Improved results of chiral limit study with the large $N_c$ standard U(3) ChPT inputs in the on-shell renormalized quark-meson model

Abstract

When the $f_{\pi}, f_{K} \text{ and } M_{\eta}^2$ given by the $ (m_{\pi},m_{K}) $ dependent scaling relations of the large $N_{c}$ standard U(3) Chiral perturbation theory (ChPT) and the infrared regularized U(3) ChPT,~are used in the on-shell renormalized 2+1 flavor quark-meson (RQM) model to find its parameters in the path to the chiral limit $(m_{\pi},m_{K}) \rightarrow 0$ away from the physical point $ (m_{\pi}^{\text{\tiny{Phys}}},m_{K}^{\text{\tiny{Phys}}})=(138,496) $ MeV,~one gets the respective framework of RQM-S model and RQM-I model.~Computing and comprehensively comparing the RQM-S and I model Columbia plots for the $m_{\sigma}=400,500\text{ and }600$ MeV,~it has been shown that the use of large $N_c$ standard U(3) ChPT inputs give the better and improved framework for the Chiral limit studies as the RQM-S model tricritical lines show the expected saturation pattern after becoming flat in the vertical meson (quark) mass $\mu-m_{K}$ ($\mu-m_{s}$) plane for all the cases of $m_{\sigma}$ whereas the divergent RQM-I model tricritical line for the $m_{\sigma}=500$ MeV becomes strongly divergent when the $m_{\sigma}=600$ MeV.