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

Abstract

Thermodynamics properties of heavy mesons are calculated within the framework of the N-dimensional radial Schr ̈dinger 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 (NV) method. The obtained results are applied for calculating the mass of spectra of charmonium, bottomonium, b ̅ and c ̅ mesons. The thermodynamics properties of heavy quarkonia such as, the mean energy, specific heat, free energy, and entropy are calculated. The effect of temperature and the dimensionality number on heavy mesons masses and thermodynamics 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.

Quarkonium masses in a hot QCD medium using conformable fractional of the Nikiforov–Uvarov method

“…(32) is compatible with Ref. [15], in which the author obtained the quarkonium mass at finite temperature in the N-dimensional space. To calculate quarkonium mass accordance to Eq.…”

“…where V (r, T ) is the Cornell potential at the finite temperature as in Ref. [15] and references therein which take following as follows…”

“…The expansion of C x and D x 2 in a power series around the characteristic radius r 0 of meson up to the second order is given Ref. [15]. The following equation is obtained…”

Mass Spectrum of Mesons via the WKB Approximation Method

“…Also, the results for the Charmed-strange meson tabulated in Table 4, are in excellent agreement with the ones obtained in Refs. [15,30] and experimental data such as the excited 1D-state [62]. Furthermore, in Table 3, the mass spectrum of the bottom-charmed meson are very close to the ones obtained with the artificial neural network method [19] and also to the 2S state experimental data [60] indicating an improvement compared to the other methods.…”

Analytic solution of multi-dimensional Schrödinger equation in hot and dense QCD media using the SUSYQM method

“…It is well-known that SUSYQM allows one to determine the eigenvalues and eigenfunctions analytically for solvable potentials model using algebraic operator formulation without solving the Schrödinger-like differential equation by the standard series method. Many authors have in recent times solved the Schrodinger-like equation with physically motivated potential models [11][12][13][14][15]. The SUSYQM was first introduced by Witten [1] for the first time as a simplest supersymmetric model in quantum field theory.…”