Research Of QCD At Finite Temperature And Finite Chemical Potential Within Quasi-particle Model

Now, it is generally accepted that the theory describing strongly interacting matter is Quantum Chromodynamics (QCD). In this theory, the elementary particle is the quantum of quark field and SU(3) gauge field——quark and gluon. The strong interaction between quarks is mediated by the exchange of gluons. Unlike the electromagnetic interaction (Abelian gauge field), the non-Abelian gauge theory is asympotically free. The coupling constant depends on the momentum transfer:it becomes strong at small momenta or large distance but becomes weak at large momenta or short distance. One of the fundamental prediction of QCD is that there is a phase transition from hadronic matter with confinement and chiral symmetry spontaneous breaking, at low temperature and/or chemical potential, to a plasma composed of quark-gluon constituents (QGP) that deconfine and restore chiral symmetry, at high temperature and/or chemical potential. Using lattice QCD, people have shown the existence of such a phase transition at zero chemical potential and finite temperature. QGP describes the relevant features of nature under extreme conditions. In particular, according to modern cosmology, it dominates the evolution of the early universe (at essentially vanishing net baryon density). In addition it also probably happens in neutron stars (at large density). Therefore the study of the thermodynamic properties of QGP has attracted considerable attention over the years from the theoretical aspects.In principle, lattice QCD provides a straightforward way to compute properties of QGP, and in particular its equation of state (EOS) at finite temperature and zero chemical potential. However, at finite chemical potential, because of the notorious sign problem of the Fermion determinant, lattice QCD method cannot be directly applied. Among the analytical approaches, the weak coupling expansion of thermodynamic quantities shows a extremely poor convergence for any temperature of practical interest. To overcome this poor convergence, people have invented many methods with a rigorous link to QCD, such as the resummed HTL scheme, φ-functional approach and so on. On the other hand, many different phenomenological models were adopted to describe the nonperturbative behavior of QGP seen in lattice simulations of QCD. Among those models, the quasi-particle QGP model with few fitting parameters was widely used to reproduce the properties of the QCD plasma. In this model at finite temperature, instead of real quarks and gluons with QCD interactions, one can consider the system to be made up of non-interacting quasi-particles with temperature-dependent effective mass, quasi-quarks and quasi-gluons. This model was first proposed by V. Goloviznin and H. Satz, and later by A. Peshier et al. After a while M.I. Gorenstein and S.N. Yang found that this model is thermodynamically inconsistent and remedied this flaw by reformulating statistical mechanics. After that V.M. Bannur also proposed a new quasi-particle model using standard statistical mechanics and avoided the thermodynamical inconsistency from the energy density rather than the pressure. Further F.G. Gardim and F.M. Steffens showed that the two models proposed by Peshier and Bannur are two extreme limits of a general formulation. In chapter2of this paper we will revisit the history of the quasi-particle model, survey several existing popular quasi-particle model and point out the problem hidden in these models. We will see that although the early researchers made a variety of effort to ensure thermodynamical consistency, there is still a temperature-dependent infinity of thermal vacuum zero point energy and this makes the partition function of the previous models ill defined. It is generally thought that enhanced fluctuations are essential characteristics of QCD phase transitions. A measure of the intrinsic statistical fluctuations in QCD is provided by the associated quark-number susceptibility (QNS), which may be used to identify the chiral critical point in the QCD phase diagram. Thus, in recent years the QNS in QCD has been extensively studied by many different methods and models. In Chapter3we will first begin with the renormalized partition function of QCD ar finite temperature and chemical potential and derive the expression of QNS. We can see that the QNS is expressed in terms of the dressed quark propagator at finite temperature and chemical potential. With the help of the Green function of quasi-particle, we calculate the QNS for a system with two light quark flavors and give a discussion of the result.In Chapter4, we will propose a solution to the problem that is illustrated in the end of Chapter2. By introducing a classical background field B(T), we successfully eliminate the T-dependent infinity of thermal vacuum energy in the partition function and make it well defined. On that basis we construct a new, thermodynamically consistent quasi-particle model without T-dependent infinity of the vacuum zero point energy. Then we use our new model to fit the latest lattice results of Borsanyi et al for (2+1) flavor system at finite temperature and zero chemical potential and make a comparsion of the result of our model with early calculations using other models. Furthermore, we generalize our quasi-particle model from finite temperature and zero chemical potential to the case of finite chemical potential and zero temperature, and calculate the EOS and other thermodynamic quantities for (2+1) flavor QCD at zero temperature and high density. We also give a discussion of our result. At the end of Chapter4we apply our new EOS to study the structure of quark star. We find that our result is consistent with recent observational data. Finally, we conclude our work with a summary and make an outlook for the future work.