AI 中文总结
研究广义弗里德伯格-李模型中点D的奇异参数空间，引入最小系统微扰保持TFL对称，打破民主极限，避免特设参数，得到现实的中微子质量层级、非零θ13和固有CP破坏，与全局拟合数据吻合良好。
AI 中文摘要
我们研究了中微子质量的广义弗里德伯格-李（FL）框架，聚焦于点D（α = β = -1/3）处的奇异参数空间。在此极限下，中微子质量矩阵呈现由S3置换对称支配的民主纹理。但精确的民主极限在现象学上被排除，因其预测简并质量谱和零反应堆角（θ13 = 0）。为使此高对称极限与实验观测相符，我们引入最小且系统的微扰以保持扭曲弗里德伯格-李（TFL）对称。该机制有效解除质量简并并以可控方式打破魔幻和μ-τ对称。我们的推导避免特设参数，建立了一个稳健框架，产生现实的倒质量层级（m3 = 0）、非零θ13和固有CP破坏。我们证明该模型预测最大大气混合和显著的狄拉克CP相位。中微子质量和雅尔斯科格不变量的数值范围与全局拟合数据吻合良好，为TFL方案内的中微子味物理提供了理论动机基础。
英文摘要
We investigate a generalized Friedberg--Lee (FL) framework for neutrino masses, focusing on the singular parameter space at Point D ($α= β= -1/3$). At this limit, the neutrino mass matrix exhibits a democratic texture governed by the $S_3$ permutation symmetry. Although theoretically profound, the exact democratic limit is phenomenologically excluded as it predicts a degenerate mass spectrum and a vanishing reactor angle ($θ_{13}=0$). To reconcile this high-symmetry limit with experimental observations, we introduce a minimal and systematic perturbation that preserves the Twisted Friedberg--Lee (TFL) symmetry. This mechanism effectively lifts the mass degeneracy and breaks the magic and $μ$--$τ$ symmetries in a controlled manner. Our derivation avoids \textit{ad hoc} parameters, establishing a robust framework that yields a realistic inverted mass hierarchy ($m_3=0$), a non-zero $θ_{13}$, and intrinsic CP violation. We demonstrate that the model predicts maximal atmospheric mixing and a significant Dirac CP phase. The obtained numerical ranges for the neutrino masses and the Jarlskog invariant show excellent agreement with global fit data, providing a theoretically motivated foundation for neutrino flavor physics within the TFL scheme.
