In physics, asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances, i.e. length scales that asymptotically converge to zero (or, equivalently, energy scales that become arbitrarily large). The willingness to question previously held truths and search for new answers resulted in a period of major scientific advancements, now known as the Scientific Revolution. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... For other uses of this term, see: Quark (disambiguation) 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ... In physics, length scale is a particular value of length or distance determined with the precision of one order (or a few orders) of magnitude. ... An asymptote to a curve is a straight line that the curve approaches in such a manner that it becomes as close as one might wish to the line by going far enough along the line. ... In physics, energy scale is a particular value of energy determined with the precision of one order (or a few orders) of magnitude. ...

Discovery

The fact that asymptotic freedom is a feature of quantum chromodynamics (QCD), the quantum field theory of the interactions of quarks and gluons, was discovered by David Gross, Frank Wilczek, and David Politzer in 1973. For their discovery, Gross, Wilczek and Politzer were awarded the Nobel Prize in Physics in 2004. Quantum chromodynamics (QCD) is the theory describing one of the fundamental forces, the strong interaction. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... In physics, gluons are the bosonic particles which are responsible for the strong nuclear force. ... David Gross and his wife in Santa Barbara David Jonathan Gross (born February 19, 1941 in Washington, D.C.) is an American physicist and string theorist. ... Frank Wilczek at Harvard University Frank Wilczek (born May 15, 1951) is an American physicist of Polish origin. ... Hugh David Politzer (born 31 August 1949) is an American theoretical physicist. ... 1973 was a common year starting on Monday. ... List of Nobel Prize laureates in Physics from 1901 to the present day. ... 2004 is a leap year starting on Thursday of the Gregorian calendar. ...

Asymptotic freedom implies that in high-energy scattering the quarks move within nucleons, such as the neutron and proton, essentially as free, non-interacting particles, and it allows physicists to calculate the cross sections of various events in particle physics reliably using parton techniques. In particle physics, scattering is a class of phenomena by which particles are deflected by collisions with other particles. ... In physics a nucleon is a collective name for the two baryons the neutron and the proton. ... Properties In physics, the neutron is a subatomic particle with no net electric charge and a mass of 939. ... Properties In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Cross section may refer to the following In geometry, Cross section is the intersection of a 3-dimensional body with a plane. ... Particles erupt from the collision point of two relativistic (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... In particle physics, the parton was a hypothetical fundamental particle considered, in the parton model of strong interactions, to be a constituent of the hadron. ...

The discovery also helped rehabilitate the reputation of quantum field theory (QFT) as a coherent description of particle interactions. Prior to 1973, many theorists suspected that QFT was rendered fundamentally incoherent by the short-distance Landau pole that arose in quantum electrodynamics and some other field theories. Asymptotically free theories, however, lack this Landau pole. The discovery of asymptotic freedom was therefore a key development toward the emergence of a Standard Model of particle physics based on quantum field theory. In physics, Landau pole is the energy scale (or the precise value of the energy) where a coupling constant (the strength of an interaction) of a quantum field theory becomes infinite. ... This article may be too technical for most readers to understand. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... Particles erupt from the collision point of two relativistic (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...

(While the Standard Model is not itself entirely asymptotically free, the phenomenon raises the possibility that it could be an effective field theory approximation to an asymptotically free grand unified theory; and since its strong interactions are asymptotically free, any Landau poles in it are banished anyway to a realm far beneath the Planck length.) In physics, an effective field theory is an approximate theory (usually a quantum field theory) that contains the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, but ignores the substructure and the degrees of freedom at shorter distances (or, equivalently, higher energies). ... Grand unification, grand unified theory, or GUT is a theory in physics that unifies the strong interaction and electroweak interaction. ... The Planck length is the natural unit of length, denoted by . ...

Screening and antiscreening

The variation in a physical coupling constant under changes of scale can be understood qualitatively as coming from the action of the field on virtual particles carrying the relevant charge. The Landau pole behavior of QED is a consequence of screening by virtual charged particle-antiparticle pairs, such as electron-positron pairs, in the vacuum. In the vicinity of a charge, the vacuum becomes polarized: virtual particles of opposing charge are attracted to the charge, and virtual particles of like charge are repelled. The net effect is to partially cancel out the field at any finite distance. Getting closer and closer to the central charge, one sees less and less of the effect of the vacuum, and the effective charge increases. In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... Corresponding to each kind of particle, there is an associated antiparticle with the same mass and spin but with many other quantum numbers flipped in sign. ... Properties The electron is a subatomic particle. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle of the electron. ...

charge screening in QED

In QCD, the same thing happens with virtual quark-antiquark pairs; they tend to screen the color charge. However, QCD has an additional wrinkle: its force-carrying particles, the gluons, themselves carry color charge, and in a different manner. Roughly speaking, each gluon carries both a color charge and an anti-color charge. The net effect of polarization of virtual gluons in the vacuum is not to screen the field, but to augment it and affect its color. This is sometimes called antiscreening. Getting closer to a quark diminishes the antiscreening effect of the surrounding virtual gluons, so the contribution of this effect would be to weaken the effective charge with decreasing distance. 1-loop vacuum polarization diagram This is the one loop contribution to the photon propagator Π due to vacuum polarization in QED. It causes a wave function renormalization for the photon, leading to a charge screening. ... In quantum chromodynamics (QCD), color or color charge refers to a certain property of the subatomic particles called quarks. ...

Since the virtual quarks and the virtual gluons contribute opposite effects, which effect wins out depends on the number of different kinds, or flavors, of quark. For standard QCD with three colors, as long as there are no more than 16 flavors of quark (not counting the antiquarks separately), antiscreening prevails and the theory is asymptotically free. In fact, there are only 6 known quark flavors. In particle physics, flavor is a property of a fermion that identifies it, a label that specifies the name of the particle. ...

Calculating asymptotic freedom

Asymptotic freedom can be derived by calculating the beta-function describing the variation of the theory's coupling constant under the renormalization group. For sufficiently short distances or large exchanges of momentum (which probe short-distance behavior, roughly because of the inverse relation between a quantum's momentum and wavelength), an asymptotically free theory is amenable to perturbation theory calculations using Feynman diagrams. Such situations are therefore more theoretically tractable than the long-distance, strong-coupling behavior also often present in such theories, which is thought to produce confinement. A separate article treats the beta-function (written with a hyphen) of physics. ... In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. ... In physics, the term renormalization refers to a variety of theoretical concepts and computational techniques revolving either around the idea of rescaling transformations, or around the process of removing infinities from the calculated quantities (see also regularization). ... In physics, momentum is a physical quantity related to the velocity and mass of an object. ... The wavelength is the distance between repeating units of a wave pattern. ... In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. ... This article needs to be cleaned up to conform to a higher standard of quality. ... This article is about a particle physics phenomenon. ...

Calculating the beta-function is a matter of evaluating Feynman diagrams contributing to the interaction of a quark emitting or absorbing a gluon. In non-abelian gauge theories such as QCD, the existence of asymptotic freedom depends on the gauge group and number of flavors of interacting particles. To lowest nontrivial order, the beta-function in an SU(N) gauge theory with n_f kinds of quark-like particle is In mathematics, an abelian group, also called a commutative group, is a group (G, *) such that a * b = b * a for all a and b in G. Abelian groups are named after Niels Henrik Abel. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In particle physics, flavor is a property of a fermion that identifies it, a label that specifies the name of the particle. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ...

where α is the theory's equivalent of the fine-structure constant, g² / (4π) in the units favored by particle physicists. If this function is negative, the theory is asymptotically free. For SU(3), the color charge gauge group of QCD, the theory is therefore asymptotically free if there are 16 or fewer flavors of quarks. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... In quantum chromodynamics (QCD), color or color charge refers to a certain property of the subatomic particles called quarks. ...

What is N?

External link

• Twenty-five years of asymptotic freedom (by David Gross) (Nobel Prize 2004 for this discovery)

References

Pokorski, Stefan, Gauge Field Theories, Cambridge: Cambridge University Press, 1987. ISBN 0-521-36846-4