AI 中文总结
研究中微子长方体精确唯象学，通过质量混合对齐推导一致性关系，发现观测条件选正常质量顺序，特定条件下\(\theta_{23}\)在较低八分体，给出相关数据，指出一阶展开不稳定，当前数据与精确对齐有张力，还提出几何对齐残差用于测试。
AI 中文摘要
我们研究了由\(m_1=m_0\sin\xi\)，\(m_2=m_0\cos\xi\sin\zeta\)和\(m_3=m_0\cos\xi\cos\zeta\)定义的几何中微子长方体的精确唯象学，其立方点对应于质量简并以及太阳和大气混合角的三极大值。通过施加质量混合对齐\(\xi=\theta_{12}\)和\(\zeta=\theta_{23}\)，我们推导出了不依赖于立方极限展开的封闭形式一致性关系。这些关系表明，观测条件\(\sin^2\theta_{12}<1/3\)选择了正常质量顺序，在由此产生的正常顺序 regime 中，物理条件\(0<\Delta m_{21}^2/\Delta m_{31}^2<1\)要求\(\theta_{23}\)位于较低八分体。代表性的基于 JUNO 的输入给出\(\sin^2\theta_{23}\simeq0.440\)，\((m_1,m_2,m_3)\simeq(0.0938,0.0942,0.1063)\mathrm{eV}\)，以及\(\sum_i m_i\simeq0.294\mathrm{eV}\)。我们证明，由于领先阶抵消，围绕三极大点的一阶展开对于太阳到大气质量分裂比在数值上是不稳定的。当前的大气角数据仅与精确对齐产生轻微张力，而基线\(\Lambda\)CDM 宇宙学中严格的中微子质量界限强烈不支持它；其在扩展宇宙学模型下的可行性仍然依赖于模型。我们最终将几何对齐残差表述为一般的零测试可观测量，为用未来的振荡和绝对质量测量测试中微子长方体提供了一个系统框架。
英文摘要
We investigate the exact phenomenology of a geometric neutrino cuboid defined by $m_1=m_0\sinξ$, $m_2=m_0\cosξ\sinζ$, and $m_3=m_0\cosξ\cosζ$, whose cubic point corresponds to mass degeneracy and the tribimaximal values of the solar and atmospheric mixing angles. Imposing the mass-mixing alignment $ξ=θ_{12}$ and $ζ=θ_{23}$, we derive closed-form consistency relations without relying on an expansion about the cubic limit. These relations show that the observed condition $\sin^2θ_{12}<1/3$ selects normal mass ordering and, in the resulting normal-ordering regime, the physical condition $0<Δm_{21}^2/Δm_{31}^2<1$ requires $θ_{23}$ to lie in the lower octant. Representative JUNO-based inputs give $\sin^2θ_{23}\simeq0.440$, $(m_1,m_2,m_3)\simeq(0.0938,0.0942,0.1063)\mathrm{eV}$, and $\sum_i m_i\simeq0.294\mathrm{eV}$. We demonstrate that the first-order expansion around the tribimaximal point is numerically unstable for the solar-to-atmospheric mass-splitting ratio because of a leading-order cancellation. Present atmospheric-angle data yield only mild tension with exact alignment, whereas stringent neutrino-mass bounds in baseline $Λ$CDM cosmology strongly disfavor it; its viability under extended cosmological models remains model dependent. We finally formulate geometric alignment residuals as general null-test observables, providing a systematic framework for testing the neutrino cuboid with future oscillation and absolute-mass measurements.
Comments41 pages
