Applicability of Hulthen-Hellmann potential to predict the mass-spectra of heavy mesons via series expansion method

TL;DR

This paper uses a temperature-dependent Hulthen-Hellmann potential and series expansion method to predict heavy meson mass spectra, achieving results closely matching experimental data.

Contribution

It introduces a temperature-dependent Hulthen-Hellmann potential and applies the series expansion method to accurately predict heavy meson spectra.

Findings

Predicted meson masses closely match experimental data

Maximum error in predictions is 0.034 GeV

Potential reduces to special cases like Coulomb and Yukawa under certain parameters

Abstract

We adopt Hulth\'en plus Hellmann potential as the quark-antiquark interaction potential for predicting the mass spectra of heavy mesons. The adopted potential was made to be temperature-dependent by replacing the screening parameter with Debye mass.The radial Schr\"odinger equation was analytically solved using the series expansion method and energy eigenvalues were obtained. The energy eigenvalues is used to predict the mass spectra of heavy mesons such as charmonium and bottomonium. Four special cases were considered when some of the potential parameters were set to zero, resulting in Hellmann potential, Yukawa potential, Coulomb potential, and Hulth\'en potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers with a maximum error of 0.034 GeV.