发表机构
Fondation Louis de Broglie; Sorbonne Université（路易·德布罗意基金会; 索邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出几何味机制，通过拓扑凝聚的几何约束融入Yukawa拉格朗日量，解决带电轻子质量等级问题并推导Koide关系，完美重现其质量谱。
AI 中文摘要
本文提出一种几何味机制，以解决带电轻子质量等级问题并形式化推导经验性Koide关系。该机制由拓扑凝聚$U(3) \rightarrow U(1) \times \boldsymbol{\text{Z}}_3$主导，味真空将连续各向同性背景（$U(1)$单态）与离散代分裂网络（$\boldsymbol{\text{Z}}_3$八重态）耦合。力学稳定性要求该真空满足严格无应力条件，即连续部分的膨胀能需完美平衡离散晶格的内聚拓扑张力。此外，连续内空间向离散节点的几何投影会产生拓扑作用相位，将内味角严格锁定在$\theta_F = -2/9$。通过将这些几何约束融入Yukawa拉格朗日量，该框架完美重现带电轻子（电子、μ子、τ子）的Koide质量谱（$Q=2/3$）。
英文摘要
This article proposes a dynamical framework to address the charged-lepton mass hierarchy and derive the empirical Koide formula. We postulate a $U(3)_F$ flavor symmetry at the high-energy scale, where a heavy dynamical flavon field couples to the electroweak Higgs sector via an effective operator. As the universe cools, spontaneous symmetry breaking of the flavor group occurs following the pattern $U(3)_F \to U(1)^3_F$. Subsequently, the electroweak symmetry breaking at the Fermi scale generates the charged-lepton mass matrix. The phenomenological values of these masses are determined in the infrared regime, where the effective potential governing the flavon VEV undergoes a dynamical vacuum alignment.The stable minimum of this potential enforces an algebraic equipartition between the flavor-singlet and flavor-octet invariants ($I_{(0)} = I_{(8)}$). This geometric equilibrium yields the Koide mass ratio ($Q=2/3$), successfully identifying the dynamically generated eigenvalues with the physical pole masses of the electron, muon, and tau.
