetry: there is the symmetry that acts on the different colors of quarks, and this is an exact gauge symmetry mediated by the gluons, and there is also a flavor symmetry which rotates different flavors of quarks to each other, or ''flavor '''SU'''(3)''. Flavor '''SU'''(3) is an approximate symmetry of the vacuum of QCD, and is not a fundamental symmetry at all. It is an accidental consequence of the small mass of the three lightest quarks.
 
In the [[QCD vacuum]] there are vacuum condensates of all the quarks whose mass is less than the QCD scale. This includes the up and down quarks, and to a lesser extent the strange quark, but not any of the others. The vacuum is symmetric under '''SU'''(2) [[isospin]] rotations of up and down, and to a lesser extent under rotations of up, down and strange, or full flavor group '''SU'''(3), and the observed particles make isospin and '''SU'''(3) multiplets.
 
The approximate flavor symmetries do have associated gauge bosons, observed particles like the rho and the omega, but these particles are nothing like the gluons and they are not massless. They are emergent gauge bosons in an approximate [[AdS/QCD|string description of QCD]].
 
=== Lagrangian ===
The dynamics of the quarks and gluons are controlled by the quantum chromodynamics Lagrangian.  The [[gauge invariant]] QCD [[Lagrangian]] is
::<math>
\mathcal{L}_\mathrm{QCD}
= \bar{\psi}_i i \left( (\gamma^\mu D_\mu)_{ij} - m\, \delta_{ij}\right) \psi_j - \frac{1}{4}G^a_{\mu \nu} G^{\mu \nu}_a
</math>
where <math>\psi_i(x) \,</math> is the quark field, a dynamical function of space-time, in the fundamental representation of the [[SU(3)|'''SU'''(3)]] gauge [[Group (mathematics)|group]], indexed by <math>i,\,j,\,\ldots</math>; <math>\mathcal{A}^a_\mu(x) \,</math> are the [[gluon field]]s, also dynamical functions of space-time, in the adjoint representation of the '''SU'''(3) gauge group, indexed by ''a'', ''b'',... The γ<sup>μ</sup> are  [[Dirac matrices]] connecting the spinor representation to the vector representation of the [[Lorentz group]].
 
The symbol <math>G^a_{\mu \nu} \,</math> represents the gauge invariant [[gluon field strength tensor]], analogous to the [[electromagnetic tensor|electromagnetic field strength tensor]], ''F''<sup>μν</sup>, in [[quantum electrodynamics]]. It is given by:<ref>{{cite article|title=The field strength correlator from QCD sum rules
|author=M. Eidemüller, H.G. Dosch, M. Jamin
|year=1999
|publisher=
|location=Heidelberg, Germany
|journal=Nucl.Phys.Proc.Suppl.86:421-425,2000
|arxiv=hep-ph/9908318
|url=http://arxiv.org/pdf/hep-ph/9908318v1.pdf}}</ref>
 
::<math>G^a_{\mu \nu} = \partial_\mu \mathcal{A}^a_\nu - \partial_\nu \mathcal{A}^a_\mu + g f^{abc} \mathcal{A}^b_\mu \mathcal{A}^c_\nu \,,</math>
 
where ''f<sub>abc</sub>'' are the [[structure constants]] of '''SU'''(3). Note that the rules to move-up or pull-down the ''a'', ''b'', or ''c'' indexes are ''trivial'', (+,... +), so that ''f<sup>abc</sup>'' = ''f<sub>abc</sub>'' = ''f''{{su|b=''bc''|p=''a''}} whereas for the ''μ'' or ''ν'' indexes one has the non-trivial ''relativistic'' rules, corresponding e.g. to the [[metric signature]] (+ − − −).
 
The constants ''m'' and ''g'' control the quark mass and coupling constants of the theory, subject to renormalization in the full quantum theory.
 
An important theoretical notion concerning  the final term of the above Lagrangian is the ''[[Wilson loop]]'' variable. This loop variable plays a most-important role in discretized forms of the QCD (see [[lattice QCD]]), and more generally, it distinguishes [[Color confinement|confined]] and deconfined states of a gauge theory. It was introduced by the [[Nobel prize]] winner [[Kenneth G. Wilson]] and is treated in a separate article.
 
===Fields===
[[File:QCD.svg|300px|right|thumb|The pattern of strong charges for the three colors of quark, three antiquarks, and eight gluons (with two of zero charge overlapping).]]
 
Quarks 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)|'''SU'''(3)]]. They also carry electric charge (either -1/3 or 2/3) and participate in [[weak interactions]] as part of [[weak isospin]] doublets. They carry global quantum numbers including the [[baryon number]], which is 1/3 for each quark, [[hypercharge]] and one of the [[flavor (particle physics)|flavor quantum numbers]].
 
Gluons are spin-1 [[boson]]s which also carry [[color charge]]s, since they lie in the [[Adjoint representation of a Lie group|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 state|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.
 
===Dynamics===
According to the rules of [[quantum field theory]], and the associated [[Feynman diagram]]s, 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. This contrasts with [[quantum electrodynamics|QED]], in which only the first kind of interaction occurs, since [[photon]]s have no charge. Diagrams involving [[Faddeev–Popov ghost]]s must be considered too (except in the [[unitarity gauge]]).
 
===Area law and confinement===
Detailed computations with the above-mentioned Lagrangian<ref>See  all standard textbooks on the QCD,  e.g., those noted above</ref> show that the effective potential between a quark and its anti-quark in a [[meson]] contains a term <math>\propto r</math>, which represents some kind of "stiffness" of the interaction between the particle and its anti-particle at large
distances, similar to the [[entropic force|entropic elasticity]] of a [[rubber]] band (see below). This leads to ''confinement''&nbsp;<ref>Only at extremely large pressures and or temperatures, e.g. for <math>T\cong 5\cdot 10^{12}</math>&nbsp;&nbsp;K or larger,  ''confinement'' gives way to a [[quark-gluon plasma]].</ref> of the quarks to the interior of hadrons, i.e. [[meson]]s and [[nucleon]]s, with typical radii R<sub>c</sub>, corresponding to  former  "[[Bag model]]s" of the hadrons<ref>[[Kenneth A. Johnson]], "The bag model of quark confinement", Scientific American, July 1979</ref>&nbsp;. The order of magnitude of the "bag radius" is 1 fm (=10<sup>−15</sup>&nbsp;m). Moreover, the above-mentioned stiffness is quantitatively related to the so-called "area law" behaviour of the expectation value of the [[Wilson loop]] product ''P<sub>W</sub>'' of the ordered coupling constants around a closed loop ''W''; i.e. <math>\,\langle P_W\rangle</math> is proportional to the ''area''  enclosed by the loop.  For this behaviour the non-abelian behaviour of the gauge group is essential.
 
==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===
{{main|Perturbative QCD}}
This approach is based on asymptotic freedom, which allows [[perturbation theory (quantum mechanics)|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===
{{main|Lattice QCD}}
[[Image:Fluxtube meson.png|right|thumb|150px|A quark and an antiquark (red color) are glued together (green color) to form a meson (result of a lattice QCD simulation by M. Cardoso et al.<ref>M. Cardoso et al., "Lattice QCD computation of the colour fields for the static hybrid quark-gluon-antiquark system, and microscopic study of the Casimir scaling", Phys. Rev. D 81, 034504 (2010) ).</ref>)]]
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]] like the [[QCDOC]] which was constructed for precisely this purpose. While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means, in particular into the explicit forces acting between  quarks and antiquarks in a meson.  However, the [[numerical sign problem]] makes it difficult to use lattice methods to study QCD at high density and low temperature (e.g. nuclear matter or the interior of neutron stars).
 
===1/N expansion===
{{main|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 effective theories may be written down which give qualitatively correct results in certain limits. In the best of cases, these may then be obtained as systematic expansions in some parameter of the QCD Lagrangian. One such [[effective field theory]] is [[chiral perturbation theory]] or ChiPT, which is the QCD effective theory at low energies. More precisely, it is a low energy expansion based on the spontaneous chiral symmetry breaking of QCD, which is an exact symmetry when quark masses are equal to zero, but for the u,d and s quark, which have small mass, it is still a good approximate symmetry. Depending on the number of quarks which are treated as light, one uses either '''SU'''(2) ChiPT or '''SU'''(3) ChiPT . Other effective theories are [[heavy quark effective theory]] (which expands around heavy quark mass near infinity), and [[soft-collinear effective theory]] (which expands around large ratios of energy scales). In addition to effective theories, models like the [[Nambu-Jona-Lasinio model]] and the [[chiral model]] are often used when discussing general features.
 
===QCD sum rules===
{{main|QCD sum rules}}
 
Based on an [[Operator product expansion]] one can derive sets of relations that connect different observables with each other.
 
===Nambu-Jona-Lasinio model===
In one of his recent works, [[Kei-Ichi Kondo]] derived as a low-energy limit of QCD, a theory linked to the [[Nambu-Jona-Lasinio model]] since it is basically a particular non-local version of the [[Polyakov-Nambu-Jona-Lasinio model]].<ref>
{{cite journal
|author=Kei-Ichi Kondo
|year=2010
|title=Toward a first-principle derivation of confinement and chiral-symmetry-breaking crossover transitions in QCD
|journal=[[Physical Review D]]
|volume=82 |page=065024
|doi=10.1103/PhysRevD.82.065024
|arxiv = 1005.0314v2|bibcode = 2010PhRvD..82f5024K
|issue=6 }}</ref> The later being in its local version, nothing but the [[Nambu-Jona-Lasinio model]] in which one has included the Polyakov loop effect, in order to describe a 'certain confinement'.
 
The [[Nambu-Jona-Lasinio model]] in itself is, among many other things, used because it is a 'relatively simple' model of [[chiral symmetry|chiral symmetry breaking]], phenomenon present up to certain conditions (Chiral limit i.e. massless fermions) in QCD itself.
In this model, however, there is no confinement. In particular, the energy of an isolated quark in the physical vacuum turns out well defined and finite.
 
==Experimental tests==<!-- This section is linked from [[Quantum chromodynamics]] -->
The notion of quark [[flavour (particle physics)|flavors]] was prompted by the necessity of explaining the properties of hadrons during the development of the [[quark model]]. The notion of color was necessitated by the puzzle of the {{SubatomicParticle|Delta++}}. This has been dealt with in the section on [[Quantum chromodynamics#History|the history of QCD]].
 
The first evidence for quarks as real constituent elements of hadrons was obtained in [[deep inelastic scattering]] experiments at [[SLAC]]. The first evidence for gluons came in [[three jet event]]s at [[PETRA]].
 
Several good quantitative tests of perturbative QCD exist:
* The [[coupling constant#QCD and asymptotic freedom|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 colliders
 
Quantitative tests of non-perturbative QCD are fewer, because the predictions are harder to make. The best is probably the running of the QCD coupling as probed through [[lattice QCD|lattice]] computations of [[heavy-quarkonium spectra]]. There is a recent claim about the mass of the heavy meson B<sub>c</sub> [http://www.aip.org/pnu/2005/split/731-1.html]. Other non-perturbative tests are currently at the level of 5% at best. Continuing work on masses and [[Form factor (QFT)|form factor]]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.
 
One qualitative prediction of QCD is that there exist composite particles made solely of [[gluon]]s called [[glueball]]s that have not yet been definitively observed experimentally.  A definitive observation of a glueball with the properties predicted by QCD would strongly confirm the theory.  In principle, if glueballs could be definitively ruled out, this would be a serious experimental blow to QCD.  But, as of 2013, scientists are unable to confirm or deny the existence of glueballs definitively, despite the fact that particle accelerators have sufficient energy to generate them.
 
==Cross-relations to solid state physics==
There are unexpected cross-relations to solid state physics. For example, the notion of [[gauge invariance]] forms the basis of the well-known Mattis [[spin glass]]es,<ref>D.C. Mattis,  Phys. Lett. 56a (1976) 421</ref> which are systems with the usual spin degrees of freedom <math>s_i=\pm 1\,</math> for ''i''&nbsp;=1,...,N,  with the special fixed  "random" couplings <math>J_{i,k}=\epsilon_i \,J_0\,\epsilon_k\,.</math>  Here the ε<sub>i</sub>  and ε<sub>k</sub> quantities can independently and "randomly" take the values ±1, which corresponds to a most-simple gauge transformation  <math>(\,s_i\to s_i\cdot\epsilon_i\quad\,J_{i,k}\to \epsilon_i J_{i,k}\epsilon_k\,\quad s_k\to s_k\cdot\epsilon_k \,)\,.</math> This means that  thermodynamic expectation values of measurable quantities, e.g. of the energy <math>{\mathcal H}:=-\sum s_i\,J_{i,k}\,s_k\,,</math> are invariant.
 
However, here the ''coupling degrees of freedom'' <math>J_{i,k}</math>, which in the QCD correspond to the ''gluons'', are "frozen" to fixed values  (quenching).  In contrast, in the QCD they "fluctuate" (annealing), and through the large number of gauge degrees of freedom the [[entropy]] plays an important role (see below).
 
For positive ''J''<sub>0</sub> the thermodynamics of the Mattis spin glass corresponds in fact simply to a "ferromagnet in disguise", just because these systems have no "[[Geometrical frustration|frustration]]“ at all. This term is a basic  measure in spin glass theory.<ref>J. Vanninemus and G. Toulouse, J.  Phys. C 10 (1977) 537</ref> Quantitatively it is identical with the loop-product <math>P_W:\,=\,J_{i,k}J_{k,l}...J_{n,m}J_{m,i}</math>  along a closed loop ''W''. However, for a Mattis spin glass - in contrast to "genuine" spin glasses - the quantity ''P<sub>W</sub>'' never becomes negative.
 
The basic notion "frustration" of the spin-glass is actually similar to the [[Wilson loop]] quantity of the QCD. The only difference is again that in the QCD one is dealing with SU(3) matrices, and that one is dealing with a "fluctuating" quantity.
Energetically, perfect absence of frustration should be non-favorable and atypical for a spin glass, which means that one should add the loop-product to the Hamiltonian, by  some kind of term representing a "punishment". - In the QCD the Wilson loop is essential for the Lagrangian rightaway.
 
The relation between the QCD and "disordered magnetic systems" (the spin glasses belong to them) were additionally stressed in a paper by Fradkin, Huberman und Shenker,<ref>E. Fradkin, B.A. Huberman, S. Shenker, ''Gauge Symmetries in random magnetic systems'', Phys. Rev. B 18 (1978) 4783-4794, [http://prb.aps.org/abstract/PRB/v18/i9/p4879-1 ]</ref> which also stresses the notion of [[Dualism|duality]].
 
A further analogy consists in the already mentioned similarity to  [[polymer physics]], where, analogously to  [[Wilson Loop]]s,  so-called "entangled nets" appear, which are important for the formation of the [[entropic force|entropy-elasticity]]  (force proportional to the length) of a rubber band. The non-abelian character of the SU(3) corresponds thereby to the  non-trivial "chemical links“, which  glue different loop segments together, and "[[asymptotic freedom]]" means in the polymer analogy simply the fact that in the short-wave limit, i.e. for <math>0\leftarrow\lambda_w\ll R_c</math>  (where ''R<sub>c</sub>'' is a characteristic correlation-length for the glued loops, corresponding to the above-mentioned "bag radius", while λ<sub>w</sub> is the wavelength of an excitation) any non-trivial correlation vanishes totally, as if the system had crystallized.<ref>A. Bergmann, A. Owen , "Dielectric relaxation spectroscopy of poly[(R)-3-Hydroxybutyrate] (PHD) during crystallization", Polymer International 53 (7) (2004) 863-868, [http://www3.interscience.wiley.com/journal/108563755/abstract?CRETRY=1&SRETRY=0]</ref>
 
There is also a correspondence between confinement in QCD - the fact that the color-field is only different from zero in the interior of hadrons - and the behaviour of the usual magnetic field in the theory of [[type-II superconductor]]s: there the magnetism is confined to the interiour of the [[Abrikosov vortex|Abrikosov flux-line lattice]],<ref>Mathematically, the flux-line lattices are described by [[Emil Artin]]'s braid group, which is nonabelian, since one braid can wind around another one.</ref>&nbsp;&nbsp; i.e., the London penetration depth ''&lambda;'' of that  theory is analogous to the confinement radius ''R<sub>c</sub>'' of  quantum chromodynamics. Mathematically, this correspondendence is supported by the second term, <math>\propto  g G^a_\mu \bar{\psi}_i \gamma^\mu T^a_{ij} \psi_j\,,</math> on the r.h.s. of the Lagrangian.
 
==See also==
* For overviews, see [[Standard Model]], its [[standard model (basic details)|field theoretical formulation]], [[strong interaction]]s, [[quark]]s and [[gluon]]s, [[hadron]]s, [[colour confinement|confinement]], [[QCD matter]], or [[quark-gluon plasma]].
* For details, see [[gauge theory]], [[quantum gauge theory|quantization procedure]] including [[BRST quantization]] and [[Faddeev–Popov ghost]]s. A more general category is [[quantum field theory]].
* For techniques, see [[Lattice QCD]], [[1/N expansion]], [[perturbative QCD]], [[Soft-collinear effective theory]], [[heavy quark effective theory]], [[chiral model]]s, and the [[Nambu-Jona-Lasinio model|Nambu and Jona-Lasinio model]].
* For experiments, see [[quark search experiment]]s, [[deep inelastic scattering]], [[jet physics]], [[quark-gluon plasma]].
* [[Symmetry in quantum mechanics]]
 
==References==
{{reflist|2}}
 
==Further reading==
* {{cite book | author=Greiner, Walter;Schäfer, Andreas | title=Quantum Chromodynamics | publisher=Springer | year=1994 | isbn = 0-387-57103-5}}
* {{cite book | author=Halzen, Francis; Martin, Alan | title=Quarks & Leptons: An Introductory Course in Modern Particle Physics | publisher=John Wiley & Sons | year=1984 | isbn = 0-471-88741-2}}
* {{cite book | author=Creutz, Michael | title=Quarks, Gluons and Lattices | publisher=Cambridge University Press | year=1985 | isbn = 978-0-521-31535-7}}
 
==External links==
*[http://pdg.lbl.gov/ Particle data group]
*[http://www.claymath.org/millennium-problems The millennium prize] for [http://www.claymath.org/millenium-problems/yang%E2%80%93mills-and-mass-gap proving confinement]
*[http://www.sciencemag.org/cgi/content/abstract/322/5905/1224 Ab Initio Determination of Light Hadron Masses]
*[http://www.sciencemag.org/cgi/content/summary/322/5905/1198 Andreas S Kronfeld] ''The Weight of the World Is Quantum Chromodynamics''
*[http://www.iop.org/EJ/article/1742-6596/125/1/012067/jpconf8_125_012067.pdf?request-id=f9ccdf0d-ee26-4856-99fb-ce5bfef07c4c Andreas S Kronfeld] ''Quantum chromodynamics with advanced computing''
*[http://www.sciencenews.org/view/generic/id/38788/title/Standard_model_gets_right_answer_for_proton,_neutron_masses Standard model gets right answer]
*[http://arxiv.org/abs/hepph/9505231 Quantum Chromodynamics]
{{Quantum field theories}}
 
{{DEFAULTSORT:Quantum Chromodynamics}}
[[Category:Particle physics]]
[[Category:Quantum field theory]]
[[Category:Quantum chromodynamics|*]]
[[Category:Concepts in physics]]

Latest revision as of 10:21, 17 February 2014

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2012 would be a good year for IPv6. Netapp's Lars Eggert continues to be measuring how many of the top 500 websites have IPv6 enabled. After last year's World IPv6 Day and this year's World IPv6 Launch, we're now around 10 percent for the top 500 sites in Finland, Germany, India, Japan, South Korea, the UK, and the US. China is lagging behind at 4.8 percent. And of the worldwide top 500 sites, 22.4 percent have an IPv6 address in the DNS, up from 8 % a year ago. However, of the Alexa top one million websites, only five percent come with an IPv6 address in the DNS.

Pedro Bial, jornalista formado, em 1980, pela PUCRio. Comeou no ano seguinte na Rede Globo, onde trabalhou no Jornal Hoje, Globo Reprter, Fantstico, entre outros, e apresenta o Big Barbour Sydney Brother Brasil desde 2002. Desenvolve projetos no cinema, escreve livrosreportagem e participa de saraus de poesia. No TEDxESPM, o Celine Bag jornalista interpretou o conto Reflexos presente no livro Contos e Poemas para Crianas Extremamente Inteligentes de Todas as Idades, organizado por Harold Bloom, narrando cada personagem da histria durante os 18 minutos da sua palestra. "Passei na frente de uma loja de computadores e aparelhos de televiso, lembrei desse conto e achei oportuno para contlo aqui." Para Bial, o autor vive um romance tanto em seus contos quanto na prpria vida. Por fim, Bial enfatiza que o conto Reflexos, rima com o que ele havia escrito no quadro de avisos para iluminar mentes: "Para que a comunicao se d, preciso reconhecer que a comunicao impossvel."

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