Color charge

 ( Gluons ) 

Han and Nambu initially designated this degree of freedom by the group SU(3), but it was referred to in later papers as "the three-triplet model". One feature of the model (which was originally preferred by Han and Nambu) was that it permitted integrally charged quarks, as well as the fractionally charged quarks initially proposed by Zweig and Gell-Mann.

Somewhat later, in the early 1970s, Gell-Mann, in several conference talks, coined the name color to describe the internal degree of freedom of the three-triplet model, and advocated a new field theory, designated as quantum chromodynamics (QCD) to describe the interaction of quarks and gluons within hadrons. In Gell-Mann's QCD, each quark and gluon has fractional electric charge, and carries what came to be called color charge in the space of the color degree of freedom.

All three colors mixed together, all three anticolors mixed together, or a combination of a color and its anticolor is "colorless" or "white" and has a net color charge of zero. Due to a property of the strong interaction called color confinement, must have a color charge of zero.

A baryon is composed of three quarks, which must be one each of red, green, and blue colors; likewise an antibaryon is composed of three antiquarks, one each of antired, antigreen and antiblue. A meson is made from one quark and one antiquark; the quark can be any color, and the antiquark has the matching anticolor.

The following illustrates the coupling constants for color-charged particles:

$\backslash psi\; =\; \backslash begin\{pmatrix\}\backslash psi\_1\backslash \backslash \; \backslash psi\_2\backslash \backslash \; \backslash psi\_3\backslash end\{pmatrix\}$  and  $\backslash overline\backslash psi\; =\; \backslash begin\{pmatrix\}\{\backslash overline\backslash psi\}^*\_1\backslash \backslash \; \{\backslash overline\backslash psi\}^*\_2\backslash \backslash \; \{\backslash overline\backslash psi\}^*\_3\backslash end\{pmatrix\}.$

$\{\backslash mathbf\; A\}\_\backslash mu\; =\; A\_\backslash mu^a\backslash lambda\_a.$

The gluons corresponding to $\backslash lambda\_3$ and $\backslash lambda\_8$ are sometimes described as having "zero charge" (as in the figure). Formally, these states are written as

$g\_3\; =\; \backslash frac\{1\}\{\backslash sqrt\{2\}\}\; (r\backslash overline\{r\}-b\backslash overline\{b\})$ and $g\_8\; =\; \backslash frac\{1\}\{\backslash sqrt\{6\}\}\; (r\backslash overline\{r\}+b\backslash overline\{b\}-2g\backslash overline\{g\})$

Mathematically speaking, the color charge of a particle is the value of a certain quadratic Casimir operator in the representation of the particle.

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 $\backslash psi\; \backslash to\; U\; \backslash psi$, where $U$ is a matrix that 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.

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 $\backslash psi\_i$ represent the th component of a quark field (loosely called the th color). The color of a gluon is similarly given by $\backslash mathbf\{A\}$, which corresponds to the particular Gell-Mann matrix it is associated with. This matrix has indices and . These are the color labels on the gluon. At the interaction vertex one has . 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.

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.

• Color confinement
• Gluon field strength tensor
• Electric charge

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