Some Studies About The QCD Phase Diagram

The critical end point (CEP) of quantum chromodynamics (QCD) is one of the most important aspects of the phase diagram of strongly interacting matter. It is thus not surprising that an intense experimental activity is nowadays dedicated to the de-tection of such a point, which involves the large facilities at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC); moreover, further experiments are expected after the development of the Facility for Antiproton and Ion Research (FAIR) at Helmholtz Centre for Heavy Ion Research (GSI); theoretically there are various mod-els and methods efforts to determine the phase diagram of QCD too. In this thesis, we provide two methods to study the QCD Phase transition:one is to use quasi-particle model, and the other is to use Dyson-Schwinger equation method. In the later ones, we discuss the effect of different quark-gluon vertex, and add chiral chemical potential to study the phase transition. The dissertation consists of five chapters:In Chapter One, we give an introduction to the related theoretical background, theoretical methods and a brief outline of some fundamental concepts.In Chapter Two, we use the improved quasi-particle model to study the thermody-namic self-consistent equation of state (EOS), remedy the problems of self-consistency in the previous quasi-particle model, and extended it to study the equation of state at finite density. We first shortly review the problem existing in previous quasi-particle models, and then use improved quasi-particle model to extend the zero density, finite temperature condition to finite density and finite temperature condition. We calculate the quark number density, energy density, quark number susceptibility and sound ve-locity at zero temperature in the improved quasi-particle model. At the end of this part, we compared our results with the ones given by the reference.In Chapter Three, we compared the quark number susceptibility obtained use BC vertex approximation and rainbow-ladder approximation when we use the Dyson-Schwinger equation method. We get the result that from the Ball-Chiu (BC) vertex derived from the vector Ward-Takahashi identity (WTI) in accord with that come from simple rainbow-ladder approximation, remedy the problem that the rainbow-ladder ap-proximation dose not satisfy the Slavnov-Taylor identity of QCD. So we could use BC vertex to study the phase transition.In Chapter Four, we are the fist one who use the Dyson-Schwinger equation method to study the phase transition at finite chiral chemical potential, this is con-sistent with the results come from phenomenological models. In our research, we use simple sperate gluon propagator and quark-gluon vertex, which facilitates the numeri-cal calculation. In the end of this part, we compare our results with the ones given by the phenomenological models.The improved quasi-particle model is thermodynamically self-consistent, so we could use this phenomenological model to study the QCD phase transition. The BC vertex satisfies some physical requirements, we can use it to study the phase transi-tion int he framework of Dyson-Schwinger equation method more strictly. When we introduce a finite chiral chemical potential, we could find the chiral critical end point (CEP5), and in further studies, we could obtain the critical end point (CEP) through the chiral critical end point. So, by introducing the chiral chemical potential, we can obtain another new method in the framework of the Dyson-Schwinger equation method to study QCD phase diagram.The last chapter presents a summary of this dissertation, and gives some outlook for the further study.