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arXiv 2207.05970nucl-th
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反常对宇称偶态模型下核和中子星状态方程的影响

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

Bikai Gao, Takuya Minamikawa, Toru Kojo, Masayasu Harada

摘要:

我们研究了$U(1)_A$异常在包含手征变体和不变质量的核子宇称偶重模型中的作用。我们的模型表示$U(1)_A$异常的Kobayashi-Maskawa-'t\,Hooft(KMT)相互作用的介子部门。在考察了KMT项在真空中的作用后,我们讨论了它对核状态方程的影响。$U(1)_A$反常增加了$η'$和$σ$介子的质量,增强了手征对称性破缺。$U(1)_A$异常扩大了手征对称真空和对称破缺真空之间的能量差;反过来,在高密度下的手征恢复比没有异常的情况下向EOS增加了更大的能量密度(通常称为袋常数),导致更软的EOS。包括这些$U(1)_A$效应,我们更新了以前构建的统一状态方程,插值的核子状态方程在$n_B \le 2n_0$($n_{0} = 0.16\, \rm{fm^{-3}}$:核饱和密度)和夸克状态方程在$n_B \ge 5n_0$。统一状态方程面临着中子星质量和半径的观测约束。与$U(1)$异常相关的EOS的软化降低了整体半径,放松了先前对手征不变质量$m_0$的约束。包括有吸引力的非线性$ρ$-$ω$耦合到对称能量中的斜率参数的改进估计,我们的新估计是$400\,{\rm MeV} \leq m_0 \leq 700\,{\rm MeV}$,$m_0$比我们以前的估计小$\sim 200$ MeV。

英文摘要:

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. 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 $n_B \le 2n_0$ ($n_{0} = 0.16\, \rm{fm^{-3}}$: 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 $ρ$-$ω$ coupling to improved estimates for the slope parameter in the symmetry energy, our new estimate is $400\,{\rm MeV} \leq m_0 \leq 700\,{\rm MeV}$, with $m_0$ smaller than our previous estimate by $\sim 200$ MeV.

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