Polarization difference between hyperons and anti-hyperons induced by external magnetic field

We investigate the quantum correlated $\Lambda \bar{\Lambda} $ production in the reaction $e^{+}e^{-} \to J/\psi \to \Lambda \bar{\Lambda}$. Since the $\Lambda$ or $\bar{\Lambda}$ has a nonzero magnetic moment, its spin will undergo a Larmor precession in the magnetic field of the detector, such as the BESIII experiment. Because of the spin precession, the angular distribution of the $\Lambda$ and $\bar{\Lambda}$ is slightly modified. Therefore, we obtain the corresponding term of the modified angular distribution due to the effect of the Larmor precession. We also estimate its potential effect on the measurements of $CP$ violation, as well as the decay asymmetry parameter and polarization of $\Lambda$. The polarization of the $\Lambda$ or $\bar{\Lambda}$ at the production vertex will rotate around the $B$-field axis, over an angle depending on the flight length in, but it still could be measured by fit to the corrected angular distribution. Of important, We conclude that a nonzero $CP$ asymmetry of order $10^{-4}$ will be caused once neglecting spin precession of the $\Lambda$ and $\bar{\Lambda}$ in the $e^{+}e^{-} \to J/\psi \to \Lambda \bar{\Lambda}$ process. The size of this $CP$ asymmetry is several times that of predicted within Standard Model in the hyperon decay. Although this effect is small, it will play an important role in future high precision experiments, such as the super-tau-charm factory.