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We study the direct CP violation in the $\tau^\pm\rightarrow K^\pm \rho^0(\omega)\nu_\tau \rightarrow K^\pm \pi^+\pi^-\nu_\tau$ decay process in theStandard Model. An interesting mechanism involving the charge symmetryviolating mixing between $\rho^0$ and $\omega$ is applied to enlarge the CPasymmetry. With this mechanism, the maximum differential and localizedintegrated CP asymmetries can reach $-(5.6^{+2.9}_{-1.7})\times10^{-12}$ and$6.3^{+2.4}_{-3.3}\times 10^{-11}$, respectively, which still leave plenty roomfor CP-violating New Physics to be discovered through this process.

Direct CP violation in $\tau^\pm\rightarrow K^\pm \rho^0 (\omega)\nu_\tau \rightarrow K^\pm \pi^+\pi^-\nu_\tau $