Polarization and Entanglement in Baryon-Antibaryon Pair Production in Electron-Positron Annihilation

Using a sample of $1.31\times 10^9$ $J/\psi$ events collected with the BESIII detector, we report the first observation of spin polarization of $\Lambda$ and $\bar\Lambda$ hyperons from the coherent production in the $J/\psi\to\Lambda\bar\Lambda$ decay. We measure the phase between the hadronic form factors to be $\Delta\Phi=(42.4\pm0.6\pm0.5)^\circ$. The decay parameters for $\Lambda\to p\pi^-$ ($\alpha_-$), $\bar\Lambda\to\bar p\pi^+$ ($\alpha_+$) and $\bar\Lambda\to\bar n\pi^0$ ($\bar\alpha_0$) are measured to be $\alpha_-=0.750\pm0.009\pm0.004$, $\alpha_+=-0.758\pm0.010\pm0.007$ and $\bar\alpha_0=-0.692\pm0.016\pm0.006$, respectively. The obtained value of $\alpha_-$ is higher by $(17\pm 3)\%$ than the current world average. In addition, the $CP$ asymmetry of $-0.006\pm0.012\pm0.007$ is extracted with substantially improved precision. The ratio $\bar{\alpha}_0/\alpha_{+} = 0.913\pm 0.028 \pm 0.012$ is also measured.