Bell inequality is violated in charmonium decays

TL;DR

This paper demonstrates the violation of Bell inequality in various charmonium decays, confirming quantum entanglement and non-separability at high energies with different spin particles.

Contribution

It provides experimental evidence of Bell inequality violation in charmonium decays, extending quantum entanglement tests to high-energy particle interactions.

Findings

Bell inequality violated with significance of 5σ or more in multiple decays.

Entanglement observed in decays involving different spins and interactions.

Quantum spin correlations persist after particle interactions with detector materials.

Abstract

The experimental data on the helicity amplitudes of charmonium decays allow us to measure entanglement in final state spin correlations and test possible violations of the Bell inequality. We find that the Bell inequality is violated with a significance of 5$\sigma$ or more in the decays $\eta_{c}, \, \chi_{c}^{0}, \, J/\psi \to \Lambda +\bar \Lambda$ $J/\psi \to \Xi^- +\bar \Xi^+,\; \Xi^0 +\bar \Xi^0, \;\Sigma^{-} +\bar \Sigma^{+},\; \Sigma^{0} +\bar \Sigma^{0}$, $\psi(3686) \to \Xi^- +\bar \Xi^+,\; \Sigma^- +\bar \Sigma^+,\; \Sigma^{0} +\bar \Sigma^{0}$, $\chi^{0}_{c}, \, \chi_{c}^{1} \to \phi+ \phi$ . The decays $\psi(3686) \to \Lambda +\bar \Lambda$ and $\Xi^0 +\bar \Xi^0$ show the same violation but with less significance. The decay $\psi(3686) \to \Omega^- + \bar \Omega^+$ displays entanglement. These results firmly establish the presence of entanglement and quantum non-separability at high energies, in a setting with particles of different spins and interacting through electroweak and strong interactions. In addition, the relatively long lifetime of some of the strange baryons produced in the decays provides a natural probe to test whether quantum spin correlations remain after the particles have interacted with the beam pipe and the first few layers of the detector.