Editing Quantum chromodynamics (section)

==Methods==
Further analysis of the content of the theory is complicated. Various techniques have been developed to work with QCD. Some of them are discussed briefly below.

===Perturbative QCD===
{{main|Perturbative QCD}}
This approach is based on asymptotic freedom, which allows [[perturbation theory (quantum mechanics)|perturbation theory]] to be used accurately in experiments performed at very high energies. Although limited in scope, this approach has resulted in the most precise tests of QCD to date.

===Lattice QCD===
{{main|Lattice QCD}}
[[Image:Fluxtube meson.png|right|thumb|150px|{{langle}}''E''<sup>2</sup>{{rangle}} plot for static quark–antiquark system held at a fixed separation, where blue is zero and red is the highest value (result of a lattice QCD simulation by M. Cardoso et al.<ref>{{cite journal |first1=M. |last1=Cardoso |first2=N. |last2=Cardoso |first3=P. |last3=Bicudo |display-authors=1 |title=Lattice QCD computation of the colour fields for the static hybrid quark–gluon–antiquark system, and microscopic study of the Casimir scaling |journal=Phys. Rev. D |volume=81 |issue= 3|pages=034504 |year=2010 |doi=10.1103/PhysRevD.81.034504 |arxiv=0912.3181 |bibcode=2010PhRvD..81c4504C |s2cid=119216789 }}</ref>)]]
Among non-perturbative approaches to QCD, the most well established is [[lattice QCD]]. This approach uses a discrete set of spacetime points (called the lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation that is then carried out on [[supercomputers]] like the [[QCDOC]], which was constructed for precisely this purpose. While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means, in particular into the explicit forces acting between  quarks and antiquarks in a meson.   However, the [[numerical sign problem]] makes it difficult to use lattice methods to study QCD at high density and low temperature (e.g. nuclear matter or the interior of neutron stars).

===1/''N'' expansion===
{{main|1/N expansion}}
A well-known approximation scheme, the [[1/N expansion|{{frac|1|''N''}} expansion]], starts from the idea that the number of colors is infinite, and makes a series of corrections to account for the fact that it is not. Until now, it has been the source of qualitative insight rather than a method for quantitative predictions. Modern variants include the [[AdS/CFT]] approach.

===Effective theories===
For specific problems, effective theories may be written down that give qualitatively correct results in certain limits. In the best of cases, these may then be obtained as systematic expansions in some parameters of the QCD Lagrangian. One such [[effective field theory]] is [[chiral perturbation theory]] or ChiPT, which is the QCD effective theory at low energies. More precisely, it is a low energy expansion based on the spontaneous chiral symmetry breaking of QCD, which is an exact symmetry when quark masses are equal to zero, but for the u, d and s quark, which have small mass, it is still a good approximate symmetry. Depending on the number of quarks that are treated as light, one uses either SU(2) ChiPT or SU(3) ChiPT. Other effective theories are [[heavy quark effective theory]] (which expands around heavy quark mass near infinity), and [[soft-collinear effective theory]] (which expands around large ratios of energy scales). In addition to effective theories, models like the [[Nambu–Jona-Lasinio model]] and the [[chiral model]] are often used when discussing general features.

===QCD sum rules===
{{main|QCD sum rules}}

Based on an [[Operator product expansion]] one can derive sets of relations that connect different observables with each other.