Non-compact extra dimensions and flavor dependence of and mesons masses in a hot QCD medium with lattice, LO and NLO parametrizations of the Debye mass
Abstract
In this paper, we consider a heavy quarkonium state in a hot QCD medium, namely the ground state of charmonium and bottomonium. The quark–antiquark potential is proposed in the form of a temperature-dependent Cornell potential, and is extended to include a temperature-dependent parameter. Then, for the proposed potential with different parametrizations of the Debye mass, the N-dimensional Schrödinger equation is analytically solved using the biconfluent Heun equation. The obtained energy eigenvalues and wave functions are employed to study the flavor dependence, the effect of dimensionality and the influence of the additional term on the mass and binding energy of 1S state of charmonium and bottomonium at finite temperature. The findings of this research are compared to those from past studies. We concluded that this work provides a simple and consistent description of quarkonium states at finite temperature in a hot QCD medium, highlighting the effect of noncompact extra dimensions and the flavor dependence of the binding energies of heavy quarkonia.
