Search for the Electric Dipole Moment of the Tau Lepton at the Super Tau-Charm Facility

Abstract: This study investigates the intrinsic electric dipole moment (EDM) of the $\tau$ lepton, an important quantity in the search for physics beyond the Standard Model (BSM). In preparation for future measurements at the Super Tau-Charm Facility (STCF), we employ Monte Carlo simulations of the $e^+e^- \rightarrow \tau^+\tau^-$ process and optimize the analysis methodology for EDM extraction. Machine learning techniques are implemented to efficiently identify signal photons and events, resulting in a significant improvement in signal-to-noise ratio. Our optimized event selection algorithm achieves $80.0\%$ signal purity with $6.3\%$ efficiency. We develop an analytical approach for $\tau$ lepton momentum reconstruction and derive the squared spin density matrix along with optimal observables. The relationship between these observables and the EDM is established, with the estimated sensitivity of $|d_\tau| < 3.89\times 10^{-18}\,e\cdot\mathrm{cm}$. These results provide a foundation for future experimental measurements of the $\tau$ lepton EDM in STCF experiments.