Puzzles of Dark Matter in the Light of Dark Atoms

The nonbaryonic dark matter of the Universe can consist of new stable charged leptons and quarks, if they are hidden in elusive 'dark atoms' of composite dark matter. Such possibility is severely constrained, since free positively charged stable species remaining after recombination can form anomalous isotopes with electrons. This problem can be solved, if there exist stable particles with charge -2 and there are no stable particles with charges +1 and -1. These conditions can be satisfied in several recently developed alternative scenarios, linking excess of -2 particles (leptons or heavy quark clusters with suppressed hadronic interactions) to baryon asymmetry. The excessive -2 charged particles are bound with primordial helium in O-helium 'atoms', maintaining specific nuclear-interacting form of the Warmer than Cold Dark Matter. O-helium looks like Bohr-like atom with heavy -2 surrounded by extended helium shell. When nuclei approach O-helium, the nuclear attraction of the helium shell polarizes O-helium. It causes dipole Coulomb repulsion, forming a shallow well outside nucleus, in which levels of O-helium-nucleus bound states can exist. The range of parameters of nuclear interaction is found, at which the binding energy of sodium with O-helium is equal to 3 keV. Annual modulations of radiative capture of O-helium to this level in the matter of DAMA/NaI and DAMA/LIBRA detectors can explain positive results of these experiments. The puzzles of direct dark matter searches appear in this case as a reflection of nontrivial nuclear physics of O-helium.