We propose a novel mechanism to reproduce the observed mass hierarchy for the scalar mesons lighter than 1 GeV (called the inverse hierarchy) regarding them as mesons made of a quark and an anti-quark ($q\bar{q}$ mesons). The source is provided by the SU(3)-flavor symmetry-breaking induced by U(1) axial anomaly. In particular, the anomaly term including the explicit-chiral symmetry-breaking plays a significant role for the light scalar meson spectrum. To be concrete, we construct a linear sigma model for the scalar mesons of $q\bar{q}$ type together with their pseudoscalar chiral partners, including an anomaly-induced explicit-chiral symmetry-breaking term. We find that, due to the proposed mechanism, the inverse hierarchy, i.e., $m\left[ a_0 (980) \right] \simeq m\left[ f_0 (980) \right] > m \left[ K_0^\ast (700) \right] > m \left[ f_0(500) \right]$ is indeed realized. Consequently, the quark content of $f_0 (500)$ is dominated by the isoscalar $\bar uu+ \bar dd$ component, and $f_0 (980)$ is by the strange quark bilinear's, $s\bar{s}$.

中文翻译：

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由异常引起的风味破坏驱动的轻标量介子的反质量层次结构

我们提出了一种新机制来重现观察到的质量等级小于 1 GeV 的标量介子（称为逆等级），将它们视为由夸克和反夸克（$q\bar{q}$ 介子）组成的介子。来源是由 U(1) 轴异常引起的 SU(3) 风味对称性破坏。特别是，包括显式手征对称破坏在内的异常项对光标量介子光谱起着重要作用。具体而言，我们为 $q\bar{q}$ 类型的标量介子及其伪标量手性伙伴构建了一个线性 sigma 模型，包括异常诱导的显式手性对称破坏项。我们发现，由于提出的机制，逆层次结构，即 $m\left[ a_0 (980) \right] \simeq m\left[ f_0 (980) \right] > m \left[ K_0^\ast (700) \右] > m \left[ f_0(500) \right]$ 确实实现了。因此，$f_0 (500)$ 的夸克含量由等标量 $\bar uu+ \bar dd$ 分量支配，而 $f_0 (980)$ 由奇异夸克双线性分量 $s\bar{s}$ 支配。