Direct CP violation in $τ^\pm\rightarrow K^\pm ρ^0 (ω)ν_τ\rightarrow K^\pm π^+π^-ν_τ$

We study the direct CP violation in the $τ^\pm\rightarrow K^\pm ρ^0 (ω)ν_τ\rightarrow K^\pm π^+π^-ν_τ$ decay process in the Standard Model. An interesting mechanism involving the charge symmetry violating mixing between $ρ^0$ and $ω$ is applied to enlarge the CP asymmetry. With this mechanism, the maximum differential and localized integrated 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 room for CP-violating New Physics to be discovered through this process.

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