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

TL;DR

This paper develops an advanced Gaussian QCD sum-rule approach to connect chiral Lagrangians with QCD, enabling analysis of scalar mesons and their mixing with glueballs, with improved resonance modeling and universality of scale factors.

Contribution

It introduces a revised Gaussian sum-rule methodology that extends analysis to higher isospin sectors and incorporates background-resonance interference, enhancing the connection between chiral Lagrangians and QCD sum-rules.

Findings

Gaussian sum-rules can distinguish between resonance models.

Background-resonance interference accurately describes scattering data.

Scale factors exhibit universality and energy independence across models.

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.