Phase structure of the on-shell parametrized 2+1 flavor Polyakov quark-meson model

Augmenting the improved chiral effective potential of the on-shell renormalized <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math> flavor 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 scheme to those in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mover accent="true"><c:mi>MS</c:mi><c:mo stretchy="true">¯</c:mo></c:mover></c:math> scheme and finding the relations between the renormalized parameters of both the schemes where the physical (pole) masses of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>π</g:mi></g:mrow></g:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>K</i:mi></i:mrow></i:math>, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>η</k:mi></k:mrow></k:math>, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>η</m:mi><m:mo>′</m:mo></m:msup></m:math> pseudoscalar mesons and the scalar <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>σ</o:mi></o:math> 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 backreaction, we have computed and compared the effect of the consistent quark one-loop correction and the quark backreaction on the scaled chiral order parameter, the QCD phase diagrams, and the different thermodynamic quantities. The results have been compared with the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:mn>2</q:mn><q:mo>+</q:mo><q:mn>1</q:mn></q:mrow></q:math> flavor lattice QCD data from the Wuppertal-Budapest Collaboration [ 73, ] and the HotQCD Collaboration [].