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 $(m_{\pi },m_K)\to 0$ away from the physical point $(m_{\pi }^{\text{Phys}},m_K^{\text{Phys}})=(138,496)$ 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.

Comments: 30 pages 22 figures