Bell nonlocality and entanglement in $\chi_{cJ}$ decays into baryon pair

We present a systematic analysis of Bell nonlocality and entanglement in $\chi_{cJ}$($J=0,1,2$) decays into baryon pair($B\bar{B}$), with particular emphasis on their production via the process $e^+e^- \to \psi(2S) \to \gamma \chi_{cJ}$ at BESIII. From the baryon-antibaryon spin density matrix, we construct measurable Bell observables and concurrence, revealing a striking hierarchy of quantum correlations: $\chi_{c0}$ decays exhibit maximal violation and entanglement; $\chi_{c1}$ decays violate Bell inequalities for $\theta_1 \in (0, \pi)$ with angle-modulated strength; we find that the $B\bar{B}$ pair in $\chi_{c2}$ decays is in a separable state, and no indication of Bell inequality violation is observed. We provide complete analytical results for $J=0,1$ and quantitative, uncertainty-aware estimations for $J=2$ based on experimental inputs from BESIII. These results establish the $\chi_{cJ}$ system produced via this radiative transition as a novel and promising platform for testing quantum entanglement and Bell nonlocality in high-energy collisions.