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| In [[physics]], '''asymptotic freedom''' is a property of some [[gauge theory|gauge theories]] that causes bonds between particles to become [[wikt:asymptote|asymptotically]] weaker as [[energy]] increases and [[length scale|distance]] decreases.
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| Asymptotic freedom is a feature of [[quantum chromodynamics]] (QCD), the [[quantum field theory]] of the [[strong nuclear force|nuclear interaction]] between [[quarks]] and [[gluon]]s, the fundamental constituents of nuclear matter.
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| Quarks interact weakly at high energies, allowing perturbative calculations by [[DGLAP]] of cross sections in deep inelastic processes of particle physics; and strongly at low energies, preventing the unbinding of [[baryons]] (like [[protons]] or [[neutrons]] with three quarks) or [[mesons]] (like [[pions]] with two quarks), the composite particles of nuclear matter.
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| Asymptotic freedom was discovered and described in 1973 by [[Frank Wilczek]], [[David Gross]], and independently by [[David Politzer]] the same year. All three shared the Nobel Prize in physics in 2004.
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| == Discovery ==
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| Asymptotic freedom was described and published in 1973 by [[David Gross]] and [[Frank Wilczek]], and also by [[David Politzer]]. Although these authors were the first to understand the physical relevance to the strong interactions, in 1969 [[Iosif Khriplovich]] discovered asymptotic freedom in the [[SU(2)]] gauge theory as a mathematical curiosity, and [[Gerardus 't Hooft]] in 1972 also noted the effect but did not publish. For their discovery, Gross, Wilczek and Politzer were awarded the [[Nobel Prize in Physics]] in 2004.
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| The discovery was instrumental in rehabilitating quantum field theory. Prior to 1973, many theorists suspected that field theory was fundamentally inconsistent because the interactions become infinitely strong at short distances. This phenomenon is usually called a [[Landau pole]], and it defines the smallest length scale that a theory can describe. This problem was discovered in field theories of interacting scalars and [[spinor]]s, including [[quantum electrodynamics]], and [[Lehman spectral representation|Lehman positivity]] led many to suspect that it is unavoidable. Asymptotically free theories become weak at short distances, there is no Landau pole, and these quantum field theories are believed to be completely consistent down to any length scale.
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| While the [[Standard Model]] is not entirely asymptotically free, in practice the Landau pole can only be a problem when thinking about the strong interactions. The other interactions are so weak that any inconsistency can only arise at distances shorter than the [[Planck length]], where a field theory description is inadequate anyway.
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| == Screening and antiscreening ==
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| [[Image:vacuum polarization.svg|thumb|200px|Charge screening in QED]]
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| 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 particle]]s carrying the relevant charge. The [[Landau pole]] behavior of quantum electrodynamics (QED, related to [[quantum triviality]]) 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.
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| 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. Each gluon carries both a color charge and an anti-color magnetic moment. The net effect of polarization of virtual gluons in the vacuum is not to screen the field, but to ''augment'' it and change 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.
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| Since the virtual quarks and the virtual gluons contribute opposite effects, which effect wins out depends on the number of different kinds, or [[flavour (particle physics)|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.
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| == Calculating asymptotic freedom ==
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| 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 [[De Broglie wavelength]]), an asymptotically free theory is amenable to [[perturbation theory (quantum mechanics)|perturbation theory]] calculations using [[Feynman diagram]]s. 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 [[colour confinement|confinement]].
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| Calculating the beta-function is a matter of evaluating Feynman diagrams contributing to the interaction of a quark emitting or absorbing a gluon. Essentially, the beta-function describes how the coupling constants vary as one scales the system <math>x \rightarrow bx</math>. The calculation can be done using rescaling in position space or momentum space (momentum shell integration). In [[non-abelian gauge theory|non-abelian]] gauge theories such as QCD, the existence of asymptotic freedom depends on the [[gauge group]] and number of [[flavor (particle physics)|flavor]]s of interacting particles. To lowest nontrivial order, the beta-function in an SU(N) gauge theory with <math>n_f</math> kinds of quark-like particle is
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| :<math>\beta_1(\alpha) = { \alpha^2 \over \pi} \left( -{11N \over 6} + {n_f \over 3} \right) </math> | |
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| where <math>\alpha</math> is the theory's equivalent of the [[fine-structure constant]], <math>g^2/(4 \pi)</math> 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.
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| For SU(3) <math>N = 3,</math>
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| and <math>\beta_1 < 0 </math> gives <math>n_f < {33 \over 2}.</math>
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| Besides QCD, asymptotic freedom can also be seen in other systems like the nonlinear <math>\sigma</math>-model in 2 dimensions, which has a structure similar to the [[SU(N)]] invariant Yang-Mills theory in 4 dimensions.
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| == See also ==
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| *[[Asymptotic safety]]
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| *[[Gluon field strength tensor]]
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| *[[Quantum triviality]]
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| == References ==
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| <div class="references-small">
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| *{{cite journal
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| |author=D.J. Gross, F. Wilczek
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| |year=1973
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| |title=Ultraviolet behavior of non-abelian gauge theories
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| |journal=[[Physical Review Letters]]
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| |volume=30 |issue= 26|pages= 1343–1346
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| |doi=10.1103/PhysRevLett.30.1343
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| |bibcode=1973PhRvL..30.1343G
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| }}
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| *{{cite journal
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| |author=D.J. Gross
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| |year=1998
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| |title=Twenty Five Years of Asymptotic Freedom
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| |doi=10.1016/S0920-5632(99)00208-X
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| |journal=Nuclear Physics B - Proceedings Supplements
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| |volume=74
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| |pages=426–446
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| |arxiv=hep-th/9809060
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| |bibcode = 1999NuPhS..74..426G }}
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| * G. 't Hooft (June 1972). Unpublished talk at the Marseille conference on renormalization of Yang-Mills fields and applications to particle physics.
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| *{{cite book
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| |author=S. Pokorski
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| |year=1987
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| |title=Gauge Field Theories
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| |publisher=[[Cambridge University Press]]
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| |isbn=0-521-36846-4
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| }}
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| *{{cite journal
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| |author=H.D. Politzer
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| |year=1973
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| |title=Reliable perturbative results for strong interactions
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| |journal=[[Physical Review Letters]]
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| |volume=30 |issue= 26|pages=1346–1349
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| |doi=10.1103/PhysRevLett.30.1346
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| |bibcode=1973PhRvL..30.1346P
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| }}</div>
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| [[Category:Quantum field theory]]
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| [[Category:Quantum chromodynamics]]
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| [[Category:Renormalization group]]
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Hi there! :) My name is Geoffrey, I'm a student studying Integrated International Studies from Piedmont, Australia.
My web blog :: 4Inkjets promo Codes