First determination of the full spin density matrix in $\psi (3686)\to \Lambda \bar{\Lambda }$

Abstract

Using $(448.1\pm 2.9)\times 10^6$ $\psi (3686)$ events collected with the BESIII detector, we present the first complete determination of the spin density matrix in $\psi (3686)\to \Lambda \bar{\Lambda }$. This provides a unified framework to study both the production dynamics and the quantum correlations of the $\Lambda \bar{\Lambda }$ system. From a five-dimensional joint angular analysis, we determine ${\alpha }_{\psi }=0.82\pm 0.02_{stat.}\pm 0.01_{syst.}$ and $\Delta \Phi =(20.6\pm 3.6_{stat.}\pm 0.6_{syst.}{)}^{\circ }$. The non-zero phase implies a transverse polarization of $\Lambda$, with a maximum value of $P_y=0.074\pm 0.013_{stat.}\pm 0.003_{syst.}$ and a significance of 6.3$\sigma$. The same framework also gives access to the spin correlations of the baryon pair and enables tests of quantum nonclassicality. The average of the Bell nonlocality measure is determined to be ${\bar{m}}_{12}=1.266\pm 0.078_{stat.}\pm 0.049_{syst.}$, yielding a violation of the Clauser-Horne-Shimony-Holt inequality with a significance of 3.7$\sigma$. These results establish $\psi (3686)\to \Lambda \bar{\Lambda }$ as a unique laboratory for unified studies of hadron production dynamics and quantum entanglement in a system of massive baryons.