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

Abstract

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.

Comments: 10 pages, 5 figures