Measurement of $CP$ violation of neutral kaon system in $J/\psi$ decay at the Super Tau-Charm Facility

In this paper, we present a preliminary study of $CP$ violation effect of $K^{0}-\bar{K}^{0}$ system in $J/\psi$ decay. The $CP$ violation parameters $\eta_{+-}$ and $\eta_{00}$ as well as their corresponding phase $\phi_{+-}$ and $\phi_{00}$ can be determined by the difference of the time-dependent decay rates between $K^{0}$ and $\bar{K}^{0}$ produced from $J/\psi \rightarrow K^{-}\pi^{+}K^{0} + c.c.$ processes. We investigate the precisions of the measurements of the CP violation effect at the Super Tau-Charm facility(STCF), a $e^{+}e^{-}$ collider with a peak luminosity of $0.5\times10^{35}\ \rm{cm}^{-2}\rm{s}^{-1}$. The parameters $\eta_{+-}$ and its phase $\phi_{+-}$ can be measured at a relative precision of $1 \times 10^{-3}$, which the statistical accuracy will be several times better than that of the existing PDG average values.