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The Quantum Chromodynamics (QCD) phase structure has been studied using thePolyakov-loop augmented quark-meson model (PQM) in the extended mean fieldapproximation (e-MFA) where the quark one-loop vacuum term is included.~Whenthe divergent vacuum term is regularized in the minimal subtraction scheme andthe curvature meson masses are used to fix the parameters,~the Polyakovquark-meson model with the vacuum term (PQMVT) becomes inconsistent as thecurvature masses are determined by calculating the self energies at zeromomentum.~The above inconsistency is remedied by the on-shell parameter fixingwhen the pion decay constant and the pole masses of the mesons are put into therelation of the couplings and running mass parameter by using the on-shell andthe minimal subtraction renormalization scheme.~Combining the modified chiraleffective potential of the on-shell renormalized quark-meson model (RQM) withthe Polyakov-loop potential that mimics the physics of theconfinement-deconfinement transition,~we get the renormalized Polyakovquark-meson (RPQM) model.~The phase diagrams and the thermodynamics details forthe PQM, PQMVT and RPQM model, have been computed and compared for differentforms of the Polyakov-loop potentials with and without the quarkback-reaction.~The results have also been compared with the available latticeQCD data.~The so called quarkyonic phase region in the phase diagram, where thechiral symmetry is restored but the quarks and anti-quarks are stillconfined,~gets reduced by the quark back-reaction in the unquenchedPolyakov-loop potential.~It altogether disappears for the chemical potentialdependent parameter $T_{0} \equiv T_{0} (\mu)$ in the Log or the PolyLog-glueform of the Polyakov-loop potential in the RPQM model.

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