Universal Scale Factors: A Bridge Between Chiral Lagrangians and QCD Sum-Rules

TL;DR

This paper establishes a universal scale factor linking Chiral Lagrangian mesonic fields to QCD quark operators, validated through QCD sum-rules and mixing angles, confirming the universality property across different meson nonets.

Contribution

It introduces a universal scale factor constrained by chiral symmetry, connecting Chiral Lagrangian fields to QCD operators, and verifies this universality using sum-rules and mixing angles.

Findings

Universal scale factor confirmed for scalar mesons

Scale factors consistent with chiral symmetry constraints

Validation through QCD sum-rules and mixing angles

Abstract

Chiral Lagrangian mesonic fields can be connected to QCD quark operators via matrix operators containing scale factors. These scale factor matrices are shown to be constrained by chiral symmetry, resulting in a universal scale factor for each Chiral Lagrangian nonet. QCD sum-rules, combined with mixing angles from Chiral Lagrangian analyses, are used to determine the scale factors for the $a_0$ isotriplet and $K_0^*$ isodoublet scalar mesons. The resulting scale factors verify the universality property, providing a validation of the scale factor matrices connecting Chiral Lagrangian mesonic fields and quark operators.