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arXiv:2311.17555

Probing entanglement and testing Bell inequality violation with $\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}$ at Belle II

K. Ehatäht, Marco E. Fabbrichesi, Luca Marzola, C. Veelken

Published Nov 29, 2023• 0 citations
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Abstract

We present a feasibility study to probe quantum entanglement and Belle inequality violation in the process $\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}$ at a center-of-mass energy of $\sqrt{s} = 10.579$ GeV. The sensitivity of the analysis is enhanced by applying a selection on the scattering angle $\vartheta$ 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 $τ^{-} \rightarrow π^{-}ν_τ$, $τ^{-} \rightarrow π^{-}π^{0}ν_τ$, and $τ^{-} \rightarrow π^{-}π^{+}π^{-}ν_τ$. 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.

DOI
10.48550/arxiv.2311.17555

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A bstract Quantum entanglement is a fundamental property of quantum mechanics. Recently, studies have explored entanglement in the tt‾ t\overline{t} tt t t ¯ system at the Large Hadron Collider (LHC) when both the top quark and anti-top quark decay leptonically. Entanglement is detected via correlations between the polarizations of the top and anti-top and these polarizations are measured through the angles of the decay products of the top and anti-top. In this work, we propose searching for evidence of quantum entanglement in the semi-leptonic decay channel where the final state includes one lepton, one neutrino, two b -flavor tagged jets, and two light jets from the W decay. We find that this channel is both easier to reconstruct and has a larger effective quantity of data than the fully leptonic channel. As a result, the semi-leptonic channel is 60% more sensitive to quantum entanglement and a factor of 3 more sensitive to Bell inequality violation, compared to the leptonic channel. In 139 fb − 1 (3 ab −1 ) of data at the LHC (HL-LHC), it should be feasible to measure entanglement at a precision of ≲ 3% (0 . 7%). Detecting Bell inequality violation, on the other hand, is more challenging. With 300 fb −1 (3 ab −1 ) of integrated luminosity at the LHC Run-3 (HL-LHC), we expect a sensitivity of 1 . 3 σ (4 . 1 σ ). In our study, we utilize a realistic parametric fitting procedure to optimally recover the true angular distributions from detector effects. Compared to unfolding this procedure yields more stable results.
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