Feasibility study of $CP$ Violation in $τ^{-}\to K_{S}π^{-}ν_τ$ decays at Super Tau Charm Facility
We report a feasibility study of $CP$ violation of $τ^{-}\rightarrow K_{S}π^{-} ν_τ$ 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 $9.7\times10^{-4}$ by measuring the decay-rate difference between $τ^{+}\rightarrow K_{S}π^{+}\barν_τ$ and $τ^{-}\rightarrow K_{S}π^{-} ν_τ$. 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 $τ^{-}\rightarrow K_{S}π^{-} ν_τ$ 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 $3.1\times10^{-4}$ with 10~ab$^{-1}$ integrated luminosity, which is equivalent to ten years data taking in this energy region at STCF.