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Semileptonic decays of doubly heavy baryons are studied in the framework ofthe relativistic quark model. The doubly heavy baryons are treated in thequark-diquark approximation. The transition amplitudes of heavy diquarks bb andbc going respectively to bc and cc are explicitly expressed through the overlapintegrals of the diquark wave functions in the whole accessible kinematicrange. The relativistic baryon wave functions of the quark-diquark bound systemare used for the calculation of the transition matrix elements, the Isgur-Wisefunction and decay rates in the heavy quark limit.Comment: 20 pages, 5 figure

Semileptonic decays of doubly heavy baryons in the relativistic quark model