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

Akanksha Tripathi1,*, Suraj Kumar Rai2,†, and Vivek Kumar Tiwari1,‡

  • 1Department of Physics, University of Allahabad, Prayagraj 211002, India
  • 2Department of Physics, Acharya Narendra Deo Kisan P.G. College, Babhnan Gonda-271313; Maa Pateswari University, Balrampur 271201, India

  • *Contact author: akankshatripathi330@gmail.com
  • †Contact author: surajrai050@gmail.com
  • ‡Contact author: vivekkrt@gmail.com
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Phys. Rev. D 114, 034039 – Published 21 August, 2026

DOI: https://doi.org/10.1103/v7c7-rqsr

Abstract

The critical regions enveloping the critical end point (CEP) in the μ−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 mσ=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, as direct meson loops are omitted under a large-Nc justification where quark-loop fluctuations dominate. 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 [, [Phys. Rev. D 108, 074002 (2023)]] 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 Haas et al. [Phys. Rev. D 87, 076004 (2013)] is employed to isolate the effects of the quark backreaction on critical fluctuations, and the results are contrasted against backreaction-free outcomes obtained using the logarithmic potential. Utilizing inputs from large-Nc standard chiral perturbation theory, phase diagrams are also computed in the light chiral limit (mπ=0), quantifying the proximity of the tricritical point to the CEP. The critical regions from the RQM/RPQM models are compared with those reported by Schaefer and Wagner [Phys. Rev. D 85, 034027 (2012)], 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 gω=2.79, rendering them highly relevant for compact star equations of state and astrophysical phenomenology.

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Phys. Rev. D 114, 034039– Published 21 August, 2026
  • Received 15 December 2025
  • Accepted 10 July 2026
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