Gravitational mass of relativistic matter and antimatter

Abstract: The universality of free fall, the weak equivalence principle (WEP), is a cornerstone of the general theory of relativity, the most precise theory of gravity confirmed in all experiments up to date. The WEP states the equivalence of the inertial, $m$, and gravitational, $m_g$, masses and was tested in numerous occasions with normal matter at relatively low energies. However, there is no proof for the matter and antimatter at high energies. For the antimatter the situation is even less clear -- current direct observations of trapped antihydrogen suggest the limits $-65 < m_g / m < 110$ not excluding the so-called antigravity phenomenon, i.e. repulsion of the antimatter by Earth. Here we demonstrate an indirect bound $0.96 < m_g/m < 1.04$ on the gravitational mass of relativistic electrons and positrons coming from the absence of the vacuum Cherenkov radiation at the Large Electron-Positron Collider (LEP) and stability of photons at the Tevatron collider in presence of the annual variations of the solar gravitational potential. Our result clearly rules out the speculated antigravity. By considering the absolute potential of the Local Supercluster (LS), we also predict the bounds $1 - 4\times 10^{-7} < m_g/m < 1 + 2\times 10^{-7}$ for an electron and positron. Finally, we comment on a possibility of performing complementary tests at the future International Linear Collider (ILC) and Compact Linear Collider (CLIC).