Second look to the Polyakov loop Nambu–Jona-Lasinio model at finite baryonic density

We revisit the Polyakov loop coupled Nambu–Jona-Lasinio model that maintains the Polyakov loop dynamics in the limit of zero temperature. This is of interest for astrophysical applications in the interior of neutron stars. For this purpose we re-examine the form of the potential for the deconfinement order parameter at finite baryonic densities. Since the modification of this potential at any temperature is formally equivalent to assigning a baryonic charge to gluons, we develop a more general formulation of the present model that cures this spurious effect and is normalized to match the asymptotic behavior of the QCD equation of state given by $\mathcal{O}({\alpha }_s^2)$ and partial $\mathcal{O}({\alpha }_s^3{\ln }^2{\alpha }_s)$ perturbative results.

Figure 1

Scaled pressure of three flavor symmetric quark matter as a function of baryonic chemical potential ${\mu }_B$ at different values of the Polyakov loop potential parameters.

Figure 2

Pressure $p$ (upper panel) and Polyakov loop modulus $|\mathrm{\Phi }|$ (lower panel) of electrically neutral matter as a function of baryonic chemical potential ${\mu }_B$ in the phase transition region. Black dotted line on the lower panel represents $|\mathrm{\Phi }|=\frac{1}{3}$.

Figure 3

Pressure $p$ (upper panel) and squared speed of sound $c_{\mathrm{s}}^2$ (lower panel) of electrically neutral matter as a function of baryonic density $n_B$ calculated for hybrid EOS with the quark phase described by the PNJL (blue curves), NJL (red curves), and MIT bag (green curves) models.