Editing Color confinement

{{Short description|Phenomenon in quantum chromodynamics}}
[[Image:Quark confinement.svg|right|thumb|350px|The color force favors confinement because at a certain range it is more energetically favorable to create a quark–antiquark pair than to continue to elongate the color flux tube. This is analogous to the behavior of an elongated rubber-band.]]
[[File:Gluon tube-color confinement animation.gif|thumb|300px|An animation of color confinement. If energy is supplied to the quarks as shown, the gluon tube elongates until it reaches a point where it "snaps" and forms a quark–antiquark pair. Thus single quarks are never seen in isolation.]]

In [[quantum chromodynamics]] (QCD), '''color confinement''', often simply called '''confinement''', is the phenomenon that [[color charge|color-charged]] particles (such as [[quark]]s and [[gluon]]s) cannot be isolated, and therefore cannot be directly observed in normal conditions below the [[Hagedorn temperature]] of approximately 2 [[tera-|tera]][[kelvin]] (corresponding to energies of approximately 130–140 M[[electron volt|eV]] per particle).<ref>{{cite book
 |last1=Barger |first1=V.
 |last2=Phillips |first2=R. 
 |year=1997
 |title=Collider Physics
 |publisher=[[Addison–Wesley]]
 |isbn=978-0-201-14945-6
}}</ref><ref>{{Cite book<!--Deny Citation Bot-->
 |last=Greensite |first=J.
 |year=2011
 |title=An introduction to the confinement problem
 |series=Lecture Notes in Physics
 |volume=821
 |publisher=[[Springer Science+Business Media|Springer]]
 |isbn=978-3-642-14381-6
 |bibcode=2011LNP...821.....G
 |doi=10.1007/978-3-642-14382-3
}}</ref>  Quarks and gluons must clump together to form [[hadron]]s. The two main types of hadron are the [[meson]]s (one quark, one antiquark) and the [[baryon]]s (three quarks).  In addition, colorless [[glueball]]s formed only of gluons are also consistent with confinement, though difficult to identify experimentally.  Quarks and gluons cannot be separated from their parent hadron without producing new hadrons.<ref>
{{cite book
 |last1=Wu |first1=T.-Y. 
 |author2-link=Woei-Yann Pauchy Hwang |last2=Hwang |first2=Pauchy W.-Y. 
 |year=1991
 |title=Relativistic quantum mechanics and quantum fields
 |pages=321
 |publisher=[[World Scientific]]
 |isbn=978-981-02-0608-6
}}</ref>

==Origin ==
There is not yet an analytic proof of color confinement in any [[non-abelian gauge theory]].  The phenomenon can be understood qualitatively by noting that the force-carrying [[gluon]]s of QCD have color charge, unlike the photons of [[quantum electrodynamics]] (QED).  Whereas the [[electric field]] between [[electric charge|electrically charged]] particles decreases rapidly as those particles are separated, the [[gluon field]] between a pair of color charges forms a narrow flux tube (or string) between them.  Because of this behavior of the gluon field, the strong force between the particles is constant regardless of their separation.<ref>
{{Cite book
 |last=Muta |first=T.
 |year=2009
 |title=Foundations of Quantum Chromodynamics: An introduction to perturbative methods in gauge theories
 |url=https://books.google.com/books?isbn=9812793534  
 |edition=3rd
 |volume=78
 |series=[[Lecture Notes in Physics]]
 |publisher=[[World Scientific]]
 |isbn=978-981-279-353-9
}}</ref><ref>
{{Cite book
 |last=Smilga |first=A.
 |year=2001
 |title=Lectures on quantum chromodynamics
 |url=https://books.google.com/books?isbn=9810243316  
 |publisher=[[World Scientific]]
 |isbn=978-981-02-4331-9
}}</ref>

Therefore, as two color charges are separated, at some point it becomes energetically favorable for a new quark–antiquark [[pair production|pair]] to appear, rather than extending the tube further. As a result of this, when quarks are produced in particle accelerators, instead of seeing the individual quarks in detectors, scientists see "[[jet (particle physics)|jets]]" of many color-neutral particles ([[meson]]s and [[baryon]]s), clustered together. This process is called ''[[hadronization]]'', ''fragmentation'', or ''string breaking''.

The confining phase is usually defined by the behavior of the [[action (physics)|action]] of the [[Wilson loop]], which is simply the path in [[spacetime]] traced out by a quark–antiquark pair created at one point and annihilated at another point. In a non-confining theory, the action of such a loop is proportional to its perimeter. However, in a confining theory, the action of the loop is instead proportional to its area. Since the area is proportional to the separation of the quark–antiquark pair, free quarks are suppressed. Mesons are allowed in such a picture, since a loop containing another loop with the opposite orientation has only a small area between the two loops. At non-zero temperatures, the [[order operator]] for confinement are thermal versions of Wilson loops known as [[Polyakov loop]]s.

==Confinement scale==
The confinement scale or QCD scale is the scale at which the perturbatively defined strong coupling constant diverges. This is known as the [[Landau pole]]. The confinement scale definition and value therefore depend on the [[renormalization]] scheme used. For example, in the [[Minimal subtraction scheme|MS-bar scheme]] and at 4-loop in the [[Coupling constant#Running coupling|running]] of <math>\alpha_s</math>, the world average in the 3-flavour case is given by<ref>{{cite web |title=Review on Quantum Chromodynamics |url=http://pdg.lbl.gov/2018/reviews/rpp2018-rev-qcd.pdf |website=Particle Data Group}}</ref>
:<math>\Lambda^{(3)}_\overline{MS} = (332 \pm 17) \,\rm{MeV} \,.</math>

When the [[exact renormalization group equation|renormalization group equation]] is solved exactly, the scale is not defined at all.{{clarification needed|date=June 2022}} It is therefore customary to quote the value of the strong coupling constant at a particular reference scale instead.

It is sometimes believed that the sole origin of confinement is the very large value of the strong coupling near the [[Landau pole]]. This is sometimes referred as ''infrared slavery'' (a term chosen to contrast with the [[Asymptotic freedom|ultraviolet freedom]]). It is however incorrect since in QCD the Landau pole is unphysical,<ref name="alpha_s review 2016">[https://arxiv.org/abs/1604.08082 A. Deur, S. J. Brodsky and G. F. de Teramond, (2016) “The QCD Running Coupling”] Prog. Part. Nucl. Phys. '''90''', 1</ref><ref name="alpha_s DSE 2016">[https://arxiv.org/abs/1612.04835 D. Binosi, C. Mezrag, J. Papavassiliou, C. D. Roberts and J. Rodriguez-Quintero, (2017) “Process-independent strong running coupling”] Phys. Rev. D '''96''', no. 5, 054026</ref> which can be seen by the fact that its position at the confinement scale largely depends on the chosen [[renormalization]] scheme, i.e., on a convention. Most evidence points to a moderately large coupling, typically of value 1-3 <ref name="alpha_s review 2016" /> depending on the choice of renormalization scheme. In contrast to the simple but erroneous mechanism of ''infrared slavery'', a large coupling is but one ingredient for color confinement, the other one being that gluons are color-charged and
can therefore collapse into gluon tubes.

==Models exhibiting confinement==
In addition to [[Quantum Chromodynamics|QCD]] in four spacetime dimensions, the two-dimensional [[Schwinger model]] also exhibits confinement.<ref name="Wilson 1974">
{{cite journal
 |last=Wilson |first=Kenneth G.
 |date=1974
 |title=Confinement of Quarks
 |journal=Physical Review D
 |volume=10 |issue=8 |pages=2445–2459 
 |bibcode=1974PhRvD..10.2445W
 |doi=10.1103/PhysRevD.10.2445
}}</ref> Compact [[Abelian group|Abelian]] [[gauge theory|gauge theories]] also exhibit confinement in 2 and 3 spacetime dimensions.<ref>
{{Cite book
 |last1=Schön |first1=Verena
 |last2=Michael |first2=Thies
 |date=2000
 |chapter=2d Model Field Theories at Finite Temperature and Density (Section 2.5)
 |editor-last=Shifman |editor-first=M.
 |title=At the Frontier of Particle Physics
 |pages=1945–2032
 |arxiv=hep-th/0008175
 |bibcode=2001afpp.book.1945S
 |doi=10.1142/9789812810458_0041
 |citeseerx=10.1.1.28.1108
 |isbn=978-981-02-4445-3
|s2cid=17401298
 }}</ref> Confinement has been found in elementary excitations of magnetic systems called [[spinon]]s.<ref name="Lake et al, 2009">
{{cite journal
 |last1=Lake |first1=Bella
 |last2=Tsvelik |first2=Alexei M.
 |last3=Notbohm |first3=Susanne
 |last4=Tennant |first4=D. Alan
 |last5=Perring |first5=Toby G.
 |last6=Reehuis |first6=Manfred 
 |last7=Sekar |first7=Chinnathambi 
 |last8=Krabbes |first8=Gernot 
 |last9=Büchner |first9=Bernd 
 |date=2009
 |title=Confinement of fractional quantum number particles in a condensed-matter system
 |journal=[[Nature Physics]]
 |volume=6 |issue=1 |pages=50–55
 |arxiv=0908.1038
 |bibcode=2010NatPh...6...50L
 |doi=10.1038/nphys1462
|s2cid=18699704
 }}</ref>

If the [[Higgs mechanism|electroweak symmetry breaking]] [[Electroweak scale|scale]] were lowered, the unbroken SU(2) interaction would eventually become confining.  Alternative models where SU(2) becomes confining above that scale are quantitatively similar to the [[Standard Model]] at lower energies, but dramatically different above symmetry breaking.<ref>
{{cite journal
 |last1=Claudson
 |first1=M.
 |last2=Farhi
 |first2=E.
 |last3=Jaffe
 |first3=R. L.
 |title=Strongly coupled standard model
 |journal=Physical Review D
 |date=1 August 1986
 |volume=34
 |issue=3
 |pages=873–887
 |doi=10.1103/PhysRevD.34.873
 |pmid=9957220
|bibcode=1986PhRvD..34..873C
 }}</ref>

==Models of fully screened quarks==
Besides the quark confinement idea, there is a potential possibility that the color charge of quarks gets fully screened by the gluonic color surrounding the quark. Exact solutions of SU(3) classical [[Yang–Mills theory]] which provide full screening (by gluon fields) of the color charge of a quark have been found.<ref name="Cahill 1978">
{{cite journal
 |last=Cahill |first=Kevin
 |title=Example of Color Screening
 |date=1978
 |journal=[[Physical Review Letters]]
 |volume=41 |issue=9 |pages=599–601  
 |bibcode=1978PhRvL..41..599C
 |doi=10.1103/PhysRevLett.41.599
}}</ref> However, such classical solutions do not take into account non-trivial properties of [[QCD vacuum]]. Therefore, the significance of such full gluonic screening solutions for a separated quark is not clear.

== See also ==
{{div col|colwidth=20em}}
* [[Lund string model]]
* [[Gluon field strength tensor]]
* [[Asymptotic freedom]]
* [[Beta function (physics)]]
* [[Yang–Mills existence and mass gap]]
* {{slink|Cornell potential#Calculation of the quark-quark potential}}
* [[Lattice gauge theory]]
* [[Dual superconductor model]]
* [[Center vortex]]
{{div col end}}

== References ==
{{Reflist}}

{{Authority control}}

[[Category:Gluons]]
[[Category:Quantum chromodynamics]]
[[Category:Quark matter]]
[[Category:Unsolved problems in physics]]