折衷味对称性无需味子
Eclectic flavour symmetries without flavons
- INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
- Dipartimento Interateneo di Fisica, Bari（巴里大学间物理系）
- INFN, Sezione di Bari（意大利国家核物理研究所巴里分部）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出无需味子的折衷味对称新框架，以积分Jacobi群实现Ω(1)，构建超对称理论及费米子质量模型，并扩展至T²/Z₄和T²/Z₂情形。
AI中文摘要：
我们开发了一个新框架，在该框架中，折衷群被实现为无需味子的味对称性。聚焦于群$\Omega(1)$，我们证明它可以实现为积分Jacobi群的有限像，即$H({\mathbb Z})$与$SL(2,{\mathbb Z})$的半直积，作用于两个模量$(\tau,z)$。Heisenberg子群$H({\mathbb Z})$保持模量$\tau$不变，其有限像$\Delta(27)$扮演传统味对称性的角色。我们提供了构建超对称Jacobi不变理论所需的要素，既适用于全局超对称理论，也适用于超引力。我们在此框架内开发了一个现实的费米子质量模型，并阐述了一个一致的CP对称性，该对称性可以在拉格朗日量层面施加，并由模量自发破缺。我们讨论了如何在适当的极限下恢复传统的折衷味描述。我们还将这一几何解释扩展到$T^2/\mathbb Z_4$和$T^2/\mathbb Z_2$折衷构建块，并阐明了为何$T^2/\mathbb Z_6$情形在结构上有所不同。
英文摘要：
We develop a new framework in which eclectic groups are realised as flavour symmetries without flavons. Focusing on the group $Ω(1)$, we show that it can be realised as a finite image of the integral Jacobi group, i.e. the semidirect product of $H({\mathbb Z})$ with $SL(2,{\mathbb Z})$, acting on two moduli $(τ,z)$. The Heisenberg subgroup $H({\mathbb Z})$ leaves the modulus $τ$ unchanged, and its finite image $Δ(27)$ plays the role of the traditional flavour symmetry. We provide the ingredients needed to construct supersymmetric Jacobi-invariant theories, both in globally supersymmetric theories and in supergravity. We develop a realistic model of fermion masses within this framework and formulate a consistent CP symmetry, which can be imposed at the Lagrangian level and broken spontaneously by the moduli. We discuss how the conventional eclectic-flavour description is recovered in an appropriate limit. We also extend this geometric interpretation to the $T^2/\mathbb Z_4$ and $T^2/\mathbb Z_2$ eclectic building blocks, and clarify why the $T^2/\mathbb Z_6$ case is structurally different.
