Calculation of Dissociation Temperature of Nucleon Using Gaussian Expansion Method

TL;DR

This paper calculates the dissociation temperature of nucleons in hot QCD medium using the Gaussian expansion method, revealing that nucleons are more resistant to melting than charmonium states.

Contribution

It introduces a novel approach combining the constituent quark model, temperature-dependent potentials, and Gaussian expansion to determine nucleon dissociation temperatures.

Findings

Nucleon dissociation temperature is higher than that of J/ψ.

The method extends lattice QCD free energy results to light quark systems.

Nucleons are more stable against melting in hot QCD medium.

Abstract

The first study of the dissociation temperature of nucleon in hot QCD medium in the framework of constituent quark model is presented. The temperature-dependent potential energy of the three quark system, taking as the internal energy of the system are obtained from the free energy of the system, and the temperature-dependent free energy is derived based on Debye-H\"uckel theory. The lattice QCD results of the free energy for heavy three-quark system are employed and extended to the light three-quark system. The Schr\"{o}dinger equation for nucleon is solved with the help of Gaussian expansion method and the dissociation temperature of the nucleon is determined according to the temperature dependence of binding energy and radii. Comparing with the dissociation temperature of $J/\psi$, the dissociation temperature of nucleon is higher. So, nucleon is more difficult to melt than Charmonium.