Feasibility study of $CP$ Violation in $tau^{-}to K_{S}pi^{-} u_{tau}$ decays at Super Tau Charm Facility

We report a feasibility study of $CP$ violation of $tau^{-}rightarrow K_{S}pi^{-} u_{tau}$ decay at a Super Tau Charm Facility~(STCF).With an expected luminosity of 1~ab$^{-1}$ collected by STCF per year at a center-of-mass energy of 4.26 GeV, the statistical sensitivity for the $CP$ violation is determined to be of order $9.7times10^{-4}$ by measuring the decay-rate difference between $tau^{+}rightarrow K_{S}pi^{+}bar{ u}_{tau}$ and $tau^{-}rightarrow K_{S}pi^{-} u_{tau}$. The analysis is performed using a reliable fast simulation software package, which can describe the detector responses properly and vary the responses flexibly for further optimization. Moreover, the energy-dependent efficiencies for reconstructing $tau^{-}rightarrow K_{S}pi^{-} u_{tau}$ are presented and the expected $CP$ sensitivity is proportional to $1/sqrt{mathcal{L}}$ in the energy region from 4.0 to 5.0 GeV. The sensitivity of $CP$ violation is of order $3.1times10^{-4}$ with 10~ab$^{-1}$ integrated luminosity, which is equivalent to ten years data taking in this energy region at STCF.