Potential Models for Heavy Quarkonium Mass Spectra

Abstract: By investigating the mass spectra of heavy quarkonium states, namely bottomonium and charmonium, the advantages anddisadvantages of different confinement potential structures in the Cornell potential model are explored. In addition, the applicabilityof Gaussian and harmonic oscillator bases, as well as the influence of the number of basis functions on the mass spectra, areinvestigated in detail. Specifically, first, the effect of the number of basis functions on the mass spectra is studied by employingtheGaussian basis combined with the linear potential. It is found that the dependence of the mass spectra on the number of basisfunctions almost disappears when the number of basis functions exceeds 10. Based on this result, 10 basis functions are adoptedinthe subsequent calculations of heavy quarkonium mass spectra. Second, the mass spectra are fitted and predicted using the Gaussianbasis combined with the linear, harmonic oscillator, error function, and screened potentials, respectively. It is found that the linearpotential exhibits better performance with the Gaussian basis. Finally, to compare the effects of different bases on the mass spectra, the harmonic oscillator basis is further employed, and the mass spectra of heavy quarkonium states are fitted and predictedunderdifferent confinement potentials. The comparison demonstrates that the mass spectra of heavy quarkoniumstates can be betterdescribed by combining the Gaussian basis with the linear potential. The theoretical results are expected to provide valuablereferences for future investigations of heavy quarkonium mass spectra and contribute to a deeper understanding of the mechanismofstrong interactions in the low-energy regime.