We extend the hadronic SU(3) nonlinear $\sigma$ model to include quark degrees of freedom. The choice of potential for the deconfinement order parameter as a function of temperature and chemical potential allows us to construct a realistic phase diagram from the analysis of the order parameters of the system. These parameters are the chiral condensate for the chiral symmetry restoration, and the scalar field $\Phi$ (as an effective field related to the Polyakov loop) for the deconfinement to quark matter. Besides reproducing lattice QCD results, for zero and low chemical potential, we are in agreement with neutron-star observations for zero temperature.

• Received 13 January 2009

DOI:https://doi.org/10.1103/PhysRevC.81.045201