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/ψ resonance is proposed. The method utilizes the differential cross-section of $$ J/\psi \to \left[\Lambda \to p{\pi}^{-}\right]\left[\Lambda \to \overline{p}{\pi}^{+}\right] $$ 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 1035 cm−2s−1. The method is discussed in the context of the weak mixing angle measurement in the same experiment.