Thermodynamics and phase diagrams of the Polyakov quark-meson model with on-shell versus curvature mass parameter fixing

The Quantum Chromodynamics (QCD) phase structure has been studied using the Polyakov-loop augmented quark-meson model (PQM) in the extended mean field approximation (e-MFA) where the quark one-loop vacuum term is included.~When the divergent vacuum term is regularized in the minimal subtraction scheme and the curvature meson masses are used to fix the parameters,~the Polyakov quark-meson model with the vacuum term (PQMVT) becomes inconsistent as the curvature masses are determined by calculating the self energies at zero momentum.~The above inconsistency is remedied by the on-shell parameter fixing when the pion decay constant and the pole masses of the mesons are put into the relation of the couplings and running mass parameter by using the on-shell and the minimal subtraction renormalization scheme.~Combining the modified chiral effective potential of the on-shell renormalized quark-meson model (RQM) with the Polyakov-loop potential that mimics the physics of the confinement-deconfinement transition,~we get the renormalized Polyakov quark-meson (RPQM) model.~The phase diagrams and the thermodynamics details for the PQM, PQMVT and RPQM model, have been computed and compared for different forms of the Polyakov-loop potentials with and without the quark back-reaction.~The results have also been compared with the available lattice QCD data.~The so called quarkyonic phase region in the phase diagram, where the chiral symmetry is restored but the quarks and anti-quarks are still confined,~gets reduced by the quark back-reaction in the unquenched Polyakov-loop potential.~It altogether disappears for the chemical potential dependent parameter $T_{0} \equiv T_{0} (\mu)$ in the Log or the PolyLog-glue form of the Polyakov-loop potential in the RPQM model.