Analytic Solution of Multi-Dimensional Schrodinger in Hot and Dense QCD Media Using SUSYQM Method

TL;DR

This paper analytically solves the N-dimensional Schrödinger equation for heavy quarkonia in hot and dense QCD media using SUSYQM, revealing how temperature and baryon chemical potential affect binding energy and dissociation.

Contribution

It introduces an analytical SUSYQM approach to solve the N-dimensional Schrödinger equation with a heavy quarkonia potential at finite temperature and chemical potential, including nonperturbative corrections.

Findings

Binding energy decreases with increasing temperature.

Binding energy is slightly sensitive to baryon chemical potential up to 0.6 GeV.

Nonperturbative corrections increase dissociation of quarkonia.

Abstract

The N-radial Schr\"odinger equation is analytically solved by using SUSYQM method, in which the heavy quarkonia potential is introduced at finite temperature and baryon chemical potential. The energy eigenvalue is calculated in the N-dimensional space. The obtained results show that the binding energy strongly decreases with increasing temperature and is slightly sensitive for changing baryon chemical potential up to 0.6 GeV at higher values of temperatures. We employed the nonperturbative corrections to the leading-order of the Debye mass at finite baryon chemical potential. We found that the binding energy is more dissociates when the nonperturbative corrections are included with the leading-order term of Debye mass in both hot and dense media. A comparison is discussed with other works such as the lattice parameterized of Debye mas. Thus, the present potential with the SUSYQM method provides satisfying results for the description of the dissociation of binding energy for heavy quarkonia in hot and dense media.