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Instead of a model-dependent treatment in terms of constituent quarks, hadrons
are represented by their interpolating quark currents taken at large virtualities.
The correlation function of these currents is introduced and treated in
the framework of the [[operator product expansion]] (OPE), where the short and
long-distance quark-gluon interactions are separated. The former are calculated
using QCD perturbation theory, whereas the latter are parametrized in
terms of universal vacuum condensates or light-cone distribution amplitudes.
The result of the QCD calculation is then matched, via dispersion relation, to
a sum over hadronic states. The sum rule obtained in this way allows to calculate
observable characteristics of the hadronic ground state. Inversely, the
parameters of QCD such as quark masses and vacuum condensate densities
can be extracted from sum rules which have experimentally known hadronic
parts. What is also very important, the interactions of quark-gluon currents
with QCD vacuum fields critically depend on the quantum numbers (spinparity,
flavor content) of these currents.
In [[quantum chromodynamics]], the [[color confinement|confining]] and strong coupling nature of the theory means that conventional perturbative techniques often fail to apply. The '''QCD sum rules''' (or '''[[Mikhail Shifman|Shifman]]–[[Arkady Vainshtein|Vainshtein]]–[[Valentine Zakharov Zakharov|Zakharov]] sum rules''') are a way of dealing with this. The idea is to work with gauge invariant operators and [[operator product expansion]]s of them. The vacuum to vacuum correlation function for the product of two such operators can be reexpressed as
 
:<math>\left\langle 0 | T\left\{ \mathcal{O}_1(x) \mathcal{O}_2(0) \right\} | 0 \right\rangle  </math>
where we have inserted hadronic particle states on the right hand side.
 
==Correlation function of quark currents==
 
{{Empty section|date=February 2013}}
 
==See also==
*[[quantum chromodynamics]]
*[[Lattice QCD]]
 
==External links==
*[http://www.scholarpedia.org/article/Shifman-Vainshtein-Zakharov_sum_rule SVZ sum rules at Scholarpedia]
*{{cite journal | last = Shifman | first = Mikhail | authorlink = Mikhail Shifman | title = Snapshot of hadrons | journal = Prog.Theor.Phys.Suppl. | volume = 131 | pages = 1 | year = 1998 | doi = 10.1143/PTPS.131.1 | url = http://ptps.oxfordjournals.org/content/131/1 | format = [[arXiv|arXiv preprint]] at [http://arxiv.org/abs/hep-ph/9802214 hep-ph/9802214]|arxiv = hep-ph/9802214 |bibcode = 1998PThPS.131....1S }}
 
[[Category:Quantum chromodynamics]]
 
 
{{particle-stub}}

Revision as of 06:29, 26 February 2014

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