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

Abstract

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 $10^{-3}$.