  Augmenting the improved chiral effective potential of the on-shell
renormalized 2+1 flavour quark-meson (RQM) model with the Polyakov-loop
potential that accounts for the deconfinement transition,~we get the Quantum
Chromodynamics (QCD) like framework of the renormalized Polyakov quark-meson
(RPQM) model.~When the divergent quark one-loop vacuum term is included in the
effective potential of the quark-meson (QM) model,~its tree level parameters or
the parameters fixed by the use of meson curvature masses,~become inconsistent
as the curvature masses involve the self energy evaluations at zero
momentum.~Using the modified minimal subtraction method,~the consistent chiral
effective potential for the RQM model has been calculated after relating the
counterterms in the on-shell (OS) scheme to those in the $\overline{\text{MS}}$
scheme and finding the relations between the renormalized parameters of both
the schemes where the physical (pole) masses of the $\pi, K, \eta$ and
$\eta^{\prime}$ pseudo-scalar mesons and the scalar $\sigma$ meson,~the pion
and kaon decay constants,~have been put into the relation of the running
couplings and mass parameter.~Using the RPQM model and the PQM Model with
different forms for the Polyakov-loop potentials in the presence or the absence
of the quark back-reaction,~we have computed and compared the effect of the
consistent quark one-loop correction and the quark back-reaction on the scaled
chiral order parameter,~the QCD phase diagrams and the different thermodynamic
quantities.~The results have been compared with the 2+1 flavor lattice QCD data
from the Wuppertal-Budapest collaboration \{JHEP 09,73(2010); PLB
730,99(2014)\} and the HotQCD collaboration \{PRD 90,094503(2014)\}.
