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

Abstract

In this study, we investigated the impact of a topological defect on the properties of heavy quarkonia using the extended Cornell potential. We solved the fractional radial Schrodinger equation (SE) using the extended Nikorov-Uvarov (ENU) method to obtain the eigen energy, which allowed us to calculate the masses of charmonium and bottomonium. One significant observation was the splitting between np and nd states, which we 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 in a manner similar to 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 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, and specific heat 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 essential in understanding the various properties and behaviors of heavy quarkonia in the presence of topological defects.