Theoretical Model Research On Critical Behavior And Phase Structure Of The QCD Matter

Quantum Chromodynamics (QCD) is a basic dynamical theory describing the strong interaction on the quark level. QCD matter has rich phase structures at finite temper-ature and density. For instance, the hadronic matter phase, the quark-gluon plasma, superconductor and superfluidity etc. Studying the transitions of different phases and the critical phenomena, determining the phase boundary and the position of QCD criti-cal point, are important issues of high energy heavy-ion collision. Generally speaking, if calculate from the QCD Lagrangian directly, we could adopt method of the perturbative theory at very high temperature and density. In the nonperturbative region, one discuss the thermodynamical properties of QCD matter and related calculated methods through lattice calculation or establishing effective models which have corresponding symmetric properties of QCD. This paper is based on the QCD effective models, and discuss the fol-lowing contents:the determination of the position of QCD critical point at finite baryon density; the crossover region of different critical behavior; the inter-influence of three phase transitions at finite isospin density and the BEC-BCS crossover in the superfluidity phase.The first three chapters subject to the basis corresponding to our work. Firstly, we have a brief review of the past studies of QCD phase structures. Then, we introduce two effective models which have the similar symmetry of QCD Lagrangian—the Nambu-Jona-Lasinio (NJL) model and the Polyakov-NJL (PNJL) model. The former is of four fermions point-like interaction and has the chiral symmetry of QCD Lagrangian. The latter is based on the NJL model and introduce a static gluon background. The PNJL model couples the chiral condensate and the Polyakov loop which both contain the quark contribution. And it has the chiral and confinement properties of QCD theory. The calculations are in the frame of the finite temperature field theory.The back part of our paper subject to the results of our study. Using the Landau the-ory of phase transitions, we analyse the phase structure of two flavor NJL model at finite temperature and finite baryon number chemical potential and give the phase diagram in the 3-dimension space of T-μ-m0. The phase diagram clearly show the difference and connection of tricritical point, critical end point and common critical point. And it also behaves as a preparation of the analysis of critical phenomena in the following. Consider-ing the special characteristics of the tricritical point at chiral limit, we analyse the critical behavior of thermodynamical quantities at the tricritical point along different phase tran-sition lines. The result shows that in the vicinity of the tricritical point, there are crossover regions ofφ4-φ6 critical behavior. We display the regions of different critical behavior. A further study shows that, the critical exponents need the Fisher renormalization when one approach the tricritical point along the first-order phase transition line.By means of energy scan to locate the QCD critical point is always one of objectives of high energy heavy ion collision experiment. Since the critical point is the end of the first order phase transition line, we consider the method of approaching the QCD critical point along the first order phase transition line in the energy scan. Our study shows that, the thermalπmesons exist not only in the chiral symmetry broken phase, but also in the chiral symmetry restored phase where the main degrees of freedom are quark and antiquarks. On the first order phase transition line the thermodynamical system is in the two phases coexistence. The character leads the order parameter and corresponding physical quantities such as the mass ofπetc. have two physical values. At the critical point these two values equal. The mass difference of the thermalπmeson in two phases result in the difference of pion abundance. And further the decay production ofπdiffers. At the critical point the difference disappears. We expect this physical picture would provide helpful enlightenment for exploring the phase boundary and critical point in experiment.At last, we study the effect of isospin chemical potential in the frame of the PNJL model. We discuss the inter-influence of the chiral, deconfinement andπsuperfluidity phase transitions, calculate the meson excitation spectra in the superfluidity phase and obtain the corresponding T-μI phase structure. The results show that the confinement property enlarges the regions of chiral condensate andπcondensate and influences the collective excitation modes of the thermodynamical system. The T-μI phase diagram is divided into four matter-state parts:the hadronic phase, the quark gluon plasma phase, the BEC superfluidity phase and the BCS superfluidity phase. In the pion superfluidity phase, when the value of the isospin chemical potential equals the double quark effective mass, there exists BEC-BCS crossover. This is the density effect.