Strengthening the Bridge Between Chiral Lagrangians and QCD Sum-Rules

Abstract

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 ($q\bar{q}$) or four-quark ($qq\bar{q}\bar{q}$) operators. Building on the demonstrated scale-factor universality for the $K_0^{\ast }$ isodoublet and $a_0$ 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 $\pi K$ scattering amplitude data and $\pi \eta$ 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 $K_0^{\ast }$ and $a_0$ mesons across a sequence of increasingly detailed resonance models.

arXiv comment13 pages, 10 figures. Proceedings article for QCD25: 28th High-Energy Physics International Conference in Quantum Chromodynamics. Published in Journal of Subatomic Particles and Cosmology

References in corpus (18)

• Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons
• Mechanism for a next-to-lowest lying scalar meson nonet
• Toy model for two chiral nonets
• Gluon Condensates and m_b(m_b) from QCD-Exponential Moments at Higher Orders
• Evidence for a scalar kappa(900) resonance in pi-K scattering
• Unitarized pseudoscalar meson scattering amplitudes in three flavor linear sigma models
• Mixing of scalar tetraquark and quarkonia states in a chiral approach
• An Effective Lagrangian with Broken Scale and Chiral Symmetry II: Pion Phenomenology
• Current correlators to all orders in the quark masses
• Two chiral nonet model with massless quarks
• QCD Sum Rule Study of the Masses of Light Tetraquark Scalar Mesons
• Chiral Nonet Mixing in pi pi Scattering
• Gaussian Sum-Rules and Prediction of Resonance Properties
• Light scalar mesons in QCD sum rules with inclusion of instantons
• Chiral Nonet Mixing in $\pi K$ Scattering
• Connections between chiral Lagrangians and QCD sum-rules
• Chiral Nonet Mixing in $\pi \eta$ Scattering
• Universal scale factors relating mesonic fields and quark operators