Weak equivalence principle (WEP) is one of the cornerstones of the modern theories of gravity, stating that the trajectory of a freely falling test body is independent of its internal structure and composition. Even though WEP is known to be valid for the normal matter with a high precision, it has never been experimentally confirmed for relativistic matter and antimatter. We make an attempt to constrain possible deviations from WEP utilizing the modern accelerator technologies. We analyze the (absence of) vacuum Cherenkov radiation, photon decay, anomalous synchrotron losses and the Compton spectra to put limits on the isotropic Lorentz violation and further convert them to the constraints on the difference between the gravitational and inertial masses of the relativistic electrons/positrons. Our main result is the 0.1% limit on the mentioned difference.
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