QCD Phase Diagram And Hadron Physics Within Dyson-Shwinger Equations Study

Nowadays, international efforts on strongly interacting matter study are focusing on two important areas:the phase diagram of strongly interacting matter and hadron prop-erties. Of these two areas, the former is aiming at an richer understanding of the mat-ters in the universe by studing the their phase diagram, while the later focuses on the structure of the hadrons and help people gain more insights deep into these particles. Actually, these two studies can be summarized as one:the micro- and macro-structure of strongly interacting matters at low energy scale. With the experimental discovery of Higgs boson, the final missing piece of standard model has been found. However, although we now have at hand a fundamental and self-sufficient theory describing the strong interaction sector—Quantum Chromodynamics, our capability to do study and calculation in this area has been largely suppressed by various complicated phenom-ena here, including confinement, spontaneous chiral symmetry breaking, non-trival vaccum and the non-perturbative nature of low energy QCD. So, in order to study the these problems, I will adopt a non-perturbative method—Dyson-Schwinger Equations method. The derivation of these equations are based on functional path integral and are thus non-perturbative in essence.The DSEs are an infinite tower of coupled, nonlinear integral equations, which provide relations between all the Green functions of a quantum field theory. However, to reduce the size of these equations, one has to make truncations and approximations inevitably. So, in this thesis, these manipulations have been performed with caution so as to respect the symmetries and properties of the studied system. For example, in the QCD phase diagram study, Cornwall-Jackiw-Tomboulis effective action was intro-duced to make rigorous definitions and consistent calculations within its framework.In order to study the case beyond chiral limit, we employed a chemical potential sup-pressed gluon propagator model and generalized its investigation from zero tempera-ture and finite chemical potential to finite temperature and chemical potential. Finally with various thermodynamical quantities being studied, a complete QCD phase dia-gram about chiral symmetry breaking was drawn in the temperature—chemical poten-tial plane. Most importantly, we gave a prediction about the location of CEP based on our model study, which is consistent with other model studies.On the other hand, in the Bethe-Salpeter Equation study of kaon, which is the Goldstone boson accompanying the spontaneous chiral symmetry breaking, the related conservation law—Axial-vetor Ward-Takahashi identity was strictly preserved. Then, with the recently developed parametrisation method, we were able to compute many moments of kaon’s Parton Distribution Amplitude(PDA) and reconstructed a PDA that is more pointwise accurate than earlier ones, since the later are all obtained from very limited moments. As we know, PDAs sever an important role in light-cone sum rules as much as vaccum condensates in QCD sum rules. The LCSR takes them as inputs to be determined by experiments while we can calculate them with accuracy using the Feynman parametrisation method and numerical calculation. Based on these leading twist PDAs, we discussed the dynamical chiral symmetry breaking within kaon and confirmed the superiority of DB kernel over the rainbow-ladder approximation. In this way, my PDA could be a more accurate input for exclusive hadronic heavy meson decays. Given all the advantages of our parametrisation method, a lot more studies on hadron properties are accessible now, including the electro-magnetic form factor and PDAs of twist-3.