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

TL;DR

This paper derives an effective thermodynamic potential incorporating instanton effects and Polyakov-loop contributions, revealing crossover transitions in chiral and deconfinement phases at finite temperature.

Contribution

It introduces a novel approach combining instanton solutions with Polyakov-loop dynamics to study phase transitions in QCD at finite temperature.

Findings

Crossover of chiral and Polyakov-loop order parameters observed.

Deconfinement critical temperature lowered by 5-10%.

Numerical transition temperatures approximately 216 MeV (chiral) and 227 MeV (deconfinement).

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.