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Chiral Thermodynamic Model of QCD and its Critical Behavior in the Closed-Time-Path Green Function Approach

By applying the closed-time-path Green function formalism to the chiral dynamical model based on an effective Lagrangian of chiral quarks with the nonlinear-realized meson fields as bosonized auxiliary fields, we then arrive at a chiral thermodynamic model for the meson fields with finite temperature. Particular attention is paid to the spontaneous chiral symmetry breaking and restoration from the dynamically generated effective composite Higgs potential of meson fields at finite temperature. It is shown that the minimal condition of the effective composite Higgs potential of meson fields leads to the thermodynamic gap equation at finite temperature, which enables us to investigate the critical behavior of the effective chiral thermodynamical model and to explore the QCD phase transition. After fixing the free parameters in the effective chiral Lagrangian at low energies with zero temperature, we determine the critical temperature of the chiral symmetry restoration and present a consistent prediction for the thermodynamical behavior of several physically interesting quantities, which include the vacuum expectation value $v_o(T)$, quark condensate $<\bar{q}q>(T)$, pion decay constant $f_π(T)$ and pion meson mass $m_π(T)$. In particular, it is also shown that the thermodynamic scaling behavior of these quantities becomes the same near the critical point of phase transition.