Bell nonlocality and entanglement in $χ_{cJ}$ decays into baryon pair
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Abstract
We present a systematic analysis of Bell nonlocality and entanglement in $χ_{cJ}$($J=0,1,2$) decays into baryon pair($B\bar{B}$), with particular emphasis on their production via the process $e^+e^- \to ψ(2S) \to γχ_{cJ}$ at BESIII. From the baryon-antibaryon spin density matrix, we construct measurable Bell observables and concurrence, revealing a striking hierarchy of quantum correlations: $χ_{c0}$ decays exhibit maximal violation and entanglement; $χ_{c1}$ decays violate Bell inequalities for $θ_1 \in (0, π)$ with angle-modulated strength; we find that the $B\bar{B}$ pair in $χ_{c2}$ 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 $χ_{cJ}$ system produced via this radiative transition as a novel and promising platform for testing quantum entanglement and Bell nonlocality in high-energy collisions.