Measurement of the weak mixing angle at a Super Charm-Tau factory with data-driven monitoring of the average electron beam polarization

A method for measuring the average longitudinal polarization of the electron beam at an electron-positron collider operating near the $J/\psi$ resonance is proposed. The method utilizes the differential cross-section of $J/\psi\to [\Lambda\to p\pi^-][\bar{\Lambda}\to\bar{p}\pi^+]$ decay. It can be used to measure the average longitudinal polarization of electrons with the statistical precision better than $10^{-3}$ at a Super Charm-Tau factory operating at the luminosity of $10^{35}~\mathrm{cm}{}^{-2}\mathrm{s}{}^{-1}$. The method is discussed in the context of the weak mixing angle measurement in the same experiment.