Comparing critical regions in Polyakov-quark-meson models: Effects of flavor (two versus 2+1) under on-shell renormalization, and on-shell versus curvature-mass parameter fixing for the two-flavor case

Abstract

We compute contours of the enhanced quark number susceptibility ratio $R_q$, normalized by the free quark gas susceptibility, around the critical end point (CEP) using the on-shell renormalized two-flavor quark-meson (RQM) model and its two Polyakov-loop-extended variants: the Log RPQM and PolyLog-glue RPQM models, employing logarithmic and PolyLog-glue forms of the Polyakov-loop potential without and with quark back-reaction, respectively. These contours are compared with those from the curvature-mass parametrized quark-meson-with-vacuum-term (QMVT) model and its logarithmic Polyakov-loop extension (Log PQMVT) [117], to assess how different treatments of quark one-loop vacuum fluctuations affect the critical region. Although the critical fluctuation regions near the RQM/Log RPQM CEP are reduced in $T$-$μ$ extent relative to the QMVT/Log PQMVT case, the higher-$T$, lower-$μ$ CEP location shifts its enhanced-susceptibility domain toward higher $T$ and lower $μ$. Since the $σ$ and $π$ curvature and pole masses differ in the RQM/Log RPQM model but coincide in QMVT/Log PQMVT, we also compare contours of the enhanced scalar susceptibility ($\sim 1/m_σ^2$) around the respective CEPs. To isolate the roles of strange flavor and the $U_A(1)$ anomaly, we compare $R_q = 2, 3, 5$ contours from our two-flavor RQM/Log RPQM/PolyLog-glue RPQM model calculations with the corresponding 2+1 flavor RQM/RPQM model very recent results in Ref [146].