Color charge is a property of quarks and gluons
that is related to the particles' strong interactions
in the theory of quantum chromodynamics (QCD).
The "color charge" of quarks and gluons is
completely unrelated to the everyday meaning
of color. The term color and the labels red,
green, and blue became popular simply because
of the loose analogy to the primary colors.
Richard Feynman referred to his colleagues
as "idiot physicists" for choosing the confusing
name.Particles have corresponding antiparticles.
A particle with red, green, or blue charge
has a corresponding antiparticle in which
the color charge must be the anticolor of
red, green, and blue, respectively, for the
color charge to be conserved in particle-antiparticle
creation and annihilation. Particle physicists
call these antired, antigreen, and antiblue.
All three colors mixed together, or any one
of these colors and its complement (or negative),
is "colorless" or "white" and has a net color
charge of zero. Free particles have a color
charge of zero: baryons are composed of three
quarks, but the individual quarks can have
red, green, or blue charges, or negatives;
mesons are made from a quark and antiquark,
the quark can be any color, and the antiquark
will have the negative of that color. This
color charge differs from electric charge
in that electric charge has only one kind
of value. However color charge is also similar
to electric charge in that color charge also
has a negative charge corresponding to each
kind of value.
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 hadrons
in 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.
== Red, green, and blue ==
In quantum chromodynamics, 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 eight gluon colors for an explanation.
The following illustrates the coupling constants
for color-charged particles:
=== Field lines from color charges ===
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 fm). This effect confines
quarks within hadrons.
== Coupling constant and charge ==
In a quantum field theory, a coupling constant
and a 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 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 ϕ(x) is applied
in electrodynamics, then one finds (using
tensor index notation):
A
μ
→
A
μ
+
∂
μ
ϕ
(
x
)
{\displaystyle A_{\mu }\to A_{\mu }+\partial
_{\mu }\phi (x)}
,
ψ
→
exp
⁡
[
+
i
Q
ϕ
(
x
)
]
ψ
{\displaystyle \psi \to \exp[+iQ\phi (x)]\psi
}
and
ψ
¯
→
exp
⁡
[
−
i
Q
ϕ
(
x
)
]
ψ
¯
{\displaystyle {\overline {\psi }}\to \exp[-iQ\phi
(x)]{\overline {\psi }}}
where
A
μ
{\displaystyle A_{\mu }}
is the photon field, and ψ is the electron
field with Q = −1 (a bar over ψ denotes
its antiparticle — the positron). Since
QCD is a non-abelian theory, the representations,
and hence the color charges, are more complicated.
They are dealt with in the next section.
== 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 flavor 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
ψ
=
(
ψ
1
ψ
2
ψ
3
)
{\displaystyle \psi ={\begin{pmatrix}\psi
_{1}\\\psi _{2}\\\psi _{3}\end{pmatrix}}}
and
ψ
¯
=
(
ψ
¯
1
∗
ψ
¯
2
∗
ψ
¯
3
∗
)
.
{\displaystyle {\overline {\psi }}={\begin{pmatrix}{\overline
{\psi }}_{1}^{*}\\{\overline {\psi }}_{2}^{*}\\{\overline
{\psi }}_{3}^{*}\end{pmatrix}}.}
The gluon contains an octet of fields (see
gluon field), and belongs to the adjoint representation
(8), and can be written using the Gell-Mann
matrices as
A
μ
=
A
μ
a
λ
a
.
{\displaystyle {\mathbf {A} }_{\mu }=A_{\mu
}^{a}\lambda _{a}.}
(there is an implied summation over a = 1,
2, ... 8). 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
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. The website
arXiv turns up 40+ results for "Casimir scaling
color", and two results for "color charge
quadratic Casimir operator", one paper in
particular "About the Casimir scaling hypothesis"
explains: "A lattice calculation shows that
the Casimir scaling hypothesis is well verified
in QCD, that is to say that the potential
between two opposite color charges in a color
singlet is proportional to the value of the
quadratic Casimir operator.".
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 → U ψ,
where U is a 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.
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 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 → gi j +
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.
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.
== See also ==
Color confinement
Gluon field strength tensor
Electric charge
