Color charge

In particle physics, color charge is a property of quarks and gluons which are related to their strong interactions in the context of quantum chromodynamics (QCD). This has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD, there are many technical differences. The "color" of quarks and gluons have nothing to do with the visual perception of color, but is a whimsical name for a property which has almost no manifestation at distances above the size of an atomic nucleus.

Quark and gluon fields and color charges

In QCD the gauge group is the non-Abelian group SU(3). The running coupling is usually denoted by αs. Each flavour of quark belongs to the fundamental representation (3) and contains a triplet of fields together denoted by ψ. The antiquark field belongs to the complex conjugate representation (3*) and also contains a triplet of fields. We can write

Related Topics:
SU(3) - Running coupling - Flavour - Fundamental representation - Representation

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::psi = egin{pmatrix}psi_1\ psi_2\ psi_3end{pmatrix}  and  overlinepsi = egin{pmatrix}overlinepsi^*_1\ overlinepsi^*_2\ overlinepsi^*_3end{pmatrix}

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The gluon contains an octet of fields, belongs to the adjoint representation (8), and can be written using the Gell-Mann matrices as

Related Topics:
Adjoint representation - Gell-Mann matrices

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::{mathbf A}_mu = A_mu^alambda_a.

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All other particles 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 and antiquarks have color charge 4/3, whereas gluons have color charge 8. All other particles have zero colour charge. Mathematically speaking, the color charge of a particle is the value of a certain quadratic Casimir operator in the representation of the particle.

Related Topics:
Particle - Trivial representation - SU(3) - Casimir operator

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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 ψ → Uψ, where U is a 3X3 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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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

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colour line representation. The meaning is the following. Let ψi represent the i-th component of a quark field (loosely called the i-th color). The color of a gluon is similarly given by a which corresponds to the particular Gell-Mann matrix it is associated with. This matrix has indices i and j. These are the color labels on the gluon. At the interaction vertex one has qi→gij+qj. 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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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.

Related Topics:
Gauge boson - Electroweak theory

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