The spontaneous breaking of chiral symmetry is examined by chiral effective theories, such as the linear $\sigma$ model and the Nambu–Jona-Lasinio (NJL) model. We discuss the properties of the sigma meson regarded as the quantum fluctuation of the chiral condensate when the chiral symmetry is spontaneously broken, mainly by the U$_{A}$(1) anomaly. We derive a mass relation among the SU(3) flavor singlet mesons, $\eta_{0}$ and $\sigma_{0}$, in the linear $\sigma$ model to be satisfied for the anomaly-driven symmetry breaking in the chiral limit, and find that it is also supported in the NJL model. With the explicit breaking of chiral symmetry, we show that both of the chiral effective models reproducing the observed physical quantities suggest that the $\sigma_{0}$ meson should have a mass smaller than $\sim$800 MeV when anomaly-driven symmetry breaking takes place.

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UA(1) 破缺项在手性有效理论的动态手性对称破缺中的作用

手性对称性的自发破坏通过手性有效理论来检验，例如线性 $\sigma$ 模型和 Nambu-Jona-Lasinio (NJL) 模型。我们讨论了当手征对称性自发破缺时，σ介子被视为手征凝聚体的量子涨落的性质，主要是由于U$_{A}$(1)异常。我们推导出线性 $\sigma$ 模型中的 SU(3) 风味单线态介子 $\eta_{0}$ 和 $\sigma_{0}$ 之间的质量关系，以满足异常驱动的对称性破坏手性极限，发现 NJL 模型也支持它。随着手性对称性的显式破坏，