Masses of the ground and excited states of fully heavy tetraquarks with open charm and/or bottom are calculated on the basis of the relativistic diquark-antidiquark picture of tetraquarks. In the framework of the quasipotential approach the relativistic potential of the diquark-antidiquark interaction is constructed with the account of both spin-dependent and spin-independent contributions. It is shown, that in the considered asymmetric in composition systems, there is a significant mixing of states of tetraquarks with the same quantum numbers, but different full spins of the tetraquark. The predicted values of the masses of such tetraquarks are compared with the decay thresholds for a pair of heavy mesons. The possibility of experimental observation of such tetraquarks is discussed.
14.40.Lb Charmed mesons
14.40.Nd Bottom mesons
14.40.Rt Exotic mesons
$^2$Lomonosov Moscow state university, Physics department