壳层驱动的费米子质量假设的秩与标度检验及带约束的中微子扩展
Rank and Scale Tests of Shell-Motivated Fermion-Mass Ansatze with a Constrained Neutrino Extension
浏览论文内容
中文总结 AI 辅助
本文检验两个八参数对数费米子质量假设，提出模型M2并构建带约束中微子扩展模型M3，利用NuFIT 6.0预测中微子质量，相关模型仍处于探索阶段。
中文摘要 AI 辅助
我们在共同标度μ = M_Z下，于一个重整化方案中评估了9个带电费米子汤川本征值，以此对两个八参数对数假设进行检验。平滑的对数线性趋势通过假设的渐近自由禁闭区中的维度转换获得了条件性重整化群动机，这为质量公式提供了动机，但未从微观上推导该公式。模型M1有一个与参数无关的秩约束R₁ = y_u y_μ² y_t/(y_e y_c² y_τ) = 1，而输入给出R₁(M_Z) = 6.662。其交替残差为明确后选择的模型M2提供了动机，M2为带电扇区分配独立的离散曲率且不增加参数数量，其唯一关系为R₂ = y_e y_μ² y_τ/(y_d y_s² y_b) = 1，而R₂(M_Z) = 0.4019。对于每个状态25%的未校准相对模型差异的示例，精确加权最小值为：M1的χ²_min = 6.003，M2的χ²_min = 1.389，自由度为1。带约束的中性扇区扩展模型M3为中微子质量本征三重态赋予了自身的截距和斜率，但共享M2的带电轻子曲率，所得12×10设计矩阵产生了第二个左零关系m₁ m₃ m_μ²/(m₂² m_e m_τ) = 1。使用NuFIT 6.0的中心分裂，M3预测正常序时最轻中微子质量m_lightest = 1.04×10⁻⁴ eV，中微子质量和sum m_ν = 0.05889 eV；倒序时则为m_lightest = 3.51×10⁻³ eV，sum m_ν = 0.10269 eV。M2和M3仍处于探索阶段，因为它们是在带电扇区诊断后选择的，且共享曲率尚未从微观上推导出来。
英文摘要
We study whether the observed hierarchy of quark and lepton masses can be described by a small set of simple relations between the three fermion generations. Using the nine charged-fermion Yukawa couplings at the common scale M_Z, we distinguish genuine mass relations from those that arise simply because a model has enough freedom to reproduce the data. A systematic scan of projector-based models identifies a particularly accurate relation between the first- and third-generation mass slopes. We then construct more restrictive models that also constrain the second generation and test them by leave-one-out reconstruction. Several six-parameter models predict all nine charged masses with errors of only a few percent; the best fixed models reduce the worst leave-one-out error to about 4% without adding continuous parameters. We also give a possible microscopic interpretation of the most successful integer relations. Two mass-independent combinations of Standard-Model quantum numbers reproduce the required charged-sector pattern, and simple twofold or threefold matching classes fix the relative coefficient before the masses are used. In a separate two-loop running test, a down-sector ratio close to 1/15 near 6 x 10^6 GeV evolves to a value close to 1/14 at M_Z. The same framework gives neutrino-mass sums near 0.059-0.061 eV for normal ordering, while one family also allows inverted ordering near 0.103 eV. These results do not prove preons or fermion compositeness, but provide concrete targets for future microscopic models.
