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| {{Multiple issues|{{More footnotes|date=March 2009}}{{Page numbers needed|date=March 2009}}}}
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| {{Standard model of particle physics}}
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| In [[particle physics]], '''color charge''' is a property of [[quark]]s and [[gluon]]s that is related to the particles' [[strong interaction]]s in the theory of [[quantum chromodynamics]] (QCD). Color charge has analogies with the notion of [[electric charge]] of particles, for example it is a [[conservation law|conserved]] charge, but because of the mathematical complications of QCD, there are many technical differences.
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| The "color charge" of quarks and gluons is completely unrelated to visual perception of [[color]],<ref>{{Citation|last=Feynman |first=Richard |authorlink=Richard Feynman |title=[[QED: The Strange Theory of Light and Matter]] |year=1985 |publisher=Princeton University Press |isbn=0-691-08388-6 |page=136 |quote=The idiot physicists, unable to come up with any wonderful Greek words anymore, call this type of polarization by the unfortunate name of 'color,' which has nothing to do with color in the normal sense.}}</ref> because it is a property that has almost no manifestation at distances above the size of an [[atomic nucleus]]. The term ''color'' was chosen because the charge responsible for the strong force between particles can be analogized to the three [[primary color]]s of light: red, green, and blue.<ref>Close (2007)</ref> Another color scheme is "red, yellow, and blue",<ref>{{cite book |author=R. Penrose| title=[[The Road to Reality]]| publisher= Vintage books|pages=648| year=2005 | isbn=978-00994-40680}}</ref> for analogy to paint. The analogy is only in the name, and the way colors mix, nothing more.
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| All three colors mixed together, or any one of these colors and its [[Complementary colors|complement (or negative)]], is "colorless" or "white". This is how the color charge on particles behaves. A combination of three particles, one with red charge, another with green charge, and another blue charge, has a net color charge of zero ("colorless"), and this combination does not interact with other color charges. Particles have corresponding [[antiparticle]]s. A particle with red, green, or blue charge has a corresponding [[antiparticle]] in which the color charge must be the color complement of red, green, and blue, respectively, for the color charge to be conserved in particle-antiparticle [[Particle creation|creation]] and [[annihilation]]. Particle physicists call these antired, antigreen, and antiblue. In all, color charge has three values, and three negatives.
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| All free particles have a color charge of zero. [[Baryon]]s are composed of three quarks, and have a net color charge of zero but the individual quarks can have red, green, or blue charges, or negatives. [[Meson]]s are made from a quark and antiquark, and again have a net color charge of zero, but the quark can be any color, and the antiquark will have the negative of that color.
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| By comparison, the electromagnetic charge has only one kind of value. Positive and negative electrical charges are the same kind of charge, as they only differ by the sign. A particle with positive charge has a corresponding antiparticle with a negative charge.
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| Historically, shortly after the existence of quarks was first proposed in 1964, [[Oscar W. Greenberg]] introduced the notion of color charge to explain how quarks could coexist inside some [[hadron]]s in [[quark model#The discovery of colour|otherwise identical quantum states]] without violating the [[Pauli exclusion principle]]. The theory of quantum chromodynamics has been under development since the 1970s and constitutes an important component of the [[Standard Model]] of particle physics.{{Citation needed|date=October 2008}}
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| ==Red, green, and blue==
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| In QCD, a quark's color can take one of three values or charges, red, green, and blue. An antiquark can take one of three anticolors, called antired, antigreen, and antiblue (represented as cyan, magenta and yellow, respectively). Gluons are mixtures of two colors, such as red and antigreen, which constitutes their color charge. QCD considers eight gluons of the possible nine color–anticolor combinations to be unique; see ''[[Gluon#Eight gluon colors|eight gluon colors]]'' for an explanation.
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| The following illustrates the [[coupling constant]]s for color-charged particles:
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| <gallery> | |
| Image:Quark_Colors.svg|The quark colors (red, green, blue) combine to be colorless
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| Image:Quark_Anticolors.svg|The quark anticolors (antired, antigreen, antiblue) also combine to be colorless
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| </gallery> | |
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| <gallery> | |
| Image:QCD Intermediate 1.png|A hadron with 3 quarks (red, green, blue) before a color change
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| Image:QCD Intermediate 2.png|Blue quark emits a blue-antigreen gluon
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| Image:QCD Intermediate 3.png|Green quark has absorbed the blue-antigreen gluon and is now blue; color remains conserved
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| File:Neutron QCD Animation.gif|An animation of the interaction inside a neutron. The gluons are represented as circles with the color charge in the center and the anti-color charge on the outside.
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| </gallery>
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| ===Field lines from color charges===
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| {{main|Field (physics)}}
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| Analogous to an [[electric field]] and electric charges, the strong force acting between color charges can be depicted using field lines. However, the color field lines do not arc outwards from one charge to another as much, because they are pulled together tightly by gluons (within 1 [[femtometre|fm]]).<ref>{{Citation|title=Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles|edition=2nd|author=R. Resnick, R. Eisberg|publisher=John Wiley & Sons|year=1985|page=684|isbn=978-0-471-87373-0}}</ref> This effect [[Color confinement|confines]] [[quark]]s within [[hadron]]s.
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| [[File:Qcd fields field (physics).svg|400px|center|thumb|Fields due to color charges, like in [[quark]]s ('''G''' is the [[gluon field strength tensor]]). These are "colorless" combinations. '''Top:''' Color charge has "ternary neutral states" as well as binary neutrality (analogous to [[electric charge]]). '''Bottom:''' Quark/antiquark combinations.<ref>{{Citation |title=McGraw Hill Encyclopaedia of Physics |first1=C.B. |last1= Parker|edition=2nd|publisher=Mc Graw Hill|year=1994|isbn=0-07-051400-3}}</ref><ref>{{Citation |author= M. Mansfield, C. O’Sullivan|title= Understanding Physics|edition= 4th |year= 2011|publisher= John Wiley & Sons|isbn=978-0-47-0746370}}</ref>]]
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| ==Coupling constant and charge==
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| In a [[quantum field theory]], a [[coupling constant]] and a [[coupling constant#Charge, color charge, etc|charge]] are different but related notions. The coupling constant sets the magnitude of the force of interaction; for example, in [[quantum electrodynamics]], the [[fine-structure constant]] is a coupling constant. The charge in a [[gauge theory]] has to do with the way a particle transforms under the gauge symmetry; i.e., its [[group representation|representation]] under the gauge group. For example, the [[electron]] has charge −1 and the [[positron]] has charge +1, implying that the gauge transformation has opposite effects on them in some sense. Specifically, if a local [[gauge transformation]] {{math|''ϕ''(''x'')}} is applied in electrodynamics, then one finds (using [[tensor index notation]]):
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| ::<math>A_\mu\to A_\mu+\partial_\mu\phi(x)</math>, <math>\psi\to \exp[iQ\phi(x)]\psi</math> and <math>\overline\psi\to \exp[-iQ\phi(x)]\overline\psi</math>
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| where <math>A_\mu</math> is the [[photon]] field, and {{mvar|ψ}} is the electron field with {{math|1=''Q'' = −1}} (a bar over {{mvar|ψ}} denotes its antiparticle — the positron). Since QCD is a [[non-abelian group|non-abelian]] theory, the representations, and hence the color charges, are more complicated. They are dealt with in the next section.
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| ==Quark and gluon fields and color charges==
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| [[File:Strong force charges.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).]]
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| In QCD the gauge group is the non-abelian group [[SU(3)]]. The ''[[coupling constant#Running coupling|running coupling]]'' is usually denoted by α<sub>s</sub>. Each [[flavor (particle physics)|flavor]] of quark belongs to the [[fundamental representation]] ('''3''') and contains a triplet of fields together denoted by {{mvar|ψ}}. The [[antiparticle|antiquark]] field belongs to the [[Hermitian conjugate|complex conjugate representation]] ('''3<sup>*</sup>''') and also contains a triplet of fields. We can write
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| ::<math>\psi = \begin{pmatrix}\psi_1\\ \psi_2\\ \psi_3\end{pmatrix}</math> and <math>\overline\psi = \begin{pmatrix}{\overline\psi}^*_1\\ {\overline\psi}^*_2\\ {\overline\psi}^*_3\end{pmatrix}.</math>
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| The gluon contains an octet of fields (see [[gluon field]]), and belongs to the [[adjoint representation of a Lie group|adjoint representation]] ('''8'''), and can be written using the [[Gell-Mann matrices]] as
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| ::<math>{\mathbf A}_\mu = A_\mu^a\lambda_a.</math>
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| (there is an [[Einstein notation|implied summation]] over ''a'' = 1, 2, ... 8). All other [[subatomic particle|particle]]s belong to the [[trivial representation]] ('''1''') of color [[SU(3)]]. The '''color charge''' of each of these fields is fully specified by the representations. Quarks have a color charge of red, green or blue and antiquarks have a color charge of antired, antigreen or antiblue. Gluons have a combination of two color charges (one of red, green or blue and one of antired, antigreen and antiblue) in a superposition of states which are given by the Gell-Mann matrices. All other particles have zero color charge. Mathematically speaking, the color charge of a particle is the value of a certain quadratic [[Casimir operator]] in the representation of the particle.
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| In the simple language introduced previously, the three indices "1", "2" and "3" in the quark triplet above are usually identified with the three colors. The colorful language misses the following point. A gauge transformation in color SU(3) can be written as {{math|''ψ'' → ''U'' ''ψ''}}, where {{mvar|U}} is a {{math|3 × 3}} matrix which belongs to the group SU(3). Thus, after gauge transformation, the new colors are linear combinations of the old colors. In short, the simplified language introduced before is not gauge invariant.
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| [[Image:vertex.png|150px|left|Color-line representation of QCD vertex]]
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| Color charge is conserved, but the book-keeping involved in this is more complicated than just adding up the charges, as is done in quantum electrodynamics. One simple way of doing this is to look at the interaction vertex in QCD and replace it by a color-line representation. The meaning is the following. Let {{mvar|ψ<sub>i</sub>}} represent the {{mvar|i}}-th component of a quark field (loosely called the {{mvar|i}}-th color). The ''color'' of a gluon is similarly given by {{math|'''A'''}} which corresponds to the particular Gell-Mann matrix it is associated with. This matrix has indices {{mvar|i}} and {{mvar|j}}. These are the ''color labels'' on the gluon. At the interaction vertex one has {{math|q<sub>''i''</sub> → g<sub>''i'' ''j''</sub> + q<sub>''j''</sub>}}. The '''color-line''' representation tracks these indices. Color charge conservation means that the ends of these color-lines must be either in the initial or final state, equivalently, that no lines break in the middle of a diagram.
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| [[Image:3gluon.png|150px|right|Color-line representation of 3-gluon vertex]]
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| Since gluons carry color charge, two gluons can also interact. A typical interaction vertex (called the three gluon vertex) for gluons involves g + g → g. This is shown here, along with its color-line representation. The color-line diagrams can be restated in terms of conservation laws of color; however, as noted before, this is not a gauge invariant language. Note that in a typical [[non-abelian gauge theory]] the [[gauge boson]] carries the charge of the theory, and hence has interactions of this kind; for example, the [[W boson]] in the electroweak theory. In the electroweak theory, the W also carries electric charge, and hence interacts with a photon.
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| ==See also==
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| {{Wiktionary}}
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| * [[Color confinement]]
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| * [[Gluon field strength tensor]]
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| ==References==
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| {{Reflist}}
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| ==Further reading==
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| *{{Citation |first=Howard |last=Georgi |title=Lie algebras in particle physics |year=1999 |location= |publisher=Perseus Books Group |isbn=0-7382-0233-9 }}.
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| *{{Citation |first=David J. |last=Griffiths |title=Introduction to Elementary Particles |year=1987 |publisher=John Wiley & Sons |location=New York |isbn=0-471-60386-4 }}.
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| *{{Citation |first=J. Richard |last=Christman |url=http://35.9.69.219/home/modules/pdf_modules/m283.pdf |title=Colour and Charm |year=2001 |work=[http://www.physnet.org Project PHYSNET] document MISN-0-283 }}.
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| *{{Citation |first=Stephen |last=Hawking |title=A Brief History of Time |year=1998 |location= |publisher=Bantam Dell Publishing Group |isbn=978-0-553-10953-5 }}.
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| *{{Citation |first=Frank |last=Close |title=The New Cosmic Onion |year=2007 |location= |publisher=Taylor & Francis |isbn=1-58488-798-2 }}.
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| {{DEFAULTSORT:Color Charge}}
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| [[Category:Gluons]]
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| [[Category:Quantum chromodynamics]]
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