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vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" 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href="https://ca.wikipedia.org/wiki/Confinament_de_color" title="Confinament de color – Catalan" lang="ca" hreflang="ca" data-title="Confinament de color" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Barevn%C3%A9_uv%C4%9Bzn%C4%9Bn%C3%AD" title="Barevné uvěznění – Czech" lang="cs" hreflang="cs" data-title="Barevné uvěznění" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Confinement" title="Confinement – German" lang="de" hreflang="de" data-title="Confinement" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Confinamiento_del_color" title="Confinamiento del color – Spanish" lang="es" hreflang="es" data-title="Confinamiento del color" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kolorkonservo" title="Kolorkonservo – Esperanto" lang="eo" hreflang="eo" data-title="Kolorkonservo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AD%D8%A8%D8%B3_%D8%B1%D9%86%DA%AF" title="حبس رنگ – Persian" lang="fa" hreflang="fa" data-title="حبس رنگ" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li 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interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Confinamento_dei_quark" title="Confinamento dei quark – Italian" lang="it" hreflang="it" data-title="Confinamento dei quark" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9B%D7%9C%D7%99%D7%90%D7%94_(%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94)" title="כליאה (פיזיקה) – Hebrew" lang="he" hreflang="he" data-title="כליאה (פיזיקה)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sz%C3%ADnbez%C3%A1r%C3%A1s" title="Színbezárás – Hungarian" lang="hu" hreflang="hu" data-title="Színbezárás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Confinement" title="Confinement – Dutch" lang="nl" hreflang="nl" data-title="Confinement" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AF%E3%82%A9%E3%83%BC%E3%82%AF%E3%81%AE%E9%96%89%E3%81%98%E8%BE%BC%E3%82%81" title="クォークの閉じ込め – Japanese" lang="ja" hreflang="ja" data-title="クォークの閉じ込め" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Confinement" title="Confinement – Low German" lang="nds" hreflang="nds" data-title="Confinement" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Uwi%C4%99zienie_koloru" title="Uwięzienie koloru – Polish" lang="pl" hreflang="pl" data-title="Uwięzienie koloru" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Confinamento_(f%C3%ADsica)" title="Confinamento (física) – Portuguese" lang="pt" hreflang="pt" data-title="Confinamento (física)" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Confinarea_culorii" title="Confinarea culorii – Romanian" lang="ro" hreflang="ro" 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mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Phenomenon in quantum chromodynamics</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Quark_confinement.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Quark_confinement.svg/350px-Quark_confinement.svg.png" decoding="async" width="350" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Quark_confinement.svg/525px-Quark_confinement.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Quark_confinement.svg/700px-Quark_confinement.svg.png 2x" data-file-width="546" data-file-height="280" /></a><figcaption>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.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Gluon_tube-color_confinement_animation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Gluon_tube-color_confinement_animation.gif/300px-Gluon_tube-color_confinement_animation.gif" decoding="async" width="300" height="178" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Gluon_tube-color_confinement_animation.gif/450px-Gluon_tube-color_confinement_animation.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/6/64/Gluon_tube-color_confinement_animation.gif 2x" data-file-width="504" data-file-height="299" /></a><figcaption>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.</figcaption></figure> <p>In <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">quantum chromodynamics</a> (QCD), <b>color confinement</b>, often simply called <b>confinement</b>, is the phenomenon that <a href="/wiki/Color_charge" title="Color charge">color-charged</a> particles (such as <a href="/wiki/Quark" title="Quark">quarks</a> and <a href="/wiki/Gluon" title="Gluon">gluons</a>) cannot be isolated, and therefore cannot be directly observed in normal conditions below the <a href="/wiki/Hagedorn_temperature" title="Hagedorn temperature">Hagedorn temperature</a> of approximately 2 <a href="/wiki/Tera-" class="mw-redirect" title="Tera-">tera</a><a href="/wiki/Kelvin" title="Kelvin">kelvin</a> (corresponding to energies of approximately 130–140 M<a href="/wiki/Electron_volt" class="mw-redirect" title="Electron volt">eV</a> per particle).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Quarks and gluons must clump together to form <a href="/wiki/Hadron" title="Hadron">hadrons</a>. The two main types of hadron are the <a href="/wiki/Meson" title="Meson">mesons</a> (one quark, one antiquark) and the <a href="/wiki/Baryon" title="Baryon">baryons</a> (three quarks). In addition, colorless <a href="/wiki/Glueball" title="Glueball">glueballs</a> 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.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Origin">Origin</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_confinement&action=edit&section=1" title="Edit section: Origin"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There is not yet an analytic proof of color confinement in any <a href="/wiki/Non-abelian_gauge_theory" class="mw-redirect" title="Non-abelian gauge theory">non-abelian gauge theory</a>. The phenomenon can be understood qualitatively by noting that the force-carrying <a href="/wiki/Gluon" title="Gluon">gluons</a> of QCD have color charge, unlike the photons of <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a> (QED). Whereas the <a href="/wiki/Electric_field" title="Electric field">electric field</a> between <a href="/wiki/Electric_charge" title="Electric charge">electrically charged</a> particles decreases rapidly as those particles are separated, the <a href="/wiki/Gluon_field" title="Gluon field">gluon field</a> 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.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Therefore, as two color charges are separated, at some point it becomes energetically favorable for a new quark–antiquark <a href="/wiki/Pair_production" title="Pair production">pair</a> 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 "<a href="/wiki/Jet_(particle_physics)" title="Jet (particle physics)">jets</a>" of many color-neutral particles (<a href="/wiki/Meson" title="Meson">mesons</a> and <a href="/wiki/Baryon" title="Baryon">baryons</a>), clustered together. This process is called <i><a href="/wiki/Hadronization" title="Hadronization">hadronization</a></i>, <i>fragmentation</i>, or <i>string breaking</i>. </p><p>The confining phase is usually defined by the behavior of the <a href="/wiki/Action_(physics)" title="Action (physics)">action</a> of the <a href="/wiki/Wilson_loop" title="Wilson loop">Wilson loop</a>, which is simply the path in <a href="/wiki/Spacetime" title="Spacetime">spacetime</a> 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 <a href="/wiki/Order_operator" title="Order operator">order operator</a> for confinement are thermal versions of Wilson loops known as <a href="/wiki/Polyakov_loop" title="Polyakov loop">Polyakov loops</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Confinement_scale">Confinement scale</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_confinement&action=edit&section=2" title="Edit section: Confinement scale"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The confinement scale or QCD scale is the scale at which the perturbatively defined strong coupling constant diverges. This is known as the <a href="/wiki/Landau_pole" title="Landau pole">Landau pole</a>. The confinement scale definition and value therefore depend on the <a href="/wiki/Renormalization" title="Renormalization">renormalization</a> scheme used. For example, in the <a href="/wiki/Minimal_subtraction_scheme" title="Minimal subtraction scheme">MS-bar scheme</a> and at 4-loop in the <a href="/wiki/Coupling_constant#Running_coupling" title="Coupling constant">running</a> of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha _{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a07a41fc35666ad575cd8f200c0c8c9b36e42d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.491ex; height:2.009ex;" alt="{\displaystyle \alpha _{s}}"></span>, the world average in the 3-flavour case is given by<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda _{\overline {MS}}^{(3)}=(332\pm 17)\,{\rm {{MeV}\,.}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>M</mi> <mi>S</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo>=</mo> <mo stretchy="false">(</mo> <mn>332</mn> <mo>±</mo> <mn>17</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">V</mi> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda _{\overline {MS}}^{(3)}=(332\pm 17)\,{\rm {{MeV}\,.}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86719742342ce5ccaed7b3f50f5b6c01e404c900" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:24.648ex; height:4.343ex;" alt="{\displaystyle \Lambda _{\overline {MS}}^{(3)}=(332\pm 17)\,{\rm {{MeV}\,.}}}"></span></dd></dl> <p>When the <a href="/wiki/Exact_renormalization_group_equation" class="mw-redirect" title="Exact renormalization group equation">renormalization group equation</a> is solved exactly, the scale is not defined at all.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (June 2022)">clarification needed</span></a></i>]</sup> It is therefore customary to quote the value of the strong coupling constant at a particular reference scale instead. </p><p>It is sometimes believed that the sole origin of confinement is the very large value of the strong coupling near the <a href="/wiki/Landau_pole" title="Landau pole">Landau pole</a>. This is sometimes referred as <i>infrared slavery</i> (a term chosen to contrast with the <a href="/wiki/Asymptotic_freedom" title="Asymptotic freedom">ultraviolet freedom</a>). It is however incorrect since in QCD the Landau pole is unphysical,<sup id="cite_ref-alpha_s_review_2016_7-0" class="reference"><a href="#cite_note-alpha_s_review_2016-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-alpha_s_DSE_2016_8-0" class="reference"><a href="#cite_note-alpha_s_DSE_2016-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> which can be seen by the fact that its position at the confinement scale largely depends on the chosen <a href="/wiki/Renormalization" title="Renormalization">renormalization</a> scheme, i.e., on a convention. Most evidences point to a moderately large coupling, typically of value 1-3 <sup id="cite_ref-alpha_s_review_2016_7-1" class="reference"><a href="#cite_note-alpha_s_review_2016-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> depending on the choice of renormalization scheme. In contrast to the simple but erroneous mechanism of <i>infrared slavery</i>, 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. </p> <div class="mw-heading mw-heading2"><h2 id="Models_exhibiting_confinement">Models exhibiting confinement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_confinement&action=edit&section=3" title="Edit section: Models exhibiting confinement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In addition to <a href="/wiki/Quantum_Chromodynamics" class="mw-redirect" title="Quantum Chromodynamics">QCD</a> in four spacetime dimensions, the two-dimensional <a href="/wiki/Schwinger_model" title="Schwinger model">Schwinger model</a> also exhibits confinement.<sup id="cite_ref-Wilson_1974_9-0" class="reference"><a href="#cite_note-Wilson_1974-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Compact <a href="/wiki/Abelian_group" title="Abelian group">Abelian</a> <a href="/wiki/Gauge_theory" title="Gauge theory">gauge theories</a> also exhibit confinement in 2 and 3 spacetime dimensions.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Confinement has been found in elementary excitations of magnetic systems called <a href="/wiki/Spinon" title="Spinon">spinons</a>.<sup id="cite_ref-Lake_et_al,_2009_11-0" class="reference"><a href="#cite_note-Lake_et_al,_2009-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>If the <a href="/wiki/Higgs_mechanism" title="Higgs mechanism">electroweak symmetry breaking</a> <a href="/wiki/Electroweak_scale" title="Electroweak scale">scale</a> 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 <a href="/wiki/Standard_Model" title="Standard Model">Standard Model</a> at lower energies, but dramatically different above symmetry breaking.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Models_of_fully_screened_quarks">Models of fully screened quarks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_confinement&action=edit&section=4" title="Edit section: Models of fully screened quarks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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 <a href="/wiki/Yang%E2%80%93Mills_theory" title="Yang–Mills theory">Yang–Mills theory</a> which provide full screening (by gluon fields) of the color charge of a quark have been found.<sup id="cite_ref-Cahill_1978_13-0" class="reference"><a href="#cite_note-Cahill_1978-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> However, such classical solutions do not take into account non-trivial properties of <a href="/wiki/QCD_vacuum" title="QCD vacuum">QCD vacuum</a>. Therefore, the significance of such full gluonic screening solutions for a separated quark is not clear. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_confinement&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Lund_string_model" title="Lund string model">Lund string model</a></li> <li><a href="/wiki/Gluon_field_strength_tensor" title="Gluon field strength tensor">Gluon field strength tensor</a></li> <li><a href="/wiki/Asymptotic_freedom" title="Asymptotic freedom">Asymptotic freedom</a></li> <li><a href="/wiki/Center_vortex" title="Center vortex">Center vortex</a></li> <li><a href="/wiki/Dual_superconductor_model" title="Dual superconductor model">Dual superconductor model</a></li> <li><a href="/wiki/Beta_function_(physics)" title="Beta function (physics)">Beta function (physics)</a></li> <li><a href="/wiki/Lattice_gauge_theory" title="Lattice gauge theory">Lattice gauge theory</a></li> <li><a href="/wiki/Yang%E2%80%93Mills_existence_and_mass_gap" title="Yang–Mills existence and mass gap">Yang–Mills existence and mass gap</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_confinement&action=edit&section=6" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBargerPhillips1997" class="citation book cs1">Barger, V.; 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