We apply the effective field theory formalism that was used to study CP violation induced by heavy new physics in the $\tau\to K_S \pi\nu_\tau$ decays to the other two-meson tau decay channels. We focus on the rate and the forward-backward asymmetries, that are predicted using current bounds on the complex Wilson coefficients of the effective Lagrangian. We discuss our outcomes for the modes with $(K/\pi)\pi^0$ and $K K_S$, that can be studied at Belle-II and a super-tau-charm facility. Our main finding is that current and forthcoming experiments would be sensitive to the maximum allowed CP rate asymmetry in the $K^\pm K_S$ modes if a precision of $5\%$ is reached on this observable, that can check as well the BaBar anomaly in $K_S\pi$. For the $\pi^\pm\pi^0$ channels, new physics would be best probed through the forward-backward asymmetry. Disentangling new sources of CP violation would be most challenging in $K^\pm\pi^0$ and the other modes.

Just appeared on arXiv: 2409.05588 Wok in collaboration with Javier Rendón and Pablo Roig