The Spectral Function Anddissociation Of Heavy Quarkonium In Strong Coupling Coulomb Potential

Quark gluon plasma (QGP) is a new state of matter, which is composed of two types of elementary particles, quarks and gluons. At high temperature and density, the gauge field theory describing strong interaction would be in the phase of quark gluon plasma where quarks are deconfined. In experiments, high energy heavy ion collision is used to study the properties of QGP where tremendous kinetic energy changes into heat energy to creat the condition of deconfinement phase transition. The properties of the quarkonium are used as a signature to study the QGP. Lattice QCD theory and potential models are two main theoretical methods for studying characters of the non-relativistic quarkonium at finite temperature.In this paper,we mainly study the characters of the quarkonium at finite temperature by spectral function in strong coupling Coulomb potential. With the Ads/CFT implied potential from the internal energy and free energy of static quark anti quark, we get the solution of the two-body wave function equation in the nonrelativistity and explore the spectral function and the dissociation temperature of various heavy quarkonium bound states finally.If modeling the heavy quarkonium as a heavy quark and its antiquark relativistic bound states, the relative motion of the wave function should satisfy the two body Dirac equation, so it belongs to the relativistic two boby problem. To solve it, we can transform the Hanmiltonian of Dirac particles in the usual repcrscntation to a rcpersentation in which it contains no odd operators by one or more canonical transformation and it becomes possible to separate out quadruple of equations for the four components wave function equation according to non-relativistic approximation[40,41], so that the two body problem changes into a single issues. In the fourth part of the paper,we tentatively study the characters of heavy quark in strong coupling Coulomb potential by one body Dirac equation. Finally, from the figures of spectral density function and energy density we have obtained the dissociation temperature of various heavy quarkonium bound states, and we also compared them to the case of heavy quarkonium in non-relativistic situation.Our results show that:in the non-relativistic case, with the increasing temperature a quarkonium bound state binding energy decreases rapidly, that is the quark and anti-quark becomes weakly bound, and thermal fluctuations can dissociate it when the binding energy is sufficiently small; The melting temperature of b quarkonium is higher than its of c quarkonium in the same context.