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| {{Merge from|Pseudo-Goldstone boson|discuss=Talk:Chiral symmetry breaking#Merger proposal|date=February 2013}}
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| {{Main|Chiral symmetry}}
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| In [[particle physics]], '''chiral symmetry breaking''' is an example of [[spontaneous symmetry breaking]] affecting the [[chiral symmetry]] of a [[gauge theory]] such as [[Quantum Chromodynamics]], the [[quantum field theory]] of the [[strong interactions]].
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| The principal and manifest consequence of this symmetry breaking is the generation of 99% of the mass of [[nucleons]], and hence the bulk of all visible matter, out of very light [[quarks]].<ref>Ta-Pei Cheng and Ling-Fong Li, ''Gauge Theory of Elementary Particle Physics'', (Oxford 1984) ISBN 978-0198519614; {{cite doi|10.1063/1.882879|noedit}}</ref> For example, for the proton, of mass ''m<sub>p</sub>''= 938 MeV, the bound quarks, with ''m<sub>u</sub>'' ≈ 2 MeV , ''m<sub>d</sub>'' ≈ 5 MeV, only contribute about 9 MeV to its mass, the bulk of it arising out of QCD chiral symmetry breaking, instead.<ref>This is a rough formal wisecrack. The actual chiral limit of the nucleon mass is about 880 MeV, cf. {{cite doi|10.1103/PhysRevD.73.114510|noedit}}.</ref>
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| [[Yoichiro Nambu]] was awarded the 2008 Nobel prize in physics for his understanding of this phenomenon.
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| The origin of the symmetry breaking may be described as an analog to [[magnetization]], the [[fermion condensate]] ([[vacuum condensate]] of [[bilinear form|bilinear]] expressions involving the [[quark]]s in the [[QCD vacuum]]),
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| :<math>\langle \bar{q}^a_R q^b_L \rangle = v \delta^{ab} ~,</math>
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| formed through nonperturbative action of QCD gluons, with ''v'' ≈ −(250 MeV)<sup>3</sup>. It is clear that this cannot be preserved under an isolated ''L'' or ''R'' rotation. The [[pion decay constant]], ''f''<sub>π</sub> ≈ 93 MeV, may be viewed as a measure of the strength of the chiral symmetry breaking.<ref>{{Cite book |last1=Peskin |first1=Michael |last2=Schroeder |first2=Daniel | title = An Introduction to Quantum Field Theory | publisher = Westview Press | year = 1995 | pages = 670 | isbn = 0-201-50397-2}}</ref>
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| For two light quarks, ''u'' and ''d'', the symmetry of the QCD Lagrangian called ''[[chiral symmetry]]'', and denoted as <math>U(2)_L \times U(2)_R</math>, can be decomposed into
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| :<math>SU(2)_L \times SU(2)_R \times U(1)_V \times U(1)_A ~.</math> | |
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| The quark condensate spontaneously breaks the <math>SU(2)_L \times SU(2)_R</math> down to the diagonal vector subgroup ''SU(2)<sub>V</sub>'', known as [[isospin]]. The resulting effective theory of baryon bound states of QCD (which describes protons and neutrons), then, has mass terms for these, disallowed by the original linear realization of the chiral symmetry, but allowed by the [[nonlinear realization|nonlinear]] (spontaneously broken) realization thus achieved as a result of the strong interactions.<ref>J Donoghue, E Golowich and B Holstein, ''Dynamics of the Standard Model'', ( Cambridge University Press, 1994) ISBN 9780521476522 .</ref>
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| The Nambu-[[Goldstone bosons]] corresponding to the three broken generators are the three [[pions]], charged and neutral. (More precisely, because of small quark masses which make this chiral symmetry only approximate, the pions are [[Pseudo-Goldstone boson]]s instead, with a nonzero, but still untypically small mass,<ref>{{cite doi|10.1103/PhysRev.175.2195|noedit}}</ref> ''m''<sub>π</sub> ≈ √{{overline|''v m''}}<sub>q</sub> / ''f''<sub>π</sub> .
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| For three quarks, ''u, d, s'', instead, the flavor-chiral symmetries likewise decompose to <math>SU(3)_L \times SU(3)_R \times U(1)_V \times U(1)_A</math>. The chiral symmetry broken is now the nondiagonal part of the respective <math>SU(3)_L \times SU(3)_R</math>; so, then, eight axial generators, corresponding to the eight light [[pseudoscalar meson]]s. The remaining eight unbroken vector generators constitute the manifest standard [[Eightfold Way (physics)|"Eightfold Way"]] flavor symmetries.
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| ==References==
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| <references/>
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| [[Category:Quantum chromodynamics]]
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| [[Category:Quantum field theory]]
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Hello. Let me introduce the author. Her name is Refugia Shryock. Hiring is his profession. Years ago we moved to Puerto Rico and my family members loves it. The thing she adores most is physique building and now she is attempting to earn cash with it.
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