Abstract
The study of the nucleon dissociation in a hot quantum chromodynamics (QCD) medium in a constituent quark model with the help of Gaussian expansion method (GEM) is presented. This is the first time this method is applied to the dissociation problem of nucleon. The temperature-dependent potentials of a three-quark system, taking as the internal energy of the corresponding system, are obtained from the free energy of the system based on Debye-H\"uckel theory. The lattice QCD results of free energy for heavy three-quark system are employed and extended to the light three-quark system. The Schr\"odinger equation for nucleon is solved with the help of GEM and the dissociation temperature of nucleon is determined according to the temperature dependence of binding energy and radius. The dissociation temperature of nucleon we calculate is about $1.16{T}_{c}$ (${T}_{c}$ is the deconfinement temperature).
Highlights
It is generally believed that a quark-gluon plasma (QGP) may be produced during relativistic heavy-ion collisions [1]
The Schrödinger equation for nucleon is solved with the help of Gaussian expansion method (GEM) and the dissociation temperature of nucleon is determined according to the temperature dependence of binding energy and radius
Before studying the dissociation of nucleon, we test the reliability of GEM on studying dissociation problem of quarkonium by comparing our results for dissociation temperatures, obtained by using GEM, with the results obtained by other methods
Summary
It is generally believed that a quark-gluon plasma (QGP) may be produced during relativistic heavy-ion collisions [1]. Study the dissociation of nucleon in a hot QCD medium with the help of Gaussian expansion method (GEM), an efficient and powerful method in few-body system [8]. For this purpose, a constituent quark model is employed and extended to finite temperature by extending the interquark potential at zero temperature to that at finite temperatures. We obtain the interquark potential of a nucleon in hot QCD medium from the free energy.
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