Chiral Invariant Mass Constraints from HESS J1731–347 in an Extended Parity Doublet Model with Isovector Scalar Meson

The recent discovery of an extremely light and small central compact object (CCO) within the supernova remnant HESS J1731-347, with mass $0.77^{+0.20}_{-0.17} \ M_\odot $ and radius $10.4^{+0.86}_{-0.78}$ km, is challenging our understanding of neutron stars. In this article, we identify it as an ultra-light neutron star (NS) and constrain the chiral invariant mass of nucleon $m_0$ from the observational data of NS using an extended parity doublet model with the isovector scalar meson $a_0(980)$. We show that the 1 $\sigma$ data from the HESS J1731-347 impose a very narrow constraint on the allowed values of $m_0$ and $L_0$ in the crossover model: $830 \,\text{ MeV} \lesssim m_0 \lesssim 900 \,\text{ MeV}$ for $L_0 = 40$ MeV, and $850 \,\text{ MeV} \lesssim m_0 \lesssim 890 \,\text{ MeV}$ for \mbox{$L_0 = 45$ MeV}. We also study the higher-order asymmertic matter properties such as the symmetry incompressibility $K_{sym}$ and the symmetry skewness $Q_{sym}$ in the presence of the $a_0$ meson. We find that $K_{sym}$ and $Q_{sym}$ are very sensitive to $m_0$ in the presence of the $a_0$ meson.