Extending the bridge connecting chiral Lagrangians and QCD Gaussian sum rules for low-energy hadronic physics

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 (qq¯) operators and four-quark (qqq¯q¯) operators. Motivated by these successful demonstrations of scale-factor universality for the K0* isodoublet and a0 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 nonperturbative 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 πK scattering amplitude data and πη 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 K0* isodoublet and a0 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 {πK,πη} scattering, but leads to the best universality and energy-independence properties of the scale factors. Published by the American Physical Society 2025