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