Relativistic Impulse Approximation in the Atomic Ionization Process induced by Millicharged Particles

The millicharged particle has become an attractive topic to probe physics beyond the Standard Model. In direct detection experiments, the parameter space of millicharged particles can be constrained from the atomic ionization process. In this work, we develop the relativistic impulse approximation (RIA) approach, which can duel with atomic many-body effects effectively, in the atomic ionization process induced by millicharged particles. The formulation of RIA in the atomic ionization induced by millicharged particles is derived, and the numerical calculations are obtained and compared with those from free electron approximation and equivalent photon approximation. Concretely, the atomic ionizations induced by mllicharged dark matter particles and millicharged neutrinos in high-purity germanium (HPGe) and liquid xenon (LXe) detectors are carefully studied in this work. The differential cross sections, reaction event rates in HPGe and LXe detectors, and detecting sensitivities on dark matter particle and neutrino millicharge in next-generation HPGe and LXe based experiments are estimated and calculated to give a comprehensive study. Our results suggested that the next-generation experiments would improve 2-3 orders of magnitude on dark matter particle millicharge $delta_{chi}$ than the current best experimental bounds in direct detection experiments. Furthermore, the next-generation experiments would also improve 2-3 times on neutrino millicharge $delta_{ u}$ than the current experimental bounds.