Masses and thermodynamic properties of a quarkonium system

Abstract

Hulthen plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the thermodynamic properties and the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmoniumand cc and bottomonium bb, and thermodynamic properties such as the mean energy, the specific heat, the free energy, and the entropy. Four special cases were considered when some of the potential parameters were set to zero, resulting in Hellmann potential, Yukawa potential, Coulomb potential, and Hulthen potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

The Impact of deformed space-phase parameters into HAs and HLM systems with the improved Hulthen plus Hellmann potentials model in the presence of temperature-dependent confined Coulomb potential within the framework of DSE

“…Worthwhile it is better to mention that for the two simultaneous limits (Θ, λ, σ) → (0, 0, 0) we recover the results of the Refs. [11,12]. It is possible to recover the results of commutative space when we consider (Θ (λ, σ) ,θ λ, σ ) equal (0,0).…”

“…The wave function and the energy spectrum of Eq. ( 8) for HHPTd model (7) are respectively given by [11,12]:…”

“…where A 1 , A 2 and A 0 are the potential strength, α is the screening parameter that controls the shape of the potential and m D (T ) is the Debye mass which is TD potential V hhp (r, T ) TD is obtained from V hhp (r) by replacing the screening parameter α with Debye mass m D (T ) that is TD and vanishes when the temperature is zero. In the same context regarding temperature, Inyang et al adopted Hulthén plus Hellmann potentials, which rendered TD by replacing the screening parameter with a Debye mass, as the quarkantiquark interaction potential for studying the thermodynamic properties and the mass spectra of heavy mesons [12].…”

Analyzing the effects of magnetic and Aharonov‐Bohm (AB) flux fields on the energy spectra and thermal properties of N2, NO, CO and H2 diatomic molecules

“…Many researchers have recently used various analytical techniques to obtain the solutions of the SE with interacting potentials [3][4][5][6]. Examples include the series expansion method [7], WKB approximation method [8,9], asymptotic iteration method (AIM) [10,11], Nikiforov-Uvaforov (NU) method [12][13][14][15], NU-functional analysis (NUFA) approach [16], and others.…”

Masses and thermal properties of a Charmonium and Bottomonium Mesons

“…For instance, Abu-Shady et al, [54] studied the TPs of HMs with extended Cornell potential. Also Inyang et al, [55] obtained the TPs of the HMs with exponential potential. Abu-Shady and Ezz-Alarab [40], solved the N-radial SE with the Trigonometric Rosen-Morse potential, and the obtained energy equation was used in studying TPs and masses of heavy and heavy-light mesons.…”