Wolfenstein Parametrization Re-examined

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 $V$: $\mathrm{\mid }{V}_{ij}{\mathrm{\mid }}^2-\mathrm{\mid }{V}_{ji}{\mathrm{\mid }}^2$ = $Z{\displaystyle \sum _k{ϵ}_{ijk}^{}}$ with $Z=\approx A^{2}\lambda^{6} (1-2\rho)$,whichiscomparableinmagnitudewiththeJarlskogparameterof$CP$violation$J\approx A^{2}\lambda^{6}\eta$\mathrm{.}Weconstraintherangesof$J$and$Z$ by using the current experimental data, and point out that the possibility of a symmetric KM matrix has almost been ruled out.