The Dielectric Function Of Quark-gluon Plasma And Phenomena Induced By The Jet In The Medium

Quantum chromodynamics (QCD) predicts that deconfined phase transition will take place at high temperature and/or high density. As a result, the nuclear matter will undergo a transition to quark-gluon plasma (QGP) which is composed of quarks and gluons. Many theoretical studies indicate that the expected high temperature will reach by colliding two ultrarelativistic heavy nuclei at sufficiently high energy in laboratory. One main goal for the Relativistic Heavy Ion Collider (RHIC) is to seek this new state of matter. RHIC have provide several different colliding systems at a variety of energies and the vast data have been collected since its operation in 2000. Though there are controversies, many physicists argue that the QGP is produced at RHIC. However, it is not a long expected weak coupled QGP, but a strongly coupled and nearly perfect quark gluon fluid with a very small viscosity. To study global properties of the QGP is an urgent topic in heavy ion community. In this thesis, we focus on the color dielectric function of the QGP and the phenomena induced by a fast parton traveling through the QGP.At first, we will briefly introduce some primary findings at RHIC, such as, elliptic flow v2, jet quenching and azimuthal dihadron correlation observable. Then, we will review foundations of finite temperature field theory, kinetic theory and hydrodynamics which are theoretical tools for the QGP.With the hard thermal loop (HTL) resummation technique, we calculate the dielectric function excited by hard gluon in the quark-gluon plasma. We find that in the space-like regionω/k< 1, the real part of the dielectric function has two nontrivial extremum structures. At the same time, at theω/k where the extrema of the real part are located, the imaginary part of the dielectric function shows resonance structures. While the real and imaginary parts of dielectric function in the HTL approximation are both monotonously in the space-like region, showing no any resonance structures. These facts imply that properties of the dielectric function in the space-like region relate to some energy exchange mechanism—Landau damping. The main contributions of the resummation calculation come from the three and four gluon interactions which reflect nonlinear and non-Abelian nature of the quark-gluon plasma. Nonlinear and non-Abelian interaction will result in nonlinear Landau damping, which determines the properties of the dielectric function in the space-like region.Within the framework of the linear response theory, by applying the dielectric function calcu- lated with the HTL resummation technique, we study the wake potential induced by a fast parton traveling through the QGP. In the backward direction, wake potential is a Lennard—Jones poten-tial at v= 0.55c, while the wake potential shows an obvious oscillatory behavior for v= 0.99c. In the forward direction, it is a modified Coulomb potential for both cases of v= 0.55c and v= 0.99c. In comparison with results calculated with the HTL dielectric function, nonlinear and non-abelian effects from the resummation calculation enhance anisotropy of the wake potential in the backward-forward directions. Finally, we give some explanations for those wake properties.Viscosity will modify the distribution functions of quark and gluon. By using quark dis-tribution function modified by shear viscosity, we derive the viscous chromohydrodynamics by expanding the kinetic equation in momenta moments and truncating the expansion at the second moment level. In terms of the viscous chromohydrodynamic equations, we can derive the polar-ization tensor and the dielectric function. Whenη/s is small, such as the AdS/CFT bound 1/4π, the real part of the dielectric function deviates from the ideal chromohydrodynamic case (η/s= 0) slightly. With the increase ofη/s, its deviation becomes larger. Meanwhile, the imaginary part exhibits the similar properties. In addition, at some modes ofω/k, the real and the imaginary parts are independent on the shear viscosity. By analyzing the mathematical structures of the dielectric function, we give some explanations for the behavior.By using the viscous dielectric function, we calculate the wake potential induced by a fast parton traveling through the viscous QGP. Through the dielectric function, shear viscosity af-fects the wake potential. The numerical analysis shows that viscous effects on wake potential are speed-dependent. In comparison with the ideal chromohydrodynamic results, shear viscosity make oscillation of wake potential more pronounced at v= 0.99c. While v= 0.55c, the viscous effects on the wake potential are so trivial in both the forward and backward directions and one can hardly distinguish all viscous potential curves from each other. Finally, we give some explanations for the speed-dependent viscous effects on the wake properties.