Year: 2026
Type: preprint
Abstract: 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 $V$.
Source: arXiv (Cornell University)
Authors: Dolan, Brian P., Nash, Charles
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213501433