Strengthening the Bridge Between Chiral Lagrangians and QCD Sum-Rules

Previous work has shown that mesonic fields in chiral Lagrangians can be systematically connected to quark-level operators in QCD sum rules through chiral-symmetry constrained and energy-independent scale factor matrices. This framework yields universal scale factors associated with each chiral nonet, whether composed of quark-antiquark (qq̄) or four-quark (qqq̄q̄) operators. Building on the demonstrated scale-factor universality for the K₀^* isodoublet and a₀ isotriplet scalar mesons, we develop a revised Gaussian QCD sum-rule methodology that extends the analysis to higher-dimensional isospin sectors. To access nonperturbative information about resonances arising from final-state interactions, we introduce a background-resonance interference approximation. This approximation successfully reproduces both $πK$ scattering amplitude data and $πη$ scattering predictions. It also motivates new resonance models that enhance the scale-factor analysis linking chiral Lagrangians to QCD sum rules. Within this refined framework, we explore the scale factors for the K₀^* and a₀ mesons across a sequence of increasingly detailed resonance models.