Engineering Confining Dilatons: A WKB Inverse Problem in Holographic QCD
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909772472647680 |
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| author | Contreras, Miguel Angel Martin Vega, Alfredo |
| author_facet | Contreras, Miguel Angel Martin Vega, Alfredo |
| contents | This work presents a WKB-based inverse problem approach within the framework of holographic bottom-up QCD to engineer confining dilatons from hadronic mass spectra. Starting from a general parameterization of nonlinear radial Regge trajectories, $M_n^2=a(n+b)^ν$, we apply the Rydberg-Klein-Rees (RKR) formula to derive the large-z behavior of the corresponding holographic confining potential. This potential is inversely related to the dilaton field profile, leading naturally to a non-quadratic dilaton $Φ(z)=(κ\,z)^{2-α}$, where the parameters ($κ$, $α$) are uniquely determined by the spectral parameters ($a$,$ν$). We successfully test this method by fitting the spectra of heavy quarkonia ($c\bar{c}$ and $b\bar{b}$), achieving good agreement with experimental data. Furthermore, we extend this formalism to describe the spectroscopy of tetraquark states by superimposing an additional potential term, derived from the Bethe-Salpeter equation for diquarks, onto the standard mesonic confining potential. This work establishes a powerful and flexible bottom-up framework for deriving confinement directly from spectral data, applicable to both conventional and exotic hadrons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Engineering Confining Dilatons: A WKB Inverse Problem in Holographic QCD Contreras, Miguel Angel Martin Vega, Alfredo High Energy Physics - Phenomenology This work presents a WKB-based inverse problem approach within the framework of holographic bottom-up QCD to engineer confining dilatons from hadronic mass spectra. Starting from a general parameterization of nonlinear radial Regge trajectories, $M_n^2=a(n+b)^ν$, we apply the Rydberg-Klein-Rees (RKR) formula to derive the large-z behavior of the corresponding holographic confining potential. This potential is inversely related to the dilaton field profile, leading naturally to a non-quadratic dilaton $Φ(z)=(κ\,z)^{2-α}$, where the parameters ($κ$, $α$) are uniquely determined by the spectral parameters ($a$,$ν$). We successfully test this method by fitting the spectra of heavy quarkonia ($c\bar{c}$ and $b\bar{b}$), achieving good agreement with experimental data. Furthermore, we extend this formalism to describe the spectroscopy of tetraquark states by superimposing an additional potential term, derived from the Bethe-Salpeter equation for diquarks, onto the standard mesonic confining potential. This work establishes a powerful and flexible bottom-up framework for deriving confinement directly from spectral data, applicable to both conventional and exotic hadrons. |
| title | Engineering Confining Dilatons: A WKB Inverse Problem in Holographic QCD |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2509.04956 |