Abstract
In this talk, we report our recent studies on an effective thermodynamic potential (Omega_eff) at finite temperature (T>0) and zero quark-chemical potential (mu_R=0), using the singular-gauge instanton solution and Matsubara formula for N_c=3 and N_f=2 in the chiral limit, i.e. m_q=0. The momentum-dependent constituent-quark mass is computed as a function of T, together with the Harrington-Shepard caloron solution in the large-N_c limit. In addition, we take into account the imaginary quark-chemical potential mu_I = A_4, indentified as the traced Polayakov-loop (Phi) as an order parameter for the Z(N_c) symmetry, characterizing the confinement (intact) and deconfinement (spontaneously broken) phases. As a consequence, we observe the crossover of the chiral (chi) order parameter sigma^2 and Phi. It also turns out that the critical temperature for the deconfinement phase transition, T^Z_c is lowered by about (5~10) % in comparison to the case with the constant constituent-quark mass. This behavior can be understood by considerable effects from the partial chiral restoration and nontrivial QCD vacuum on the Phi. Numerical results show that the crossover transitions occur at (T^chi_c,T^Z_c) ~ (216,227) MeV.
Highlights
We note that the phase structure of quantum chromodynamics (QCD), as a function of temperature T and quark-chemical potential μ, represents the breaking patterns of the relevant symmetries in QCD
Interestingly enough, the Polyakov-loop-augmented Nambu-Jona-Lasinio model describes the crossover of the two different QCD order parameters for the chiral and Z(Nc) symmetries, represented by the chiral condensate qq ∝ σ2 and the traced Polyakov loop φ ≡ Φ, respectively [7,8,9,10,11, 14]
As for TcZ estimated in the lattice QCD (LQCD), using the clover-improved Wilson fermions it was determined about 210 MeV [6], which is rather compatible with ours
Summary
We note that the phase structure of quantum chromodynamics (QCD), as a function of temperature T and quark-chemical potential μ, represents the breaking patterns of the relevant symmetries in QCD. Our strategy is rather simple and practical as follows: i) Using the instanton distribution function at finite T from the caloron solution with trivial holonomy (the Harrington-Shepard caloron) [30, 31], we first compute the instanton density and average size of instanton as functions of T , resulting in that the instanton effect remains finite even beyond the critical temperature Tc ∼ ΛQCD Taking into account these ingredients, we obtain (k(three momentum), T (temperature))-dependent constituent-quark mass M, Mk,T , which plays the most important role in the present approach. Considering the chiral and Z(Nc) symmetries on the same footing as in the pNJL model, we introduce the imaginary quark-chemical potential μI ≡ A4, which corresponds to the uniform color gauge field in the Polyakov gauge It will be identified later as the traced Polyakov loop Φ, as an order parameter for the spontaneous breakdown of Z(Nc) symmetry, i.e. the deconfinement phase transition. We note that this talk is based on Ref. [32], and more details on the theoretical evaluations can be found there
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