Masses and thermodynamic properties of heavy mesons in the non-relativistic quark model using the Nikiforov\u2013Uvarov method

T. A. Abdel-Karim,Sh. Y. Ezz-Alarab,M. Abu-Shady

doi:10.1186/s42787-019-0014-0

T. A. Abdel-Karim, Sh. Y. Ezz-Alarab + Show 1 more

Open Access

https://doi.org/10.1186/s42787-019-0014-0

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Abstract

Thermodynamic properties of heavy mesons are calculated within the framework of the N-dimensional radial Schrödinger equation. The Cornell potential is extended by including the quadratic potential plus the inverse of quadratic potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov–Uvarov (NU) method. The obtained results are applied for calculating the mass of spectra of charmonium, bottomonium, b overline{mathrm{c}}, and c overline{mathrm{s}} mesons. The thermodynamic properties of heavy quarkonia such as the mean energy, the specific heat, the free energy, and the entropy are calculated. The effect of temperature and the dimensionality number on heavy meson masses and thermodynamic properties is investigated. The obtained results are improved in comparison with other theoretical approaches and in a good agreement with experimental data. We conclude that the present potential well describes thermodynamic properties in the three-dimensional space and also the higher dimensional space.

Highlights

Thermodynamics is the branch of physics concerned in temperature and their relation to energy
We extend the Cornell potential to include the quadratic potential and the inverse quadratic potential which play an important role in improving quarkonium properties such as in [26, 27]
Quarkonium masses we calculate the spectra of the heavy quarkonium system such as charmonium and bottomonium that have the quark and antiquark flavor; the mass of quarkonium is calculated in 3-dimensional space (N = 3)

Summary

Introduction

Thermodynamics is the branch of physics concerned in temperature and their relation to energy. We aim to calculate the N-dimensional Schrödinger equation analytically by using Nikiforov–Uvarov (NU) method firstly, and apply the present results to find the properties of quarkonium particles which are not considered in other works such as thermodynamic properties for charm matter. In the “The Schrödinger equation with the extended Cornell potential” section, the energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space.

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