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.
Categories: hep-ph