In
quantum chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type ...
(QCD), color confinement, often simply called confinement, is the phenomenon that
color-charged particles (such as
quark
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly ...
s and
gluon
A gluon ( ) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles. Gluons bind ...
s) cannot be isolated, and therefore cannot be directly observed in normal conditions below the
Hagedorn temperature of approximately 2
tera
TERA is a shielded twisted pair connector for use with Category 7 twisted-pair data cables, developed by The Siemon Company and standardised in 2003 by the International Electrotechnical Commission (IEC) with the reference IEC 61076-3-104.
Th ...
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...
(corresponding to energies of approximately 130–140 MeV per particle). Quarks and gluons must clump together to form
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 ...
s. The two main types of hadron are the
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, ...
s (one quark, one antiquark) and the
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 classifie ...
s (three quarks). In addition, colorless
glueballs formed only of gluons are also consistent with confinement, though difficult to identify experimentally. Quarks and gluons cannot be separated from their parent hadron without producing new hadrons.
Origin
There is not yet an analytic proof of color confinement in any
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 grou ...
. The phenomenon can be understood qualitatively by noting that the force-carrying
gluon
A gluon ( ) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles. Gluons bind ...
s of QCD have color charge, unlike the photons of
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 ...
(QED). Whereas the
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field ...
between
electrically charged
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 respectiv ...
particles decreases rapidly as those particles are separated, the
gluon field between a pair of color charges forms a narrow
flux tube (or string) between them. Because of this behavior of the gluon field, the strong force between the particles is constant regardless of their separation.
Therefore, as two color charges are separated, at some point it becomes energetically favorable for a new quark–antiquark
pair to appear, rather than extending the tube further. As a result of this, when quarks are produced in particle accelerators, instead of seeing the individual quarks in detectors, scientists see "
jets" of many color-neutral particles (
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, ...
s and
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 classifie ...
s), clustered together. This process is called ''
hadronization
Hadronization (or hadronisation) is the process of the formation of hadrons out of quarks and gluons. There are two main branches of hadronization: quark-gluon plasma (QGP) transformation and colour string decay into hadrons. The transformation o ...
'', ''fragmentation'', or ''string breaking''.
The confining phase is usually defined by the behavior of the
action of the
Wilson loop, which is simply the path in
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
traced out by a quark–antiquark pair created at one point and annihilated at another point. In a non-confining theory, the action of such a loop is proportional to its perimeter. However, in a confining theory, the action of the loop is instead proportional to its area. Since the area is proportional to the separation of the quark–antiquark pair, free quarks are suppressed. Mesons are allowed in such a picture, since a loop containing another loop with the opposite orientation has only a small area between the two loops. At non-zero temperatures, the
order operator
In quantum field theory, an order operator or an order field is a quantum field version of Landau's order parameter whose expectation value characterizes phase transitions. There exists a dual version of it, the disorder operator or disorder ...
for confinement are thermal versions of Wilson loops known as
Polyakov loop
In quantum field theory, the Polyakov loop is the thermal analogue of the Wilson loop, acting as an order parameter for confinement in pure gauge theories at nonzero temperatures. In particular, it is a Wilson loop that winds around the compa ...
s.
Confinement scale
The confinement scale or QCD scale is the scale at which the perturbatively defined strong coupling constant diverges. This is known as the
Landau pole
In physics, the Landau pole (or the Moscow zero, or the Landau ghost) is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite. Such a possibility was pointed out by the phy ...
. The confinement scale definition and value therefore depend on the
renormalization scheme used. For example, in the MS-bar scheme and at 4-loop in the
running
Running is a method of terrestrial locomotion allowing humans and other animals to move rapidly on foot. Running is a type of gait characterized by an aerial phase in which all feet are above the ground (though there are exceptions). This i ...
of
, the world average in the 3-flavour case is given by
:
When the
renormalization group equation is solved exactly, the scale is not defined at all. It is therefore customary to quote the value of the strong coupling constant at a particular reference scale instead.
It is sometimes believed that the sole origin of confinement is the very large value of the strong coupling near the
Landau pole
In physics, the Landau pole (or the Moscow zero, or the Landau ghost) is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite. Such a possibility was pointed out by the phy ...
. This is sometimes referred as ''infrared slavery'' (a term chosen to contrast with the
ultraviolet freedom). It is however incorrect since in QCD the Landau pole is unphysical,
[A. Deur, S. J. Brodsky and G. F. de Teramond, (2016) “The QCD Running Coupling”](_blank)
Prog. Part. Nucl. Phys. 90, 1[D. Binosi, C. Mezrag, J. Papavassiliou, C. D. Roberts and J. Rodriguez-Quintero, (2017) “Process-independent strong running coupling”](_blank)
Phys. Rev. D 96, no. 5, 054026 which can be seen by the fact that its position at the confinement scale largely depends on the choice
renormalization scheme, i.e. on a convention. Most evidences point to a moderately large coupling, typically of value 1-3
depending of the choice of renormalization scheme. In contrast to the simple but erroneous mechanism of ''infrared slavery'', a large coupling is but one ingredient for color confinement, the other one being that gluons are color-charged and
can therefore collapse into gluon tubes.
Models exhibiting confinement
In addition to
QCD
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type o ...
in four spacetime dimensions, the two-dimensional
Schwinger model also exhibits confinement.
[
] Compact
Abelian
Abelian may refer to:
Mathematics Group theory
* Abelian group, a group in which the binary operation is commutative
** Category of abelian groups (Ab), has abelian groups as objects and group homomorphisms as morphisms
* Metabelian group, a grou ...
gauge theories also exhibit confinement in 2 and 3 spacetime dimensions. Confinement has been found in elementary excitations of magnetic systems called
spinons.
[
]
If the
electroweak symmetry breaking scale were lowered, the unbroken SU(2) interaction would eventually become confining. Alternative models where SU(2) becomes confining above that scale are quantitatively similar to the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
at lower energies, but dramatically different above symmetry breaking.
[
]
Models of fully screened quarks
Besides the quark confinement idea, there is a potential possibility that the color charge of quarks gets fully screened by the gluonic color surrounding the quark. Exact solutions of SU(3) classical
Yang–Mills theory
In mathematical physics, Yang–Mills theory is a gauge theory based on a special unitary group SU(''N''), or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using t ...
which provide full screening (by gluon fields) of the color charge of a quark have been found.
[
] However, such classical solutions do not take into account non-trivial properties of
QCD vacuum. Therefore, the significance of such full gluonic screening solutions for a separated quark is not clear.
See also
*
Lund string model
In particle physics, the Lund string model is a phenomenological model of hadronization. It treats all but the highest- energy gluons as field lines, which are attracted to each other due to the gluon self-interaction and so form a narrow tube ...
*
Gluon field strength tensor
In theoretical particle physics, the gluon field strength tensor is a second order tensor field characterizing the gluon interaction between quarks.
The strong interaction is one of the fundamental interactions of nature, and the quantum fiel ...
*
Asymptotic freedom
In quantum field theory, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases.
Asymptotic fre ...
*
Center vortex
*
Dual superconducting model
*
Beta function (physics)
*
Lattice gauge theory
In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice.
Gauge theories are important in particle physics, and include the prevailing theories of elementary particles: quantum ...
*
Yang–Mills existence and mass gap
References
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Gluons
Quantum chromodynamics
Quark matter
Unsolved problems in physics