The Study Of The Potential Model Of The Quarkonium And Its Dissociation

Quark gluon plasma is a new form of matter where quark and gluon are considered to be de-confined. Theoretically, QCD theory, describing the strong interaction, predicts that there may be a transition from the ordinary hadronic matter to QGP matter under extreme conditions of high temperature and high density; while in the big bang theory, it did exist this new matter in the early stages of the big bang. Experimentally, in order to find the existence of QGP, one has to create such extreme conditions for instance with heavy ion collision. In recent years, the RHIC collider located at Brookhaven National Laboratory collide two beams of particles at center of mass energy-sNN=200GeV. It was believed that there should be a phase transition from hadron to de-confined matter at RHIC through the related observables, proving the existence of QGP preliminarily.Though QGP has been verified in the experiments preliminarily, this new material just exist in a very short time. It will undergo the hadronization process and be confined again. i.e. QGP can not be detected directly, but probed by some related observation data at the end stage of the experiment, called the signals of QGP. The topic of our work, the dissociation of the quarko-nium is one of these signals. Theoretically, concerning the research of quarknonium, the most common approach is the effective potential model method. Considering the large constituent mass, the interaction of q and q can be described by effective potential under the non-relativistic limit. Related properties such as the dissociation temperature can be determined by this potential model.The potential is a strongly coupled quantity which should be resolved by non-perturbative method. Considering the conventional methods, for instance, Lattice QCD, Dyson-Schwinger equation, some resummation method in quantum field theory, holographic dual, and so on. Lat-tice QCD is the only way starting from the first principles but has some technical deficiencies that only applicable to high temperature and low density area. DS equation can be used to resolve some non-perturbative Green functions, but need to do some approximation in the procedure of the solution. They all have their limitations. The holographic dual opens a new avenue towards analytic treatments of the strong coupling limit of a gauge theory. Respect to the holographic principle, the weak coupling gravitational theory in D+1dimension is related to the D dimen-sional strongly coupled field theory on its boundary. One of the most important application is AdS/CFT. However, the conformal theory is not QCD. There is a gap between them. A cousin of AdS/CFT with an infrared cutoff, AdS/QCD, has been actively investigated which is more phenomenological. Either AdS/CFT or AdS/QCD show remarkable results, such as viscosity ratio η/s, jet quenching parameter, diffusion coefficient, etc. Also, there are some results about the quark potential model.The leading order quark potential calculated by AdS/CFT is a Coulomb potential at zero temperature while a truncated Coulomb potential at finite temperature, which means the inter-action has its certain range. The potential vanishes beyond this range. For AdS/QCD, the linear potential can be provided at zero temperature, and the nonzero temperature behavior were found to fit lattice data quite well. Results from Lattice calculation show the screening effect at finite temperature. It is a smooth screening behavior like the Yukawa potential which is exponential decay.In our work, we shall explore analytically the screening property of the heavy-quark po-tential within the framework of AdS/QCD. The results show that under a fairly general condi-tions of the metric underlying AdS/QCD, the screening remains kink-like, like that of the super Yang-Mills. In other words, AdS/QCD cannot provide a exponentially screening potential in the plasma phase. We shall also point out the kink-like screening potential may violate fundamen-tal principles of quantum field theories. On the other side, in N=4SYM field theory, using a ladder diagram resummation formula, the quark potential at zero temperature qualitativly con-sistent with the AdS/CFT’s result. We extended this resummation formula to finite temperature in order to check the coincidence of these two methods at finite temperature. Our results show the disparity of these two methods’calculation. We analyze that maybe the resummation for-mula has its own limitations, or the treatment of the propagator at finite temperature is relatively simple in our work. We have to do some further study and discussion in the future.Furthermore, in the previous work, the heavy quarkonium melting has been examined within the potential model with the AdS/CFT implied potential function (holographic poten-tial). In our work, we considered the relativistic effect on basis of the NR limit, and calculated the first order correction of the quarkonium dissociation temperature. Starting from the Hamilto-nian of the two body Dirac equation, under the Foldy-Wouthuysen transformation, we expanded the Hamiltonian in series of the velocity v, reserving to the first order correction v4. Respect to the perturbative calculation, in spite of the large constituent mass, the correction is significant in size, especially for J/Ψ. In addition, the first order relativistic correction will lower the dissoci-ation temperature with a holographic potential. We will give a detailed analysis and explanation in Chapter4to these results.