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Abstract
A framework of operator product expansion (OPE) allows us to study high-energy behaviour of Green functions. A calculation of such Green functions within chiral perturbation theory (χPT) or resonance chiral theory (RχT) and subsequent matching of the result to the OPE enables us to determine constraints for unknown parameters of the effective theories. We present such procedure for Green functions in the odd-intrinsic parity sector of QCD.
Highlights
IntroductionHaving to determine the behaviour of Green functions at high energies, operator product expansion (OPE) is a suitable framework
The amplitudes of physical processes can be computed using the LSZ reduction formula from the Green functions, the vacuum expectation values of time ordered products of composite operators Oi(xi): Π(p, q) = d4 x d4y e−i(p·x+q·y) 0 T O1(x)O2(y)O3(0) 0 . (1)Within our context, the operators Oi(xi) stand for any of the non-singlet vector Vμa(x) = q(x)γμT aq(x) and axial-vector Aaμ(x) = q(x)γμγ5T aq(x) chiral currents or scalar S a(x) = q(x)T aq(x) and pseudoscalar Pa(x) = iq(x)γ5T aq(x) densities
Having to determine the behaviour of Green functions at high energies, operator product expansion (OPE) is a suitable framework. It says that at large external momenta, the Green function can be written down as a sum of Wilson coefficients proportional to vacuum averages of composite gauge-invariant local operators made of quark and gluon fields, i.e. the QCD condensates
Summary
Having to determine the behaviour of Green functions at high energies, OPE is a suitable framework. It says that at large external momenta (or, in QCD, at short distances), the Green function can be written down as a sum of Wilson coefficients proportional to vacuum averages of composite gauge-invariant local operators made of quark and gluon fields, i.e. the QCD condensates. We are mostly interested in Green functions that belong to the odd-intrinsic parity sector of QCD. Such Green functions are VV P , AAP , V AS and anomalous correlators VV A and AAA. To calculate contribution of resonances to these Green functions, we use the NLO resonance Lagrangian, described in detail in Ref. [1]
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