AI 中文总结
该研究将模强CP解扩展至非阿贝尔有限模对称性，揭示模反常条件，借助正则性使QCD角为0并产生夸克质量层级，还提出模对称性可作R对称性，通过显式模型阐释相关机制。
AI 中文摘要
强CP问题与夸克质量层级可探测同一紫外结构，我们通过将模强CP解扩展至非阿贝尔有限模对称性来证明这一点。这揭示了有限表示下此前被忽略的模反常条件，正则性消除了QCD角对CP破缺模的依赖，使$\bar\theta=0$；对于正模权重，正则性还迫使夸克汤川行列式在尖点处消失，从而形成夸克间显著的质量层级。我们进一步强调模对称性充当R对称性，在适度附加假设下，这使QCD角不受伸缩子影响，一个显式模型阐释了该机制。
英文摘要
The strong $\mathcal{CP}$ problem and quark mass hierarchies can probe the same ultraviolet structure. We show this by extending modular strong-$\mathcal{CP}$ solutions to non-Abelian finite modular symmetries. This reveals a previously overlooked modular-anomaly condition from the finite representations. Regularity removes the dependence of the QCD angle on the $\mathcal{CP}$-breaking modulus, yielding $\barθ=0$. For positive modular weight, it also forces the quark Yukawa determinant to vanish at the cusp. This leads to pronounced mass hierarchies among the quarks. We further stress that modular symmetries act as R-symmetries. Under moderate additional assumptions, this renders the QCD angle independent of the dilaton. An explicit model illustrates the mechanism.
Comments6 pages, 1 figure; Supplemental Material included
