Measurement of the Michel Parameter ${\xi^{\prime}}$ in Tau-Lepton Decays at the Super Charm-Tau Factory

Abstract

In this paper, we present a feasibility study of the first measurement of the longitudinal polarization of a muon from the $\tau$-lepton decay to extract the Michel parameter $\xi^{\prime}$ at the future Super Charm-Tau Factory (SCTF). The expected number of $\mu^{-}\to e^{-}\nu_{\mu}\bar{\nu}_{e}$ events on the full SCTF data was estimated, possible background processes were studied, and methods of their suppression were suggested. Statistical accuracy was estimated to be $\sigma_{\xi^{\prime}}\approx 0.02$, which enables a new verification of the Standard Model at high precision level.