A Geometric Parametrization of the Cabibbo-Kobayashi-Maskawa Matrix and the Jarlskog Invariant

Abstract

In this paper we give a geometric parametrization to the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix and the Jarlskog invariant, which is based on two flag manifolds $SU(3)/U(1{)}^2$. To treat a fourth generation of quarks on CP violation we generalize the parametrization to one based on two flag manifolds $SU(4)/U(1{)}^3$.

Comments: Latex ; 14 pages ; 2 figures ; minor changes