Impacts of the U (1) A anomaly on nuclear and neutron star equation of state based on a parity doublet model

We examine the role of the U (1_{) A} anomaly in a parity doublet model of nucleons which include the chiral variant and invariant masses. Our model expresses the U (1_{) A} anomaly by the Kobayashi-Maskawa-'t Hooft (KMT) interaction in the mesonic sector. After examining the roles of the KMT term in vacuum, we discuss its impacts on nuclear equations of state (EOS). The U (1_{) A} anomaly increases the masses of the η^' and σ mesons and enhances the chiral symmetry breaking. Also, the U (1_{) A} anomaly enlarges the energy difference between chiral symmetric and symmetry broken vacuum; in turn, the chiral restoration at high density adds a larger energy density (often referred as a bag constant) to EOSs than in the case without the anomaly, leading to softer EOSs. Including these U (1_{) A} effects, we update the previously constructed unified equations of state that interpolate the nucleonic EOS at n_B≤2 n₀ (n₀=0.16 fm⁻³ ; nuclear saturation density) and quark EOS at n_B≥5 n₀ . The unified EOS is confronted with the observational constraints on the masses and radii of neutron stars. The softening of EOSs associated with the U (1) anomaly reduces the overall radii, relaxing the previous constraint on the chiral invariant mass m₀. Including the attractive nonlinear ρ -ω coupling for the reduced slope parameter in the symmetry energy, our new estimate is 400 MeV ≤m₀≤700 MeV , with m₀ smaller than our previous estimate by ≈200 MeV.