Neutron star matter based on a parity doublet model including the $a_0(980)$ meson

We study the effect of the isovector-scalar meson $a_0$(980) on the properties of nuclear matter and the neutron star (NS) matter by constructing a parity doublet model with including the $a_0$ meson based on the chiral SU(2)$_L\times$SU(2)$_R$ symmetry. We also include the $\omega$-$\rho$ mixing contribution to adjust the slope parameter at the saturation. We find that, when the chiral invariant mass of nucleon $m_0$ is smaller than about 800 MeV, the existence of $a_0$(980) enlarges the symmetry energy by strengthening the repulsive $\rho$ meson coupling. On the other hand, for large $m_0$ where the Yukawa coupling of $a_0$(980) to nucleon is small, the symmetry energy is reduced by the effect of $\omega$-$\rho$ mixing. We then construct the equation of state (EoS) of a neutron star matter to obtain the mass-radius relation of NS. We find that, in most choices of $m_0$, the existence of $a_0$(980) stiffens the EoS and makes the radius of NS larger. We then constrain the chiral invariant mass of nucleon from the observational data of NS, and find that $580 \,\text{ MeV} \lesssim m_0 \lesssim 860 \,\text{ MeV}$ for $L_0=57.7$ MeV.