Abstract
A review of familiar results of the three-point Green functions of currents in the odd-intrinsic parity sector of QCD is presented. Such Green functions include very well-known examples of VVP , VAS or AAP correlators. We also shortly present some of the new results for VVA and AAA Green functions with a discussion of their high-energy behaviour and its relation to the QCD condensates.
Highlights
The Green functions are defined as the vacuum expectation values of the time ordered products of the composite operators
The first one is that of low external momenta where the dynamics is governed by the means of chiral perturbation theory and resonance chiral theory (RχT)
The second regime corresponds to the high energies where the asymptotic freedom allows us to use the perturbative approach in terms of the strong coupling αs and where the asymptotics of the correlators for large euclidean momenta is given by the operator product expansion (OPE)
Summary
The Green functions ( called as correlators) are defined as the vacuum expectation values of the time ordered products of the composite operators. In our case, such operators stand either for chiral vector and axial-vector currents Vμ,a = qγμT aq , Aμ,a = qγμγ5T aq, or scalar and pseudoscalar densities S a = qT aq , Pa = iqγ5T aq, where q stands for the triplet of light quarks (q = u, d, s), T a are the SU(3) generators (T a = λa/2), and a = 1 . The spin-zero operators, usually called the QCD condensates, contribute to the vacuum expectation value. We will see that such QCD condensates play an important role in an evaluation of the OPE of the corresponding Green functions
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