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

TL;DR

This work develops a complete spin‑density‑matrix framework for χ_{cJ} → B\bar{B} decays (J=0,1,2) to study Bell nonlocality and quantum entanglement in high‑energy collisions. By propagating polarization from the χ_{cJ} through the decay chain using helicity amplitudes and Wigner rotations, it derives analytical and numerical predictions for the Bell measure m_{12} and concurrence C across all three J values, revealing a pronounced hierarchy: χ_{c0} yields maximal Bell violation and entanglement (C=1, m_{12}=2), χ_{c1} produces angle‑dependent nonlocal correlations with a mixed, but detectable, entangled state, and χ_{c2} decays are largely separable with no BI violation within current parameter constraints. The analysis relies on measured helicity ratios (r_i) and phase differences (ΔΦ_i) from BESIII and baryon‑angle parameters (x, ΔΦ) extracted from angular distributions, providing concrete, testable predictions for BESIII and future tau‑charm facilities. Overall, χ_{cJ} decays offer a calibrated, high‑energy platform to probe quantum foundations and entanglement in a relativistic, hadronic environment, linking fundamental quantum information concepts to observable collider phenomena.

Abstract

We present a systematic analysis of Bell nonlocality and entanglement in $χ_{cJ}$ decays into baryon pair ($B\bar{B}$) ($J=0,1,2$). 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 $B\bar B$ in $χ_{c2}$ decays is in separable state, and no indication is found for the Bell inequality violation. We provide complete analytical results for $J=0,1$ and quantitative, uncertainty-aware estimations for $J=2$ using experimental inputs. The results indicates that the $χ_{cJ}$ system as a novel platform for testing quantum entanglement in high-energy collisions.

Figures (5)

• Figure 1: The decays of $J/\psi \to \gamma \chi_{cJ}$ and $\chi_{cJ} \to B\bar{B}$
• Figure 2: The Horodecki condition $\mathbf{m}_{12}$ as functions of $\cos \theta_{1}$ of the baryon in $e^{+}e^{-} \to \psi(2S) \to \gamma \chi_{c1}, \chi_{c1} \to B\bar{B}$ decays. The parameter $r_1$ is fixed at $1.307\pm 0.057$
• Figure 3: The Horodecki condition $\mathbf{m}_{12}$ as functions of $\cos \theta_1$ in $\chi_{c2} \to B\bar{B}$ decays with $r2, r3$ fixed to the measurements BESIII:2025gof. The line is calculated with the center value of $x$.
• Figure 4: The concurrence $\mathcal{C}[\rho]$ as functions of $\cos \theta_{1}$ in $e^{+}e^{-} \to \psi(2S) \to \gamma \chi_{c1}, \chi_{c1} \to B\bar{B}$ decays.
• Figure 5: The concurrence $\mathcal{C}[\rho]$ as functions of $\cos \theta_{1}$ in $e^{+}e^{-} \to \psi(2S) \to \gamma \chi_{c2}, \chi_{c2} \to B\bar{B}$ decays. The line is calculated with the center values of $x$.