Spin precession in magnetic field effects the search of CP violation in $\Lambda$ decay

We investigate the joint $\Lambda \bar{\Lambda} $ production in the reaction $e^{+}e^{-} \to \Lambda \bar{\Lambda}$. We consider the spin precession of $\Lambda$ in the external magnet and driven the corresponding corrected term of the distribution of the angle of final states. We also estimate its potential threat on the measurement of Charge-Parity Violation (CPV) as well as the decay parameter of $\Lambda$. We conclude that an additional CPV ($10^{-5}$ level) will be caused in the experiment, once the experimenter neglect this effect.