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arXiv:1302.6438 · Progress of Theoretical and Experimental Physics

Testing Bell's inequality using charmonium decays

S. Chen, Y. Nakaguchi, S. Komamiya

Published Jun 1, 2013• 18 citations
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Abstract

This paper discusses the feasibility of testing Bell's inequality with the charmonium decays |$\eta _{\mathrm {c}} \rightarrow \Lambda \overline {\Lambda }$|⁠, |$\chi _{{\mathrm {c}}0} \rightarrow \Lambda \overline {\Lambda }$| and |${\mathrm {J}}/\psi \rightarrow \Lambda \overline {\Lambda }$|⁠. We develop a new formulation of Bell's inequality represented with particles’ orientations, which can be measured straightforwardly in experiment, and seek to ascertain if it is violated in these decay processes. It is shown that the ηc channel and the |$\chi _{c0}$| channel maximally violate Bell's inequality, while the |${\mathrm {J}}/\psi $| channel gives no inconsistency with it. Simulations dealing with experimental aspects are also implemented. The expected statistical fluctuations and achievable significance are estimated as a function of sample size.

DOI
10.1093/ptep/ptt032

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Probing entanglement and testing Bell inequality violation with e+e−→τ+τ−\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}e+e−→τ+τ− at Belle II
We present a feasibility study to probe quantum entanglement and Belle inequality violation in the process e+e−→τ+τ−\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}e+e−→τ+τ− at a center-of-mass energy of s=10.579\sqrt{s} = 10.579s​=10.579 GeV. The sensitivity of the analysis is enhanced by applying a selection on the scattering angle ϑ\varthetaϑ in the τ+τ−τ^{+}τ^{-}τ+τ− center-of-mass frame. We analyze events in which both τττ leptons decay to hadrons, using a combination of decay channels τ−→π−νττ^{-} \rightarrow π^{-}ν_ττ−→π−ντ​, τ−→π−π0νττ^{-} \rightarrow π^{-}π^{0}ν_ττ−→π−π0ντ​, and τ−→π−π+π−νττ^{-} \rightarrow π^{-}π^{+}π^{-}ν_ττ−→π−π+π−ντ​. The spin orientation of the τττ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of 200200200 million τ+τ−τ^{+}τ^{-}τ+τ− events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations.
Higgs boson decays produce pairs of W bosons in a maximally entangled state, the spins of which can be expected to violate Bell inequalities. We show that the spin density matrix of the W± pair may be reconstructed experimentally from the directions of the charged lepton decay products, and from it the expectation values of various Bell operators determined. Numerical simulations of H→WW⁎ decays indicate that violation of a generalised CHSH inequality is unlikely to be measurable, however the CGLMP inequality is near-maximally violated. Experimental Bell tests could be performed at a variety of colliders and in different production channels. If reconstruction effects and backgrounds can be controlled then statistically significant violations could be observable even with datasets comparable to those already collected at the LHC.
We present a feasibility study to probe quantum entanglement and Bell inequality violation in the process e+e−→τ+τ− at a center-of-mass energy of s=10.579 GeV . The sensitivity of the analysis is enhanced by applying a selection on the scattering angle ϑ in the τ+τ− center-of-mass frame. We analyze events in which both τ leptons decay to hadrons, using a combination of decay channels τ−→π−ντ , τ−→π−π0ντ , and τ−→π−π+π−ντ . The spin orientation of the τ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of 200 million τ+τ− events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations. Published by the American Physical Society 2024