Comparison of chiral limit studies in curvature mass versus on-shell renormalized quark-meson model using ChPT

Consistent chiral limit has been investigated in the curvature mass parametrized quark-meson (QM) model with the quark one-loop vacuum term (QMVT) employing the infrared regularized Chiral perturbation theory (ChPT) predicted scaling of the pion,~kaon decay constants $f_{\pi}, f_{K}$ and $M_{\eta}^2 = m_{\eta}^2 + m_{\eta^{\prime}}^2$ when the $\pi \ \text{and} \ K$ meson masses are reduced as one moves away from the physical point in the Columbia plot.~Comparing the QMVT model Columbia plots with the corresponding Columbia plots computed,~in the very recent work of Ref.~\cite{vkt25} using the on-shell renormalized QM (RQM) model and the earlier work of Ref.~\cite{Resch} using functional renormalization group techniques in the extended mean field approximation of QM (e-MFA:QM-FRG) model,~it has been estimated how the first, second and crossover chiral transition regions in the $m_{\pi}-m_{K}$($m_{ud}-m_{s}$) and the $\mu-m_{K}$($\mu-m_{s}$) planes,~get modified by different methods of implementing the quark one-loop vacuum fluctuations in the QM model.~Since both the e-MFA:QM-FRG and the QMVT model,~use curvature meson masses to fix the parameters and the dimensional regularization of vacuum divergences are incorporated equivalently,~the differences in their results can be attributed to different methods of approaching the chiral limit.