  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
behaviour 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.
