$CP$ Invariance Study of $J/\psi\to\Lambda\bar\Lambda$ and $\Lambda$ Nonpleptonic Decays in Helicity Frame

We present the joint helicity amplitudes for $J/\psi \to \Lambda \bar{\Lambda}$, $\Lambda(\bar\Lambda)$ decays to different final states in the helicity frame. Two observables to search for $CP$ violation in $J/\psi\to\Lambda\bar\Lambda$ can be expressed with the information of helicity angles of baryon and antibaryon. Four decay parameters of $\Lambda$ and $\bar\Lambda$, namely, $\alpha_-,\alpha_+,\alpha_0$ and $\bar\alpha_0$, can be obtained with the joint helicity amplitude equations by the likelihood fit method. With the data sample of $10^{10}$ $J/\psi$ decays accumulated by BESIII, the precision of the measurements is estimated to be about $10^{-3}$.