Effects Of Finite Chemical Potential On The Heavy-quark Potential In An Anisotropic Medium

The exploration of Quark Gluon Plasma (abbreviated as QGP) is currently one of the core contents in high-energy heavy ion physics. QGP, with a net color charge, cannot be directly observed in experiments and one has to rely on the final color-neutral particle spectrum to analyze its physical properties. In recent 30 years, as an effective "probe" to understand the QGP, quarkonium studies have attracted more and more attentions from theoretical physicists. In the thesis, we will focus on the related issues.In the real time formalism of finite temperature quantum field theory, we ob-tain the gluon self-energy at leading order by computing the corresponding Feynman diagrams under hard-thermal-loop approximation. Furthermore, utilizing the Dyson-Schwinger equation, the resumed gluon propagator is calculated whose Fourier trans-form in the static limit defines the heavy-quark potential due to one gluon exchange. We analyze the effects of the finite chemical potential on the heavy-quark potential in an anisotropic medium. It shows that finite chemical potential will modify the in-medium Debye screening mass which eventually gives corrections to the heavy-quark potential.Using the relevant results, we plot the heavy-quark potential in an anisotropic medium with finite chemical potential. We find that corrections to the heavy-quark potential caused by anisotropies have an opposite effect as compared to those caused by the finite chemical potential. Under certain conditions, the potential curve recovers to the ideal case approximately.Under extreme conditions, i.e., the Bohr radius of the bound state is much less than the screening length in the medium, analytical results of the binding energy and decay width can be computed by using the perturbative contributions of the heavy-quark potential. In particular, we discuss the corresponding corrections to the above physical quantities which arise due to the introduction of the chemical potential and anisotropies.Finally, for the widely studied bound states in current experiments, such as J/Ψ and Y, with certain models for the non-perturbative heavy-quark potential, we obtain the J/Ψ dissociation conditions in a simple manner based on the idea of the effec-tive screening mass. In a non-ideal medium, the dissociation conditions are jointly determined by the temperature, chemical potential and anisotropies.