Document Type

Article

Publication Date

5-14-2025

Department

Engineering

Keywords

multiquark bound states, QCD phenomenology, quantum chromodynamics, sigma models, sum rules, light mesons

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 (π‘žβ’Β―π‘ž) operators and four-quark (π‘žβ’π‘žβ’Β―π‘žβ’Β―π‘ž) operators. Motivated by these successful demonstrations of scale-factor universality for the 𝐾*0 isodoublet and π‘Ž0 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 nonperturbative 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 πœ‹β’πΎ scattering amplitude data and πœ‹β’πœ‚ 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 π‘Ž0 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 {πœ‹β’πΎ,πœ‹β’πœ‚} scattering, but leads to the best universality and energy-independence properties of the scale factors.

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Source Publication Title

Physical Review D

Publisher

American Physical Society

Volume

111

Issue

9

First Page

094023

DOI

10.1103/PhysRevD.111.094023

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