Phases of QCD: lattice thermodynamics and a field theoretical model

Abstract

We investigate three-colour QCD thermodynamics at finite quark chemical potential. Lattice QCD results are compared with a generalized Nambu Jona-Lasinio model in which quarks couple simultaneously to the chiral condensate and to a background temporal gauge field representing Polyakov loop dynamics. This so-called PNJL model thus includes features of both deconfinement and chiral symmetry restoration. The parameters of the Polyakov loop effective potential are fixed in the pure gauge sector. The chiral condensate and the Polyakov loop as functions of temperature and quark chemical potential are calculated by minimizing the thermodynamic potential of the system. The resulting equation of state, (scaled) pressure difference and quark number density at finite quark chemical potential are then confronted with corresponding Lattice QCD data.

Figures (10)

• Figure 1: Scaled pressure, entropy density and energy density as functions of the temperature in the pure gauge sector, compared to the corresponding lattice data taken from Ref. Boyd.
• Figure 2: Scaled Polyakov loop effective potential $\mathcal{U}(\Phi,T)/T^4$ as a function of $\Phi$ for two values of temperature $T$.
• Figure 3: Polyakov loop as a function of temperature in the pure gauge sector, compared to corresponding lattice results taken from Ref. Kaczmarek:2002mc.
• Figure 4: Left: scaled chiral condensate and Polyakov loop $\Phi(T)$ as functions of temperature at zero chemical potential. Right: plots of $\partial\langle\bar{\psi}\psi\rangle/\partial T$ and $\partial\Phi/ \partial T$.
• Figure 5: Averaged sum and difference of $\Phi$ and $\bar{\Phi}$ as functions of the temperature at finite $\mu$.