Non-perturbative Study Of Hadron Properties And Chiral Phase Transition

Quantum Chromodynamics (QCD) is the basic theory of hadron physics. Because of the non-perturbative property of QCD in the low energy region, there are very rich physics phenomenology. There are two typical features of low energy QCD:color con-finement and dynamical chiral symmetry breaking (DCSB). We study the properties of low energy QCD within the framework of Dyson-Schwinger Equations(DSEs) mainly from two aspects. On the one hand, studying hadron physics under contact interaction model. On the other hand, studying chiral phase transition of QCD in finite temperature and/or finite chemical potential.In chapter 2, we firstly introduce the DSEs in quantum field theory. Take Quantum Electrodynamics as an example, deriving the DSE of fermion and gauge boson by functional. Further more, the symmetries of QCD are introduce:BRST symmetry and chiral symmetry, and also discussed the DCSB. However, all hadron states in the nature are in the status of bound state of quarks and/or anti-quarks. Because of color confinement, it still failure to find free quark state in nature. Then, the bound state problem in QCD seems especially important. In the last of this chapter, we introduce two body bound state equation, that is Bethe-Salpeter Equation(BSE), and three body bound state equation, that is Faddeev Equation.In chapter 3, vector (?) vector contact interaction model under Rainbow-Ladder truncation is employed to study the non-perturbative properties of quark propagator. The mass function of quark is relative momentum independent since the contact in-teraction is momentum independent. However, we introduce cutoff since the contact interaction in non-renormalizable. We employed proper time regularization, which p-reserves the confinement of quark. π meson, which regard as the simplest and the most important hadron, is viewed as quark-antiquark bound state and the pseudo-goldstone boson through dynamical approximate chiral symmetry breaking simultaneously. The cutoff we introduced breaks the poincare symmetry, which caused the axial-vector current is not conserved in concrete calculations. In studying baryon’s bound state, static approximation is widely used. In static approximation, the interaction kernel of quark-diquark is momentum independent so that the amplitudes of baryon are momen-tum independent. While in the non-static case, the masses of nucleon and △++ and the chebyshev moments of BS amplitudes are displayed. In addition, we discussed the tensor charge of nucleon in the case of static and non-static.In chapter 4, we study the equation of state(EOS) of QCD firstly. Under "Qin-Chang" model, we obtain quark propagator at zero temperature and zero chemical potential numerically. Using three conjugate complex poles formula, the quark propa-gator at T=0 and μ=0 is fitted. Then, the fitted quark propagator was generalized to T=0 and μ≠0. The chemical equilibrium and electric charge neutrality conditions are used to constrain various chemical potential, namely μu,μd,μs and μe, and there is only one chemical potential is independent. In cases of two flavors and three fla-vors, we discussed the average energy per baryon. It is showed that the average energy per baryon is much lower in three flavor case. Next in importance, in the violet im-proved "Maris-Tandy" model, the chiral susceptibility is used to locate the critical end point(CEP). After introduce chiral chemical potential, the location of CEP in the plane of μ5-T and μ5-μ are studied. Our numerical results shows that it is consistence with Lattice.