Entanglement-sensitive observables in $e^+e^- \to \tau^+\tau^-$ at STCF: a detector-level feasibility study

Abstract

Quantum entanglement in $\tau^+\tau^-$ production provides a direct probe of non-classical spin correlations in a relativistic quantum system, with the $\tau$ decay products serving as spin analyzers. We investigate the detector-level feasibility of such measurements in $e^+e^-\to\tau^+\tau^-$ at the Super Tau-Charm Facility (STCF) at $\sqrt{s}=7$ GeV, using the $\rho\rho$ and $\pi\rho$ decay channels. Signal and dominant background processes are simulated with the full STCF detector and reconstruction framework. Dedicated reconstruction and event-selection procedures yield overall signal efficiencies of approximately $4.5\%$ and $4.8\%$, with corresponding purities of about $87.6\%$ and $93.2\%$ for the $\rho\rho$ and $\pi\rho$ channels, respectively. From the reconstructed decay kinematics, the $\tau^+\tau^-$ spin-density matrix is inferred and the concurrence $C[\rho]$ together with the Bell-sensitive quantity $m_{12}[C]$ are evaluated in a selected fiducial region. For the benchmark requirement $|\cos\theta|<0.2$ and an integrated luminosity of $1~\mathrm{ab}^{-1}$, the projected relative precision on $C[\rho]$ is about $2.2\%$ in both channels, while that on $m_{12}[C]$ is approximately $1.4\%$ for $\rho\rho$ and $1.5\%$ for $\pi\rho$, including statistical and detector-resolution uncertainties. The reconstructed $m_{12}[C]$ shows a larger separation from its reference threshold in the $\rho\rho$ channel, making this topology particularly sensitive to Bell-type spin correlations. These results demonstrate the detector-level feasibility of probing quantum entanglement and non-classical spin correlations in hadronic $\tau$ decays at STCF.