Comparative analysis of critical regions for the renormalized quark-meson model with and without Polyakov loop potential

TL;DR

The paper investigates how critical fluctuations near the QCD critical end point depend on the treatment of quark vacuum fluctuations and the presence of Polyakov-loop dynamics in 2+1 flavor quark-meson models. By employing on-shell renormalization for the quark vacuum and comparing RPQM variants with different Polyakov-loop potentials, the authors map phase diagrams, locate the CEP and TCP in light-chiral and physical-point scenarios, and quantify critical regions via quark-number susceptibilities. The main findings show that on-shell renormalization strengthens the 't Hooft coupling and shifts the CEP upward, with the Polyakov-loop back reaction further modifying the size and shape of the critical region; these results align with lattice and FRG indications of the QCD phase structure. The work thus clarifies the role of vacuum corrections and confinement dynamics in shaping critical fluctuations and provides a benchmark for comparing curvature-mass based studies against on-shell renormalized frameworks.

Abstract

The critical regions enveloping the critical end point (CEP) in the chemical potential-temperature plane of phase diagrams, have been mapped by drawing the contours of the normalized quark number susceptibility in the on-shell renormalized two plus one flavor quark meson model (RQM) and Polyakov loop enhanced renormalized Polyakov quark meson (RPQM) model when sigma meson mass=400 and 500 MeV. The renormalized t Hooft coupling c gets significantly stronger when the meson self energies due to quark loops are computed using the pole masses of mesons and parameters are fixed on shell in the Ref. [141] after consistent treatment of the quark one-loop vacuum fluctuation for the RQM model where the light and strange chiral symmetry breaking strengths also become weaker. The impact of the above novel features on the critical fluctuations have been computed. The improved PolyLog-glue form of the Polyakov loop potential of the Ref. [46], is employed to study the effect of the quark back reaction on critical fluctuations and results are compared with the scenario where quark back reaction is absent in the RPQM model with the Log form of the Polyakov loop potential. Using the large Nc standard chiral perturbation theory inputs,~the phase diagrams are computed in the light chiral limit of zero pion mass and the proximity of the tricritical point (TCP) with the CEP is quantified in the chemical potential-temperature plane.The RQM, RPQM model critical regions are compared with those reported in the Ref. [118] by different treatment of quark one-loop vacuum term where curvature masses of mesons are used to fix the parameters of the quark meson(QM), Polyakov quark meson (PQM) model.

Figures (8)

• Figure 1: Temperature variations of the non-strange condensate $x$ in [a] and it's derivative $\partial x/ \partial T$ in [b] for the RQM, Log RPQM and PolyLog-glue RPQM model for the physical point $m_{\pi}=138$ MeV and the light chiral limit $m_{\pi}=0$ with $m_K=496$ MeV.
• Figure 2: The RQM model phase diagrams for the $m_{\sigma}=400 \text{ and } 500$ MeV computed for the physical point and light chiral limit parameters, are presented in the left panel (a) while the right panel (b) presents the phase diagrams for the QM model and PolyLog-glue PQM model when the $m_{\sigma}=500$ MeV at the physical point. Line types and position of the critical end points (CEP) and tricritical points (TCP) are labeled. The lines enveloping the CEP of different phase diagrams are the contours of constant quark number susceptibility ratio $R_q=2$.
• Figure 3: The phase diagrams for the $m_{\sigma}=400 \text{ and } 500$ MeV computed for the physical point and light chiral limit parameters, are presented in the left panel (a) for the Log RPQM model and right panel (b) for the PolyLog-glue RPQM model. Line types and position of the critical end points (CEP) and tricritical points (TCP) are labeled in the Figs. The lines enveloping the CEP of different phase diagrams are the contours of constant quark number susceptibility ratio $R_q=2$.
• Figure 4: The phase diagrams for the physical point and light chiral limit parameters when the $m_{\sigma}=400 \text{ and } 500$ MeV are presented in the reduced temperature and chemical potential $\mu_{r}-T_{r}$ plane in the left panel (a) for the RQM and Log RPQM model and right panel (b) for the PolyLog-glue RPQM model. Other features of the phase diagrams are same as in the Fig.\ref{['fig:mini:fig3']}. The $T_{r}=\frac{T}{T_{c}^{\chi}}$ is obtained after dividing the temperature $T$ by the pseudo-critical temperature $T_{c}^{\chi}$ at which the chiral crossover transition occurs on the temperature axis at $\mu=0$. The $\mu_{r}=\frac{\mu}{\mu_{0}}$ is defined after dividing the chemical potential $\mu$ by the highest chemical potential $\mu_{0}$ at which first order chiral phase transition on the $\mu$ axis occurs at $T=0$.
• Figure 5: The $R_q=2,3$ susceptibility contours for the QM model are plotted in the left panel (a) while the $R_q=2,3,5$ contours for the RQM model are plotted in the right panel (b).