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 σ or more in the decays η c , χ c 0 , J / ψ → Λ + Λ ¯ , J / ψ → Ξ − + Ξ ¯ + , Ξ 0 + Ξ ¯ 0 , Σ − + Σ ¯ + , Σ 0 + Σ ¯ 0 , ψ ( 3686 ) → Ξ − + Ξ ¯ + , Σ − + Σ ¯ + , Σ 0 + Σ ¯

arXiv:2406.17772Physical review. D/Physical review. D.Sep 23, 202427 citations

arXiv:2305.04982

Bell inequality is violated in $B^0\to J/ψ\, K^{\star}(892)^0$ decaysBell inequality is violated in $B^0\to J/ψ\, K^{\star}(892)^0$ decays

Marco E. Fabbrichesi, Roberto Floreanini B, Emidio Gabrielli A, Luca Marzola

Published May 8, 2023• 0 citations

arXiv HTML PDF

Abstract

B^0\to J/ψ\,K^*(892)^0

to compute the entanglement among the polarizations of the final vector mesons and the violation of the Bell inequality that it entails. We find that quantum entanglement can be detected with a significance well above 5

σ

(nominally 84

σ

) and Bell inequality is violated with a significance well above 5

σ

(nominally 36

σ

) -- thereby firmly establishing these distinguishing feature of quantum mechanics at high energies in a collider setting and in the presence of strong and weak interactions. Entanglement is also present and the Bell inequality is violated in other decays of the

B

mesons into vector mesons, but with lesser significance.

DOI: 10.48550/arxiv.2305.04982

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Bell inequality is violated in

B^0\to J/ψ\, K^{\star}(892)^0

decays

B^0\to J/ψ\,K^*(892)^0

σ

(nominally 84

σ

) and Bell inequality is violated with a significance well above 5

σ

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mesons into vector mesons, but with lesser significance.

Entanglement and Bell inequality violation in

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decays

The decays of the

B

meson into vector mesons, observed at the LHCb experiment, provide an ideal laboratory to investigate particle physics phenomena with quantum information theory methods. In this article, we focus on the decays yielding a pair of

\itΦ

mesons to investigate the presence of entanglement in the spin correlations of the system and quantify the amount of Bell inequality violation it entails. Our results show that the present LHCb data allows access to entanglement and to the Bell inequality violation with a significance exceeding the 5

σ

threshold in both the cases. This demonstrates that the strong and electroweak interactions responsible for the

B

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H\rightarrow W W^*

H → W W ∗ and

H\rightarrow Z Z^*

H → Z Z ∗ , in which

W^*

W ∗ and

Z^*

Z ∗ are off-shell states, and the WW , WZ and ZZ di-boson production in proton collisions. The polarization density matrix of the di-boson state is determined by the amplitude of the production process and can be experimentally reconstructed from the angular distribution of the momenta of the final states into which the gauge bosons decay. We show that a suitable instance of the Bell inequality is violated in

H\rightarrow Z Z^*

H → Z Z ∗ to a degree that can be tested at the LHC with future data. The same Bell inequality is violated in the production of WW and ZZ boson pairs for invariant masses above 900 GeV and scattering angles close to

\pi /2

π / 2 in the center of mass frame. LHC data in this case are not sufficient to establish the violation of the Bell inequality. We also analyze the prospects for detecting Bell inequality violations in di-boson final states at future

e^+e^-

e + e - and muon colliders. A further observable that provides a lower bound on the amount of polarization entanglement in the di-boson system is computed for each of the examined processes. The analytic expressions for the polarization density matrices are presented in full in an Appendix. We also provide the unitary matrices required in the optimization procedure necessary in testing the Bell inequalities.