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

Abstract

We examine the role of the $\mathrm{U}{(1)}_{A}$ anomaly in a parity doublet model of nucleons which include the chiral variant and invariant masses. Our model expresses the $\mathrm{U}{(1)}_{A}$ 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 $\mathrm{U}{(1)}_{A}$ anomaly increases the masses of the ${\ensuremath{\eta}}^{\ensuremath{'}}$ and $\ensuremath{\sigma}$ mesons and enhances the chiral symmetry breaking. Also, the $\mathrm{U}{(1)}_{A}$ 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 $\mathrm{U}{(1)}_{A}$ effects, we update the previously constructed unified equations of state that interpolate the nucleonic EOS at ${n}_{B}\ensuremath{\le}2{n}_{0}$ (${n}_{0}=0.16\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$; nuclear saturation density) and quark EOS at ${n}_{B}\ensuremath{\ge}5{n}_{0}$. 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 $\ensuremath{\rho}\text{\ensuremath{-}}\ensuremath{\omega}$ coupling for the reduced slope parameter in the symmetry energy, our new estimate is $400\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}\ensuremath{\le}{m}_{0}\ensuremath{\le}700\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, with ${m}_{0}$ smaller than our previous estimate by $\ensuremath{\approx}$200 MeV.