Model Studies On The Heavy-Quark Potential In The Quark-Gluon Plasma

Since the 1980s,high-energy physicists began to pay attention to the basic prop-erties of strong interaction matter at high temperature and high density and their implementation in high-energy heavy-ion collisions.As an important "probe" for understanding QGP,the suppression of heavy quarkonium production is one of the core issue in this field.In the nonrelativistic limit,based on the correct form of the heavy-quark potential,the physical properties of quarkonia in medium can be obtained by solving the Schrodinger equation.In this thesis,we focus on the heavy-quark potential and complete the following two works.Based on the latest simulation results of lattice Quantum Chromodynamics on the complex heavy-quark potential,we construct the phenomenological model of heavy-quark potential in the real-time formalism of finite temperature field theory.On the one hand,besides the perturbative gluon propagator from the hard thermal loop resumed theory,we introduce the static nonperturbative contribution induced by the dimension two gluon condensates.The Fourier transform of the retarded/advanced propagator determines the real part of the heavy-quark potential which defines the binding en-ergy of the quarkonia in the hot and dense medium.On the other hand,given the p0 dependent form of the nonperturbative contribution from the retarded/advanced propagator,and then the symmetric propagator in static limit can be obtained in the theoretical framework of finite temperature field theory without resorting to any other extra assumption.Accordingly,its Fourier transform determines the imaginary part of the potential.The appearance of the imaginary part is connected with the Landau damping effect of the low frequency gauge field,which is related to the decay width of the bound state and provides necessary information on the dissociation of quarkonium in QGP.The heavy-quark potential model constructed in this thesis can quantitative-ly describe the lattice data.As compared with other existed potential models,the imaginary part has been greatly improved,which is crucial for further understanding the properties of quarkonium in QGP.In recent years,much attention has been paid to the nonideal QGP with nonze-ro shear viscosity.The shear viscosity of the system is related to the anisotropic distribution of partons in momentum space.In the QGP with shear viscosity,the rotational symmetry of the heavy-quark potential is broken due to the angular depen-dence appearing in the Debye mass.Accordingly,the study of the basic properties of quarkonium in the medium involves solving the three dimensional Schrodinger e-quation,which greatly increases the difficulties especially on the numerical method.In this thesis,we propose an effective Debye mass by performing an quantum av-erage of the anisotropic Debye mass in the(?,?)space,thus eliminate the angular dependence in the potential which is effectively one-dimensional.In order to show the rationality of the effective potential,on the one hand,we perturbatively compute the binding energies of the quarkonia and the leading order contribution is determined by the one-dimensional effective potential.The numerical results show that the high-order contributions largely suppressed,which provides support for the rationality of the anisotropic effective Debye mass.On the other hand,we compute the binding energies and decay width of the quarkonia by solving the effective one-dimensional and three-dimensional Schrodinger equation,respectively.The results directly verify the rationality of the anisotropic effective Debye mass.Therefore,using the effective Debye mass proposed in this thesis can improve the efficiency and accuracy of the existed numerical algorithm.Furthermore,it is also efficient to deal with some other complicated problems related to quarkonium in a viscous QGP.