CP violation in $J/\psi \rightarrow \Lambda \bar \Lambda$

We study CP violation in $J/\psi \rightarrow \Lambda \bar{\Lambda}$ decay. This decay provides a good place to look for CP violation. Some observables are very sensitive to the $\Lambda$ electric dipole moment $d_\Lambda$ and therefore can be used to improve the experimental upper bound on $d_\Lambda$. CP violations in the lepton pair decays of $J/\psi$ and $\Upsilon$ are also discussed.