Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2501.12601 |
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Inhaltsangabe:
- 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 $πK$ scattering amplitude data and $πη$ 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 $\{πK,πη\}$ scattering, but leads to the best universality and energy-independence properties of the scale factors.