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

TL;DR

This paper compares different methods of studying the chiral limit in quark-meson models, focusing on how vacuum fluctuation treatments affect the phase transition regions in the Columbia plot.

Contribution

It provides a comparative analysis of the curvature mass and on-shell renormalized approaches in the quark-meson model, highlighting differences in chiral transition predictions.

Findings

Different methods modify the chiral transition regions in the Columbia plot.

Both models use curvature meson masses and dimensional regularization, but differ in vacuum fluctuation implementation.

Results suggest the approach to the chiral limit significantly impacts phase transition predictions.

Abstract

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.