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
本文提出一个基于谐波模式的四级模对称性，通过θ常数假设从轻子质量推导出夸克质量和CKM矩阵，并预测中微子质量谱，与实验数据高度吻合。
AI 中文摘要
夸克和带电轻子的质量比遵循一个简单的模式。对数代际步长以二比一的比率出现，如同其八度音程，且上下夸克比较与下轻子比较之间的排序互为镜像。该模式被解读为在$Z_N$时钟上的电荷计数，在第四级实现，且仅在其倍数的级别实现，这激发了模四级和有限群$S_4$，其中代际位于$T$电荷$(3,1,0)$的三重态，镜像位于符号单态。带电轻子质量比位于一个θ修饰的格点上，精度为$0.02\\%$，这设定了基底$\varepsilon=0.18664$，取为$14/75$，以及谐波模量$\tau=1.0685i$。在相同数据上识别的权重一半θ常数中的五个假设，从三个轻子质量和电弱尺度重现了六个夸克质量。另外两个假设和一个关于$|V_{td}|$的经验关系闭合了CKM矩阵，给出$|V_{us}|=\sqrt{m_d/m_s}=0.2255$，$|V_{cb}|=0.04197$，$|V_{ub}|=0.003721$，以及$\delta=1.138$，而测量值为$1.139\pm0.023$，且无连续参数。随之而来的幺正三角形，顶点为$(0.161,0.348)$，而测量值为$(0.161\pm0.010,0.347\pm0.010)$，以及$J=3.11\times10^{-5}$，而测量值为$(3.09\pm0.07)\times10^{-5}$。相同的结构承载着中微子。单个θ插入给出$\sin\theta_{13}=\theta_2(\tau)m_2/m_3$，这在207天的JUNO数据上以$0.7\sigma$成立，且谐波条件完成了一个正常有序的谱，其中$m_1=0.25$~meV，$\Sigma m_\nu=0.0589$~eV，一个CP守恒相位$\delta_{CP}=\pi$，以及有效马约拉纳质量量子化在$1.3$至$3.9$~meV。紫外完备化属于磁化环面类，其中Pati--Salam是自然的规范嵌入。
英文摘要
The mass ratios of the quarks and charged leptons follow a simple pattern. The logarithmic generation steps come in a two to one ratio, a note to its octave, and the ordering is mirrored between the up-down and down-lepton comparisons. The pattern, read as charge counting on a $Z_N$ clock, is realized at level four and at no level that is not a multiple of four, which motivates modular level four and the finite group $S_4$, with the generations in the triplet at $T$ charges $(3,1,0)$ and the mirror in the sign singlet. The charged-lepton mass ratios lie on a theta-dressed lattice at $0.02\%$, which sets the base $\varepsilon=0.18664$, taken as $14/75$, and the harmonic modulus $τ=1.0685i$. Five postulates in the weight one-half theta constants, identified on the same data, reproduce the six quark masses from three lepton masses and the electroweak scale. Two more and one empirical relation for $|V_{td}|$ close the CKM matrix, giving $|V_{us}|=\sqrt{m_d/m_s}=0.2255$, $|V_{cb}|=0.04197$, $|V_{ub}|=0.003721$, and $δ=1.138$ against the measured $1.139\pm0.023$, with no continuous parameter. The unitarity triangle follows, with apex $(0.161,0.348)$ against the measured $(0.161\pm0.010,0.347\pm0.010)$, and $J=3.11\times10^{-5}$ against $(3.09\pm0.07)\times10^{-5}$. The same structure carries the neutrinos. A single theta insertion gives $\sinθ_{13}=θ_2(τ)m_2/m_3$, which holds at $0.7σ$ on the 207-day JUNO data, and the harmonic condition completes a normal-ordered spectrum with $m_1=0.25$~meV, $Σm_ν=0.0589$~eV, a CP-conserving phase $δ_{CP}=π$, and effective Majorana masses quantized at $1.3$ to $3.9$~meV. The ultraviolet completion belongs to the magnetized torus class, with Pati--Salam the natural gauge embedding.
