AI 中文总结
该研究识别夸克与轻子混合数据的两种相称结构，利用层级参数ε重现FX角与Jarlskog不变量，量子化幺正三角形并预言轻子CP相位，还关联中微子质量比，结果可在多个实验检验。
AI 中文摘要
我们在已测量的夸克与轻子混合数据中识别出两种相称结构，一种是乘法结构，另一种是角结构，且二者存在精确关系。利用层级参数ε≡|V_ub|^(3/10)=0.1869±0.0018，已测量的Fritzsch–Xing（FX）角满足sinθ_u=ε^(26/18)、sinθ_d=ε^(17/18)、sinθ=ε^(34/18)，其系数与1的偏差在2.5%以内，且相位取极大值，φ_FX=92.3°±2.7°，接近π/2。单位系数在百分位水平上重现了剩余的模，并确定了导出的Jarlskog不变量J=ε^(111/18)sinφ_FX，与已测量的3.08(14)×10^-5相符。该结构的重相位不变像为在π/24晶格（即数字时钟）上量子化的幺正三角形，(α,β,γ)=(12,3,9)×7.5°，通过α≈φ_FX和定理tanβ≈√ε，在1σ水平上与数据一致；度级的γ与67.5°–68°相符。对于轻子，仅角结构起作用，其由第1列和第3列构成、无马约拉纳相位的PMNS类比在同一晶格上要求δ_CP在上八分区约为296°，在下八分区约为244°，可在DUNE和Hyper-Kamiokande上检验。夸克与轻子三角形共享夸克测量得到的β=22.5°（对轻子为预测值），相差两个晶格单位，推论为δ_CP≈-δ≈295°。同一ε设定了中微子质量比r≡m_2/m_3=ε^(19/18)，且PMNS第一行遵循r的幂次：(r^(1/9), r^(1/3), (√3/2)r)，两种关系均在0.2σ水平上，可在JUNO上检验。本分析仅局限于参数化层面，未假设任何动力学。
英文摘要
We identify two commensurate structures in the measured quark and lepton mixing data, one multiplicative and one angular, and their exact relation. With the hierarchy parameter $\varepsilon\equiv|V_{ub}|^{3/10}=0.1869\pm0.0018$, the measured Fritzsch--Xing (FX) angles satisfy $\sinθ_u=\varepsilon^{26/18}$, $\sinθ_d=\varepsilon^{17/18}$, and $\sinθ=\varepsilon^{34/18}$ with coefficients within $2.5\%$ of unity, and the phase is maximal, $ϕ_{\rm FX}=92.3^\circ\pm2.7^\circ$ against $π/2$. Unit coefficients reproduce the remaining moduli at the percent level and fix the derived Jarlskog invariant, $J=\varepsilon^{111/18}\sinϕ_{\rm FX}$, matching the measured $3.08(14)\times10^{-5}$. The rephasing-invariant image of this structure is a unitarity triangle quantized on the $π/24$ lattice, a digital clock, $(α,β,γ)=(12,3,9)\times7.5^\circ$, consistent with data at $1σ$ through $α\simeqϕ_{\rm FX}$ and the theorem $\tanβ\simeq\sqrt{\varepsilon}$; degree-level $γ$ confronts $67.5^\circ$--$68^\circ$. For the leptons, where only the angular structure can act, its PMNS analog, formed from columns $1$ and $3$, free of Majorana phases, on the same lattice requires $δ_{\rm CP}\simeq296^\circ$ in the upper octant or $244^\circ$ in the lower, testable at DUNE and Hyper-Kamiokande. The quark and lepton triangles share $β=22.5^\circ$, measured for quarks, predicted for leptons, and differ by a transfer of two lattice units, with corollary $δ_{\rm CP}\simeq-δ\simeq295^\circ$. The same $\varepsilon$ sets the neutrino mass ratio, $r\equiv m_2/m_3=\varepsilon^{19/18}$, and the PMNS first row follows in powers of $r$, $(r^{1/9},\,r^{1/3},\,\tfrac{\sqrt{3}}{2}r)$, both relations at $0.2σ$ and testable at JUNO. The analysis is confined to the parameterization level; no dynamics is assumed.
