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from Part VII - Power corrections in QCD
The anatomy of the SVZ expansion
For definiteness, let us illustrate our discussion from the generic two-point correlator:
where JH(x) is the hadronic current of quark and/or gluon fields. Here, the analysis is in principle much simpler than in the case of deep inelstic scatterings, because one has to sandwich the T-product of currents between the vacuum rather than between two proton states. Following SVZ [1], the breaking of ordinary perturbation theory at low q2 is due to the manifestation of non-perturbative terms appearing as power corrections in the operator product expansion (OPE) of the Green function à la Wilson [222]. In this way, one can write:
provided that m2 – q2 ≫ Λ2. For simplicity, m is the heaviest quark mass entering into the correlator; ν is an arbitrary scale that separates the long- and short-distance dynamics; C are theWilson coefficients calculable in perturbative QCD by means of Feynman diagrams techniques; 〈O〉 are the non-perturbative (non-calculable) condensates built from the quarks or/and gluon fields. Though, separately, C and 〈O〉 are (in principle) ν-dependent, this ν-dependence should (in principle) disappear in their product.
The case D = 0 corresponds to the naïve perturbative contribution.
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