New symmetries in microphysics, new stable forms of matter around us
  Extension of particle symmetry implies new conserved charges and the lightest particles, possessing such charges, should be stable. Created in early Universe, stable charged heavy leptons and quarks can exist and, hidden in elusive atoms bound by Coulomb attraction, can play the role of dark matter. The problem of this scenario is that in the expanding Universe it is not possible to recombine all the charged particles into elusive "atoms", and positively charged particles, which escape such recombination, bind with electrons in atoms of anomalous isotopes with pregalactic abundance, generally exceeding terrestrial upper limits. Realistic scenarios of composite dark matter, avoiding this problem of anomalous isotope over-production, inevitably predict the existence of primordial "atoms", in which primordial helium traps all the free negatively charged heavy constituents with charge -2. Study of the possibility for such primordial heavy alpha-particle with compensated charge to exist as well as the search for the stable charged constituents in cosmic rays and accelerators provide crucial test for the new forms of stable matter. 
Maxim Yu. Khlopov