A new approach to the parametrization of the Cabibbo-Kobayashi-Maskawa matrix

Abstract

The CKM-matrix V is written as a linear combination of the unit matrix I and a matrix U which causes intergenerational-mixing. It is shown that such a V results from a class of quark-mass matrices. The matrix U has to be hermitian and unitary and therefore can depend at most on 4 real parameters. The available data on the CKM-matrix including CP-violation can be reproduced by $V=(I+iU)/\sqrt{2}$. This is also true for the special case when U depends on \textit{only 2 real parameters}. There is no CP-violating phase in this parametrization. Also, for such a V the invariant phase $Φ\equiv ϕ_{12}+ϕ_{23}-ϕ_{13}$, satisfies a criterion suggested for `maximal' CP-violation.