The existence of cosmological dark matter is in the bedrock of the modern cosmology. The dark matter is assumed to be nonbaryonic and to consist of new stable particles. However if composite dark matter contains stable electrically charged leptons and quarks bound by ordinary Coulomb interaction in elusive dark atoms, these charged constituents of dark atoms can be the subject of direct experimental test at the colliders. In such models the excessive negatively double charged particles are bound with primordial helium in O-helium atoms, maintaining specific nuclear-interacting form of the dark matter. The successful development of composite dark matter scenarios appeals to experimental search for doubly charged constituents of dark atoms, making experimental search for exotic stable double charged particles experimentum crucis for dark atoms of composite dark matter. (abridged)
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