Wolfenstein Parametrization Re-examined

Abstract

The Wolfenstein parametrization of the $3\times 3$ Kobayashi-Maskawa (KM) matrix $V$ is modified by keeping its unitarity up to the accuracy of $O({\lambda }^6)$. This modification can self-consistently lead to the off-diagonal asymmetry of $V$: $|V_{ij}{|}^2-|V_{ji}{|}^2$ = $Z\sum _k{ϵ}_{ijk}^{}$ with $Z=\approx A^2{\lambda }^6(1-2\rho )$, which is comparable in magnitude with the Jarlskog parameter of $CP$ violation $J\approx A^2{\lambda }^6\eta$. We constrain the ranges of $J$ and $Z$ by using the current experimental data, and point out that the possibility of a symmetric KM matrix has almost been ruled out.

Comments: 5 Latex pages including a figure; Two references are added