Impacts of anomaly on nuclear and neutron star equation of state based on a parity doublet model

Abstract

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 ${\eta }^{\prime }$ and $\sigma$ mesons and enhances the chiral symmetry breaking. 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 $n_B\le 2n_0$ ($n_0=0.16\mathrm{f}{\mathrm{m}}^{-3}$: nuclear saturation density) and quark EOS at $n_B\ge 5n_0$. 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 $m_0$. Including the attractive nonlinear $\rho$-$\omega$ coupling to improved estimates for the slope parameter in the symmetry energy, our new estimate is $400\mathrm{MeV}\le m_0\le 700\mathrm{MeV}$, with $m_0$ smaller than our previous estimate by $\sim 200$ MeV.

arXiv comment14 pages

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