The self-polarization of relativistic electrons or positrons moving in a magnetic field at a storage ring occurs through the emission of spin-flip synchrotron radiation, known as the Sokolov-Ternov effect. The resulting transverse polarizations of the colliding electrons and positrons, away from the depolarization resonances, allow for precise investigation of the spin entangled hyperon-antihyperon pairs via virtual photon or charmonium decay. The feasibility study reveals a promising increase in the statistical sensitivity of the CP violation signal after considering the transverse polarizations of the lepton beams. Published by the American Physical Society 2024