PreprintCC BY 4.0arXiv
The Geometry of the CKM matrix, the Standard Model and RG fixed points
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=Tbackslash SU(3)/T, and T=U(1)× 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 S3, which appears in the guise of the vertices of a hexagon in V.
Related
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BibTeX
@misc{dolan2026geometry,
title = {{The Geometry of the CKM matrix, the Standard Model and RG fixed points}},
author = {Brian P. Dolan and Charles Nash},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18884},
eprint = {2609.18884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18884},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Geometry of the CKM matrix, the Standard Model and RG fixed points
AU - Brian P. Dolan
AU - Charles Nash
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.18884
UR - https://arxiv.org/abs/2609.18884
AB - 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=Tbackslash SU(3)/T, and T=U(1)× 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.
ER -