Probing entanglement and testing Bell inequality violation with ${\text{e}}^{+}{\text{e}}^{-}\to {\tau }^{+}{\tau }^{-}$ at Belle II

Abstract

We present a feasibility study to probe quantum entanglement and Belle inequality violation in the process ${\text{e}}^{+}{\text{e}}^{-}\to {\tau }^{+}{\tau }^{-}$ 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 ${\tau }^{+}{\tau }^{-}$ center-of-mass frame. We analyze events in which both $\tau$ leptons decay to hadrons, using a combination of decay channels ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$, ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$, and ${\tau }^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$. The spin orientation of the $\tau$ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of $200$ million ${\tau }^{+}{\tau }^{-}$ 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.

Comments: 24 pages, 4 figures