CKM矩阵的几何、标准模型与重整化群不动点
The Geometry of the CKM matrix, the Standard Model and RG fixed points
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中文总结 AI 辅助
本文研究标准模型中CKM矩阵的几何，将其视为双陪集空间元素，揭示其奇点对应重整化群不动点，并指出外尔群S3以六边形顶点形式出现。
中文摘要 AI 辅助
我们研究了标准模型中费米子混合矩阵的几何。所研究的主要结构是CKM矩阵$V$，它被视为双陪集空间$M$的一个元素，其中$M=T\ackslash SU(3)/T$，且$T=U(1)\ imes U(1)$。空间$M$被赋予黎曼度量，并具有点奇点（已证明这些点奇点对应于已知的重整化群不动点）以及连接这些不动点的线奇点。诱导这些性质的许多关键离散对象是$SU(3)$的外尔群$W$，$W$是对称群$S_3$，它以$V$中六边形的顶点形式出现。
英文摘要
We investigate the geometry of the Fermion mixing matrix in the Standard Model. The principal structure studied is the CKM matrix, $V$, viewed as an element of the double coset space $M$, where $M=T\backslash SU(3)/T$, and $T=U(1)\times U(1)$. The space $M$ is given a Riemannian metric, and has both point singularities, which it is shown correspond to the known renormalization group fixed points, and line singularities connecting the fixed points. A key discrete object inducing many of these properties is the Weyl group, $W$, of $SU(3)$, $W$ being the symmetric group $S_3$, which appears in the guise of the vertices of a hexagon in $V$.
发表机构
- Dublin Institute for Advanced Studies（都柏林高等研究院）
- Maynooth University（梅努斯大学）
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