发表机构
Nagoya Aoi University（名古屋青大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出三体完整性机制，通过循环三态质量算符在 θ3=0 时实现 SU(3)→SU(2)×U(1) 破缺，并重现标准模型超荷，为对称性破缺方向选择提供玩具模型。
AI 中文摘要
我们证明三体完整性可以选择常规的 $SU(3)\to SU(2)\times U(1)$ 破缺方向。在当前构造中，三个粒子具有特殊性：在去除质心坐标后，它们是最小的一维少体系统，具有二维相对空间，从而允许在成对接触通过匹配条件编码后，围绕三重重合点形成闭合回路。一个循环三态质量算符给出 \\[ M^{[k]}=M_0+2\Delta\cos\\!\left(\frac{\theta_3+2\pi k}{3}\right),\qquad k=0,1,2. \\] 在 $\theta_3=0$ 时，谱分裂为 $3\to2+1$，诱导的质量算符正比于 Cartan 生成元 $T_8$。因此其交换子为 $SU(2)\times U(1)$。在类似三统一（trinification）的嵌入中，不同的左、右扇区完整性留下超荷组合，该组合在通常的三统一物质分配下重现标准模型的超荷。该构造是选择破缺方向的玩具机制；秩约化和真空选择需要额外的动力学。
英文摘要
We show that a three-body holonomy can select the conventional $SU(3)\to SU(2)\times U(1)$ breaking direction. Three particles are special in the present construction: after removal of the center-of-mass coordinate they are the minimal one-dimensional few-body system with a two-dimensional relative space, allowing a closed cycle around the triple-coincidence point once pairwise contacts are encoded by matching conditions. A cyclic three-state mass operator gives \[ M^{[k]}=M_0+2Δ\cos\!\left(\frac{θ_3+2πk}{3}\right),\qquad k=0,1,2. \] At $θ_3=0$ the spectrum splits as $3\to2+1$, and the induced mass operator is proportional to the Cartan generator $T_8$. Its commutant is therefore $SU(2)\times U(1)$. In a trinification-like embedding, distinct left- and right-sector holonomies leave the hypercharge combination which reproduces the Standard-Model hypercharges for the usual trinification matter assignment. The construction is a toy mechanism for selecting the breaking direction; additional dynamics are required for rank reduction and vacuum selection.
Comments8 pages, no figure
