$CP$ asymmetries in $\tau\to K_S\pi\nu_\tau$ decays

We present here the CP asymmetries in the decay rate and angular distributions of $\tau\to K_S\pi\nu_\tau$ decays in the Standard Model (SM) and beyond (BSM). The CP asymmetries in the SM are induced by the CP violation in $K^0-\bar{K}^0$ mixing. To investigate the BSM CP-violating (CPV) effects, a model-independent analysis is performed by using the low-energy effective field theory (LEFT) framework at $\mu=2$~GeV. If one further assumes the BSM physics to stem from above the electroweak scale, the LEFT shall then be matched onto the SM effective field theory (SMEFT), the operators of which contributing to $\tau\to K_S\pi\nu_\tau$ decays will also contribute to the neutron electric dipole moment (EDM) and $D^0-\bar{D}^0$ mixing. The stringent bounds from the latter suggest that no remarkable CPV effects can be observed in either the decay rate or the angular distributions. The prospects for future measurements of these observables are also mentioned.
Comment: 8 pages, 3 figures, and 1 table; proceedings to the 2024 International Workshop on Future Tau Charm Facilities (FTCF2024)