Comparative analysis of critical regions: The renormalized quark-meson model under Polyakov loop, quark back-reaction, and vector interaction effects

Abstract

The critical regions enveloping the critical end point (CEP) in the $\mu$-$T$ plane are mapped by computing the contours of normalized quark number susceptibility within the on shell renormalized 2+1 flavor quark-meson (RQM) and Polyakov loop enhanced renormalized Polyakov quark meson (RPQM) models for $m_\sigma = 400$ and 500 MeV.The apparent precision for the results of CEP coordinates merely reflects numerical binning of two decimal places rather than the effect of including full thermal and vacuum quantum fluctuations. The renormalized 't Hooft coupling c becomes substantially stronger in the RQM model when the meson self energies due to quark loops are computed using the pole masses of mesons and parameters are fixed on shell in Ref [143] after a consistent treatment of quark one loop vacuum fluctuations while the light and strange chiral symmetry breaking strengths also become weaker. We evaluate the impact of these novel features on critical fluctuations. Furthermore, the improved PolyLog glue form of the Polyakov loop potential from Ref [46] is employed to isolate the effects of the quark back reaction on critical fluctuations, and the results are contrasted against back reaction free outcomes obtained using the logarithmic potential. Utilizing inputs from large $N_c$ standard chiral perturbation theory, phase diagrams are also computed in the light chiral limit ($m_\pi = 0$), quantifying the proximity of the tricritical point (TCP) to the CEP. The critical regions from the RQM/RPQM models are compared with those reported in Ref [120], where curvature masses are used for parameter fixing. Phase diagrams incorporating vector interactions in the RQM/RPQM model reveal that the CEP and first-order transition survive up to a robust coupling of $g_\omega = 2.79$, rendering them highly relevant for compact star equations of state and astrophysical phenomenology.