Bell inequality is violated in charmonium decays

The experimental data on the charmonium decay helicity amplitudes make it possible to measure entanglement in final state spin correlations and test the violation of the Bell inequality it may entail. We find that the Bell inequality is violated with a significance of 5σ or more in the decays ηc, \, χc⁰, \, J/ψ ,\, ψ(3686) → Λ + Λ, J/ψ → Ξ⁻ + Ξ⁺,\; Ξ⁰ + Ξ⁰, \;Σ⁻ + Σ⁺,\; Σ⁰ + Σ⁰, ψ(3686) → Ξ⁻ + Ξ⁺,\; Σ⁻ + Σ⁺,\; Σ⁰ + Σ⁰, χ⁰c ,\, χc¹ → φ+ φ. The decay ψ(3686) → Ξ⁰ + Ξ⁰ shows the same violation but with less significance. The decay ψ(3686) → Ω⁻ + Ω⁺ 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 present after the particles have interacted with the beam pipe and the first few layers of the detector.