An effective thermodynamic potential from the instanton with Polyakov-loop contributions

Abstract

We derive 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. The momentum-dependent constituent-quark mass is also obtained as a function of T, employing 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, translated as the traced Polayakov-loop (Phi) as an order parameter for the Z(N_c) symmsetry, characterizing the confinement (intact) and deconfinement (spontaneously broken) phases. As a result, we observe the crossover of the chiral (chi) order parameter sigma^2 and Phi. It also turns out that the critical temperature for the deconfinment phase transition, T^Z_c is lowered by about (5-10)% in comparison to the case with a constant constituent-quark mass. This behavior can be understood by considerable effects from the partial chiral restoration and nontrivial QCD vacuum on Phi. Numerical calculations show that the crossover transitions occur at (T^chi_c,T^Z_c) ~ (216,227) MeV.

15 pages, 7 figures

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• Vector-current correlation and charge separation via chiral-magnetic effect
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• Thermal conductivity of the quark matter for the SU(2) light-flavor sector
• Quark-gluon mixed condensate for the SU(2) light-flavor sector at finite temperature
• QCD Chiral restoration at finite $T$ under the Magnetic field: Studies based on the instanton vacuum model