Color charge is the gauge group charge of Quantum chromodynamics, associated with its symmetry. A quark transforms in the fundamental three-dimensional representation, an antiquark in its conjugate, and a lepton is a singlet. The word color is a label for this charge, unrelated to visible light.
The group-theoretic tensor multiplying the kinematic part of a Feynman diagram involving color charge. It is obtained by contracting internal indices among gauge generators, invariant tensors and structure constants of a Lie algebra. For instance, one gluon exchange on a single quark line contributes ; averaging or summing the squared tensor over external colour labels gives the corresponding color average in a squared scattering amplitude.
A quark-gluon Feynman vertex whose initial and final quark have the same chosen color charge basis label. Such vertices exist: the diagonal Gell-Mann matrices act nontrivially on the red basis vector. Their gluons are traceless colour-octet combinations, not colour singlets. A ninth singlet generator proportional to the identity is absent from SU(3).
A uniform incoherent initial mixture of two independently prepared fundamental color charges requires an average over their initial possibilities, together with a sum over unobserved final color charges. This differs from preparing a coherent color singlet. For quark-antiquark annihilation through one vector in the adjoint representation, gives . For the exchange contraction , by the SU(N) fundamental completeness relation. The negative overlap reverses the sign of the corresponding Abelian interference term.
In distinct-flavour quark annihilation, the one-photon exchange color charge tensor is , whereas the one-gluon tensor is . Their inner product after the external color charge sum is , since the fundamental gauge generators of are traceless. Thus the averaged squared scattering amplitude has no leading electromagnetic–strong interference term for this process. Fixed external color charge components, or processes with different exchange pairings, need not share this cancellation.
A colour singlet transforms in the trivial representation of the SU(3) colour group. Global colour rotations leave it invariant, and its colour generators annihilate it. A three-quark colour singlet uses the completely antisymmetric colour tensor; a quark–antiquark singlet contracts their colour indices.
For a colorless parent decaying through a color-diagonal interaction into a quark and antiquark, the three orthogonal matching-color states add incoherently. The inclusive flavor decay width is times the one-color width. In a parton scattering rate, an initial color average instead cancels the matching final color sum.
