探究可行的Froggatt-Nielsen类味纹理的几何结构
Probing the Geometry of Viable Froggatt-Nielsen-like Flavor Textures
- Roma Tre University（罗马第三大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
该研究在可控玩具景观中，以18个整数指数表示味纹理点，通过质量比和CKM可观测量截断定义可行性，经分析发现Froggatt-Nielsen指数空间无强线性压缩，未提供揭示味理论几何的自然坐标。
中文摘要 AI 辅助
我们在可控的玩具景观中探究可行的Froggatt-Nielsen类味纹理的几何结构。在首次纹理层面分析中，每个点由进入上型和下型Yukawa矩阵的18个整数指数表示，未施加特定Froggatt-Nielsen模型的额外电荷因子化约束。通过对夸克质量比和选定CKM可观测量进行截断来定义可行性。我们构建了四个基准集合，范围从仅质量约束到纳入本研究考虑的全部CKM可观测量，并在原始指数空间中研究所得点云。主成分分析未显示强线性压缩的证据：所有基准中，需15个主成分解释90%的方差。包括TwoNN和Levina-Bickel估计量在内的近邻固有维数诊断支持相同定性结论，产生量级为10-12的高有效维数。这些结果并不排除其他坐标中存在隐藏的味理论几何；相反，它们表明原始Froggatt-Nielsen指数可能并非揭示此类几何的自然坐标。
英文摘要
We investigate the geometry of viable Froggatt--Nielsen-like flavor textures in a controlled toy landscape. In this first texture-level analysis, each point is represented by the eighteen integer exponents entering the up- and down-type Yukawa matrices, without imposing the additional charge-factorization constraints of specific Froggatt--Nielsen models. Viability is imposed through cuts on quark mass ratios and selected CKM observables. We construct four benchmark ensembles, ranging from masses-only constraints to the inclusion of the full set of CKM observables considered in this work, and study the resulting point clouds in the raw exponent space. Principal-component analysis shows no evidence for strong linear compression: in all benchmarks, fifteen principal components are required to account for 90% of the variance. Nearest-neighbour intrinsic-dimensionality diagnostics, including TwoNN and Levina--Bickel estimators, support the same qualitative conclusion, yielding high effective dimensions of order 10-12. These results do not rule out hidden flavor-theory geometry in other coordinates; rather, they suggest that raw Froggatt--Nielsen exponents may not provide natural coordinates for revealing such a geometry.
