Prospects of $CP$ violation in $\Lambda$ decay with polarized electron beam at STCF

Based on $1.89 \times 10^8$ $J/\psi \rightarrow \Lambda \bar{\Lambda}$ Monte Carlo (MC) events produced from a longitudinally-polarized electron beam, the sensitivity of $CP$ violation of $\Lambda$ decay is studied with fast simulation software. In addition, the $J/\psi \rightarrow \Lambda \bar{\Lambda}$ decay can also be used as a process to optimize the detector response using the interface provided by the fast simulation software. In the future, STCF is expected to obtain 3.4 trillion $J/\psi$ events, and the statistical sensitivity of $CP$ violation of $\Lambda$ decay via $J/\psi \rightarrow \Lambda \bar{\Lambda}$ process is expected to reach $\mathcal O$~$(10^{-5})$ when the electron beam polarization is 80\%.