The infrared regularized and the large $N_c$ standard U(3) chiral perturbation theory (ChPT) predicted scaling of the pion, kaon decay constants $f_{\pi }$, $f_K$, and $M_{\eta }^2=m_{\eta }^2+m_{{\eta }^{\prime }}^2$, has been used in the renormalized $2+1$ flavor quark-meson (RQM) model to find a consistent path to the chiral limit as the $\pi$ and $K$ meson masses approach zero. Using the inputs from the above two prescriptions of the ChPT, the Columbia plots are drawn and compared in the $m_{\pi }-m_K$ and the light strange quark mass $m_{ud}-m_s$ planes, free from any ambiguity or heuristic adjustment in the model parameter fixing away from the physical point. The on-shell renormalization of the parameters and consistent treatment of the divergent quark one-loop vacuum fluctuations in the RQM model make the axial $U_A(1)$ anomaly significantly stronger, and the light (strange) explicit chiral symmetry breaking strength becomes weaker by a small (relatively large) amount. The first-order chiral transition region in the $m_{\pi }-m_K$ and $\mu -m_K$ planes of the Columbia plots generated using the inputs from both versions of the ChPT increases due to the above novel features of the RQM model. Comparing our results (in the presence of the axial $U_A(1)$ anomaly) regarding the softening effect of the quark one-loop vacuum fluctuations on the chiral transition, it looks overestimated in a recent functional renormalization group study. The $U_A(1)$ symmetry and the $S{U}_A(3)$ chiral symmetry restoration in the chiral limit takes place at the same transition temperature.

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• Effective field theory
• Phenomenology
• QCD phase transitions
• Quantum chromodynamics
• Quark-gluon plasma
• Relativistic heavy-ion collisions
• Renormalization
• Sigma models
• Spontaneous symmetry breaking
• Strong interaction
• Symmetries