Extending the Bridge Connecting Chiral Lagrangians and QCD Gaussian Sum-Rules for Low-Energy Hadronic Physics

Abstract

It has previously been demonstrated that the mesonic fields in chiral Lagrangians can be related to the quark-level operators of QCD sum-rules via energy-independent (constant) scale factor matrices constrained by chiral symmetry. This leads to universal scale factors for each type of chiral nonet related to quark-antiquark (\(q\bar{q}\)) operators and four-quark (\(qq\bar{q}\bar{q}\)) operators. Motivated by these successful demonstrations of scale-factor universality for the \(K_0^*\) isodoublet and \(a_0\) isotriplet scalar mesons, a revised Gaussian QCD sum-rule methodology is developed that enables the extension to higher-dimensional isospin sectors, including the possibility of mixing with glueball components. Moreover, to extract non-perturbative information about a resonance stemming from the final state interactions of its decay products, a background-resonance interference approximation is developed and shown to provide an excellent description of both \(\pi K\) scattering amplitude data and \(\pi\eta\) scattering calculations. This background-resonance interference approximation inspires new resonance models as ingredients in the scale-factor analysis connecting chiral Lagrangians and QCD Gaussian sum-rules. Using the revised Gaussian QCD sum-rule methodology, key properties of the scale factors are examined for the \(K_0^*\) isodoublet and \(a_0\) isotriplet scalar mesons for a sequence of increasingly sophisticated resonance models. Gaussian sum-rules are demonstrated to have sufficient resolution to distinguish between different resonance models, and it is shown that the background-resonance interference approximation not only describes \(\{\pi K,\,\pi\eta\}\) scattering, but leads to the best universality and energy-independence properties of the scale factors.