Limited Temperature In Heavy Quarkonium Mass Spectra

Content:Content:The widely accepted theory of strong interaction—Quantum chromodynamics (QCD) gives someimportant predictions that under extreme conditions of high temperature or/and high density the degrees of freedomfor hadron systems assume the form of quarks and gluons—the fundamental degrees of freedom of QCD. This isso-called quark-gluon plasm (QGP). QGP is an important state of matter, it is relevant to the early evolution ofour universe. Meantime, QCD in high temperature manifests some characteristics, such as the suppression of J/ψ,the deconfinement of quarks and the restoration of chiral symmetry spontaneous breaking. Research on QGP is animportant topic of particle physics, it is crucial for one to have a deep insight into QCD and to reveal the evolutionof the universe. The phase transition phenomenon in QGP has been investigated extensively and deeply, i.e., ifa true phase transition happens when a hadron system evolves from hadron phase whose fundamental degrees offreedom are hadrons to QGP, if it happens, what is the nature of this phase transition. The basic theory of QGP isQuantum field theory at finite temperature. At low temperature QGP becomes weakly interacting pion gas while athigh temperature, the interaction between quarks and/or gluons is very weak, both cases can be handled effectivelyby perturbation theory. However, at the vicinity of critical point of a phase transition, the system is composed ofboth hadrons and quarks and gluons, perturbation theory cannot be applied here. At present, most theoretic studyresorts to lattice simulations or phenomenological models based on lattice calculations.Investigating the effects at various temperature on the masses and decays of quark bound states is an importantaccess to reveal the nature of QGP, especially its nature at critical temperature . In this paper, we will discuss themass spectrums of heavy quarkonia in QGP. At zero temperature, the quark pair is bound in a potential well dueto confinement. When temperature rises, the interaction at large distance between quarks becomes weaker andweaker due to screening effects and confinement vanishes, i.e. deconfinement happens. Now, the quarkoniumbecomes dissociative and cannot be bound together. Various phenomenological potentials at finite temperature areused to study the charmonium and bottomonium and one finds that J/ψwill become dissociative at T～1.2T_c andbottomonium becomes dissociative at T～4T_c.In this paper we calculate the masses of charmonium and bottomonium with temperature 0.8Tc-2Tc. Ourcalculations show that the mass of quarkonium becomes smaller when temperature rises and the s-wave state forcharmonium dissociates at T～1.2T_c and does not dissociate until T～2T_c although exited states dissociate at thistemperature for bottomonium.