On-shell versus curvature mass parameter fixing schemes in the quark-meson model and its phase diagrams

We compute and compare the effective potential phase structure for quark-meson model in an extended mean-field approximation when vacuum one-loop quark fluctuations are included parameters fixed using different renormalization prescriptions. When divergence is regularized under minimal subtraction scheme, fixing of curvature masses scalar pseudoscalar mesons has been termed as with term (QMVT). However, this prescription becomes inconsistent we notice that mass akin to defining meson by self-energy evaluation at vanishing momentum. In work, apply recently reported exact on-shell parameter version where two flavors coupled eight $S{U}_{L}(2)\ifmmode\times\else\texttimes\fi{}S{U}_{R}(2)$ linear sigma isosinglet $\ensuremath{\sigma}$ ($\ensuremath{\eta}$), isotriplet $\stackrel{\ensuremath{\rightarrow}}{{a}_{0}}$ ($\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\pi}}$) (pseudoscalar) mesons. The then renormalized (RQM) physical (pole) pion decay constant put into relation running couplings schemes. plots, diagrams order temperature variations both RQM QMVT exactly identical ${m}_{\ensuremath{\sigma}}=616\text{ }\text{ }\mathrm{MeV}$. potential, ${m}_{\ensuremath{\sigma}}<616\text{ }\mathrm{MeV}$, deepest model. An interesting trend reversal observed ${m}_{\ensuremath{\sigma}}>616\text{ }\mathrm{MeV}$ deepest. find similar ${m}_{\ensuremath{\sigma}}$ dependent differences nature variations. Furthermore, $S{U}_{A}(2)$ chiral ${U}_{A}(1)$ axial symmetry breaking/restoration their interplay can also be investigated framework.