The Bridge Between Chiral Lagrangians and QCD Sum-Rules

TL;DR

This paper reviews how scale-factor matrices connect mesonic fields in chiral Lagrangians with quark structures in QCD sum-rules, providing a method to analyze mesonic states and their mixing.

Contribution

It introduces a methodology using scale-factor matrices and mixing angles to relate QCD sum-rules with chiral Lagrangians, applied to the $a_0$ meson system.

Findings

Scale factors agree with chiral Lagrangian vacuum expectation values.

Method successfully disentangles mesonic states.

Sensitivity of scale factors to gluon condensate explored.

Abstract

Properties of the scale-factor matrices forming a bridge between the mesonic fields of chiral Lagrangians and quark-level structures of QCD sum-rules are reviewed. The scale-factor matrices combined with mixing angles provide a physical projection of a QCD correlation function matrix that disentangles the mesonic states. This methodology is illustrated for the isotriplet $a_0(980)$-$a_0(1450)$ system, and the scale factors are determined from the combined inputs of QCD sum-rules and chiral Lagrangians. The resulting scale factors are shown to be in good agreement with the vacuum expectation values in the chiral Lagrangian framework. The sensitivity of the scale factors on the gluon condensate QCD sum-rule parameter is explored.