Properties and Behaviors of Heavy Quarkonia: Insights through Fractional Model and Topological Defects

M. Abu-shady (Department of Mathematics and Computer Sciences, Faculty of Science, Menoufia University, Shibin El Kom, Egypt) ; H.M. Fath-Allah (Higher Institute of Engineering and Technology, Menoufia, Egypt)

In this study, we investigated the impact of a topological defect (λ) on the properties of heavy quarkonia using the extended Cornell potential. We solved the fractional radial Schrödinger equation (SE) using the extended Nikiforov-Uvarov (ENU) method to obtain the eigenvalues of energy, which allowed us to calculate the masses of charmonium and bottomonium. One significant observation was the splitting between nP and nD states, which attributed to the presence of the topological defect. We discovered that the excited states were divided into components corresponding to 2l+1, indicating that the gravity field induced by the topological defect interacts with energy levels like the Zeeman effect caused by a magnetic field. Additionally, we derived the wave function and calculated the root-mean radii for charmonium and bottomonium. A comparison with the classical models was performed, resulting in better results being obtained. Furthermore, we investigated the thermodynamic properties of charmonium and bottomonium, determining quantities such as energy, partition function, free energy, mean energy, specific heat, and entropy for P-states. The obtained results were found to be consistent with experimental data and previous works. In conclusion, the fractional model used in this work proved an essential role in understanding the various properties and behaviors of heavy quarkonia in the presence of topological defects.

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      "value": "In this study, we investigated the impact of a topological defect (<math id=\"M1\"><mi>\u03bb</mi></math>) on the properties of heavy quarkonia using the extended Cornell potential. We solved the fractional radial Schr\u00f6dinger equation (SE) using the extended Nikiforov-Uvarov (ENU) method to obtain the eigenvalues of energy, which allowed us to calculate the masses of charmonium and bottomonium. One significant observation was the splitting between nP and nD states, which attributed to the presence of the topological defect. We discovered that the excited states were divided into components corresponding to <math id=\"M2\"><mn>2</mn><mi>l</mi><mo>+</mo><mn>1</mn></math>, indicating that the gravity field induced by the topological defect interacts with energy levels like the Zeeman effect caused by a magnetic field. Additionally, we derived the wave function and calculated the root-mean radii for charmonium and bottomonium. A comparison with the classical models was performed, resulting in better results being obtained. Furthermore, we investigated the thermodynamic properties of charmonium and bottomonium, determining quantities such as energy, partition function, free energy, mean energy, specific heat, and entropy for P-states. The obtained results were found to be consistent with experimental data and previous works. In conclusion, the fractional model used in this work proved an essential role in understanding the various properties and behaviors of heavy quarkonia in the presence of topological defects."
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Published on:
02 March 2024
Publisher:
Hindawi
Published in:
Advances in High Energy Physics (2024)

DOI:
https://doi.org/10.1155/2024/2730568
arXiv:
2309.14310
Copyrights:
Copyright © 2024 M. Abu-shady and H. M. Fath-Allah.
Licence:
CC-BY-3.0

Fulltext files: