CP violation in $\tau\to K_S \pi\nu_\tau$ decays attracted a lot of attention, due to the BaBar anomaly in the corresponding rate asymmetry, at 2.8 sigma from the SM prediction, coming from neutral Kaon mixing.
Within an effective field theory formalism, only extreme fine-tuning would allow understanding such a measurement as caused by heavy new physics. This is currently being scrutinized at Belle-II, who presented preliminary results in the Moriond conference, now in agreement (at 1.2 sigma) with the SM prediction.
Here we summarize the results of applying the same formalism to the other two-meson tau decay channels, which can help solve this conundrum. Our main conclusion is that current and future experiments would be sensitive to the maximum allowed CP rate asymmetry in the related $K^\pm K_S$ modes with a measurement having 5$\%$ precision.
Leandro Cieri