Phase structure of the Polyakov-quark-meson model

The relation between the deconfinement and chiral phase transition is explored in the framework of a Polyakov-loop-extended two-flavor quark-meson (PQM) model. In this model the Polyakov loop dynamics is represented by a background temporal gauge field which also couples to the quarks. As a novelty an explicit quark chemical potential and $N_f$-dependence in the Polyakov loop potential is proposed by using renormalization group arguments. The behavior of the Polyakov loop as well as the chiral condensate as function of temperature and quark chemical potential is obtained by minimizing the grand canonical thermodynamic potential of the system. The effect of the Polyakov loop dynamics on the chiral phase diagram and on several thermodynamic bulk quantities is presented.

Figure 1

The normalized chiral condensate $⟨\overline{q}q⟩$ and the Polyakov loop $\Phi$ as a function of temperature for $\mu =0$. A chiral crossover is found at $T\sim 180\mathrm{MeV}$ and a deconfinement crossover at a similar temperature.

Figure 2

The normalized Polyakov loop variable $\overline{\Phi }$ for large temperatures for several chemical potentials $\mu$.

Figure 3

The temperature dependence of $\partial ⟨\overline{q}q⟩/\partial T$ and $\partial \Phi /\partial T$ for $\mu =0$. The Polyakov variable is scaled by a factor of 5.

Figure 4

The normalized chiral quark condensate $⟨\sigma ⟩$ as a function of temperature for three different chemical potentials $\mu =0$, 168, 270 MeV. For $\mu =270\mathrm{MeV}$ a first-order transition is found at $T_c\sim 81\mathrm{MeV}$.

Figure 5

The same as Fig. 4 for the normalized Polyakov loops $\overline{\Phi }$ and $\Phi$.

Figure 6

Chiral phase diagrams for the PQM model. Upper lines for a $\mu$-independent Polyakov loop potential and lower lines with $\mu$-dependent corrections. The CEP’s are approximately located at $(T_c,{\mu }_c)=(163,164)\mathrm{MeV}$ (upper case) and at (150, 168) MeV (lower case).

Figure 7

Scaled pressure $p/p_{\mathrm{SB}}$ for three different quark chemical potentials, $\mu =0$, 168, 270 MeV. $T_c(\mu =0)=184\mathrm{MeV}$.

Figure 8

Scaled pressure $p/p_{\mathrm{SB}}$ for $\mu =0$. The PQM model prediction (solid line) is compared to lattice results for $N_{\tau }=4$ and $N_{\tau }=6$. Lattice data taken from Ref. 64.

Figure 9

The same as described in the legend to Fig. 7 for the scaled entropy $s/s_{\mathrm{SB}}$.

Figure 10

Scaled pressure difference $\Delta p/T^4$ for three different chemical potentials. The curves correspond to $\mu =100$, 168, 270 MeV from below.

Figure 11

The same as described in the legend to Fig. 10 for the quark number density $n_q/T^3$. The dashed lines denote the corresponding Stefan-Boltzmann limits.

Figure 12

The scaled chiral susceptibility ${\chi }_q/T^2$ as a function of temperature for three different quark chemical potentials, $\mu =0$, 168, 270 MeV.