发表机构
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文提出π/12模型，描述带带电轻子μ-τ破缺的轻子混合，通过TM₁中微子部分与带电轻子2-3旋转构造，预测CP相位、ε₂等，可由Hyper-Kamiokande检验，质量预测符合DESI限制。
AI 中文摘要
轻子混合矩阵的第一列包含两个独立的幅值条件：三极大范数|U_{e1}|²=2/3以及μ-τ平衡条件|U_{μ1}|=|U_{τ1}|。我们通过ε₁≡(3/2)|U_{e1}|²-1和ε₂≡3(|U_{τ1}|²-|U_{μ1}|²来参数化它们的破缺，并表明当前数据对这两个参数的中心值处理存在差异：包含首次JUNO测量结果时，ε₁=+0.014±0.010与零一致，而ε₂=+0.29⁺⁰·⁰⁷₋₀·₁₃数值较大，但在全局拟合轮廓似然下仅以1.5σ的置信度不排斥零值，驱动相位的测量仍较差。这种不对称性选择了π/12模型。其中微子部分为TM₁，满足电子行条件|U_{e2}|/|U_{e3}|=2+√3，该条件确定sin²θ₁₃=(2-√3)/12=0.02233，sin²θ₁₂=0.31811。带电轻子的2-3旋转R₂₃(θₑ,α)使电子行完全不变，并产生ε₂=sin2θₑcosα。在S₄×C₄×C₃×C₂的实现中，该旋转来自单个额外的 flavon（ flavon 为粒子物理中的 flavon 场），其 alignment（对齐）迫使α=0；自然角度θₑ≈2°可重现θ₂₃偏离极大值的情况，同时将CP相位固定为δ=272°±2°，产生近最大的CP破坏，对应的ε₂=-0.066。当前θ₂₃-δ测量因此成为一项尖锐的检验：预测的δ在同一轮廓似然下与当前中心值相差1.7σ，预测的ε₂符号与测量值相反，Hyper-Kamiokande对δ的设计精度为20°，可在3σ置信度下解决该问题。质量预测保持不变，在ΛCDM下当前DESI限制中，Σm_ν=65.6 meV，m_{ββ}=5.4 meV。
英文摘要
The first column of the lepton mixing matrix carries two independent magnitude conditions: the trimaximal norm $|U_{e1}|^2=2/3$ and the $μ$--$τ$ balance $|U_{\mu1}|=|U_{\tau1}|$. Parameterizing their violation by $\varepsilon_1\equiv\tfrac32|U_{e1}|^2-1$ and $\varepsilon_2\equiv3(|U_{\tau1}|^2-|U_{\mu1}|^2)$, we show that current data treat the two differently in central value: with the first JUNO measurement included, $\varepsilon_1=+0.014\pm0.010$ is consistent with zero, while $\varepsilon_2=+0.29^{+0.07}_{-0.13}$ is large but disfavors zero at only $1.5σ$ on the profile likelihood of the global fit, since the phase that drives it remains poorly measured. This asymmetry selects a specific framework, the $π/12$ model. Its neutrino sector is $\mathrm{TM}_1$, supplemented by the electron-row condition $|U_{e2}|/|U_{e3}|=2+\sqrt3$ that fixes $\sin^2θ_{13}=(2-\sqrt3)/12=0.02233$ and $\sin^2θ_{12}=0.31811$. A charged-lepton 2--3 rotation $R_{23}(θ_e,α)$ leaves the electron row exactly invariant and generates $\varepsilon_2=\sin2θ_e\cosα$. In a concrete $S_4\times C_4\times C_3\times C_2$ realization, a single additional flavon alignment forces $α=0$; a natural angle $θ_e\simeq2^\circ$ then reproduces the observed departure of $θ_{23}$ from maximal while pinning $δ=272^\circ\pm2^\circ$, near-maximal CP violation with $\varepsilon_2=-0.066$. The result is a sharp test: the predicted $δ$ sits $1.7σ$ from the present central value on the same profile likelihood, the predicted $\varepsilon_2$ has the opposite sign to the measured one, and the Hyper-Kamiokande design precision of $20^\circ$ on $δ$ resolves the question at the $3σ$ level. The mass predictions are inherited unchanged, $Σm_ν=65.6$ meV and $m_{ββ}=5.4$ meV, placing the model at the current DESI bound in $Λ$CDM.
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