Dark atom solution for puzzles of direct dark matter searches

The puzzles of direct dark matter searches can find solution in the model of dark atoms, called O-helium, containing stable -2 charged lepton-like heavy particle O ⁻⁻ bound by ordinary Coulomb interaction with primordial helium 4 nuclei. Specific properties of this nuclear interacting dark matter can explain positive results of DAMA/NaI and DAMA/LIBRA experiments and negative results in cryogenic and heavy nuclei (like xenon) detectors. Astrophysical and collider probes for dark atom models as well as open questions of O-helium nuclear interaction with matter are discussed. (paper)