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 meanings of
color
Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are assoc ...
and
charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* ''Charge!!'', an album by The Aqu ...
. The term ''color'' and the labels red, green, and blue became popular simply because of the loose analogy to the
primary color
A set of primary colors or primary colours (see spelling differences) consists of colorants or colored lights that can be mixed in varying amounts to produce a gamut of colors. This is the essential method used to create the perception of a ...
s.
Some particles have corresponding
antiparticle
In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
s. A particle with red, green, or blue charge has a corresponding
antiparticle
In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
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
Creation may refer to:
Religion
*''Creatio ex nihilo'', the concept that matter was created by God out of nothing
* Creation myth, a religious story of the origin of the world and how people first came to inhabit it
* Creationism, the belief tha ...
and
annihilation
In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons. The total energy ...
. 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. Due to a property of the strong interaction called
color confinement
In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color-charged particles (such as quarks and gluons) cannot be isolated, and therefore cannot be directly observed in normal conditions b ...
,
free particle
In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies. In classical physics, this means the particle is present in a "field-free" space. I ...
s must have a color charge of zero: a
baryon
In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classif ...
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
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, ...
is made from one quark and one antiquark; the quark can be any color, and the antiquark has the matching anticolor.
Shortly after the existence of quarks was first proposed in 1964,
Oscar W. Greenberg
Oscar Wallace Greenberg (born February 18, 1932) is an American physicist and professor at University of Maryland College of Computer, Mathematical, and Natural Sciences. In 1964, he posited the existence of quarks that obeyed parastatistics as ...
introduced the notion of color charge to explain how quarks could coexist inside some
hadron
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the e ...
s in
otherwise identical quantum states without violating the
Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulat ...
. 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 (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 ''
eight gluon colors'' for an explanation.
The following illustrates the
coupling constants for color-charged particles:
Image:Quark_Colors_with_white.svg, The quark colors (red, green, blue) combine to be colorless
Image:Quark_Anticolors.svg, The quark anticolors (antired, antigreen, antiblue) also combine to be colorless
Image:QCD Intermediate 1.png, A hadron with 3 quarks (red, green, blue) before a color change
Image:QCD Intermediate 2.png, Blue quark emits a blue–antigreen gluon
Image:QCD Intermediate 3.png, Green quark has absorbed the blue–antigreen gluon and is now blue; color remains conserved
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.
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
Confines is a town and municipality in the Santander Department in northeastern Colombia.
External links
*
Municipalities of Santander Department
{{Santander-geo-stub ...
quarks within
hadron
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the e ...
s.
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
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
, the
fine-structure constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between el ...
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
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
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
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie group ...
is applied in electrodynamics, then one finds (using
tensor index notation
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be c ...
):
where
is the
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
field, and is the electron field with (a bar over 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
![Strong force charges](https://upload.wikimedia.org/wikipedia/commons/b/b6/Strong_force_charges.svg)
In QCD the gauge group is the non-abelian group
SU(3)
In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1.
The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the specia ...
. The ''
running coupling
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between tw ...
'' is usually denoted by
. Each
flavor
Flavor or flavour is either the sensory perception of taste or smell, or a flavoring in food that produces such perception.
Flavor or flavour may also refer to:
Science
*Flavors (programming language), an early object-oriented extension to Lis ...
of quark belongs to the
fundamental representation In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible representation, irreducible finite-dimensional representation of a semisimple Lie algebra, semisimple Lie group
or Lie algebra whose highest weig ...
(3) and contains a triplet of fields together denoted by
. The
antiquark field belongs to the
complex conjugate representation
In mathematics, if is a group and is a representation of it over the complex vector space , then the complex conjugate representation is defined over the complex conjugate vector space as follows:
: is the conjugate of for all in .
is ...
(3
*) and also contains a triplet of fields. We can write
::
and
The gluon contains an octet of fields (see
gluon field
In theoretical particle physics, the gluon field is a four-vector field characterizing the propagation of gluons in the strong interaction between quarks. It plays the same role in quantum chromodynamics as the electromagnetic four-potential in ...
), and belongs to the
adjoint representation
In mathematics, the adjoint representation (or adjoint action) of a Lie group ''G'' is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if ''G'' is G ...
(8), and can be written using the
Gell-Mann matrices
The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics.
They span the Lie algebra of the SU(3) group in t ...
as
::
(there is an
implied summation over ''a'' = 1, 2, ... 8). All other
particle
In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass.
They vary greatly in size or quantity, from ...
s belong to the
trivial representation In the mathematical field of representation theory, a trivial representation is a representation of a group ''G'' on which all elements of ''G'' act as the identity mapping of ''V''. A trivial representation of an associative or Lie algebra is a ...
(1) of color
SU(3)
In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1.
The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the specia ...
. 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, or 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 mathematics, a Casimir element (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping algebra of a Lie algebra. A prototypical example is the squared angular momentum operato ...
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
, where
is a 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
represent the -th component of a quark field (loosely called the -th color). The ''color'' of a gluon is similarly given by
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.
![3gluon](https://upload.wikimedia.org/wikipedia/commons/a/a8/3gluon.png)
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
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations ( Lie group ...
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
In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color-charged particles (such as quarks and gluons) cannot be isolated, and therefore cannot be directly observed in normal conditions b ...
*
Gluon field strength tensor
*
Electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
References
Further reading
*.
*.
*.
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{{DEFAULTSORT:Color Charge
Gluons
Quantum chromodynamics