In the framework based on the quasipotential method and relativistic quark model, we investigate the heavy-quark fragmentation into double-heavy baryons with spin J = 1/2, 3/2. Adopting a two-step scenario for the fragmentation, we take into account relativistic corrections to the fragmentation probabilities at both stages of the production process for the double-heavy diquark and double-heavy baryon, correspondingly. We take into account all possible relativistic corrections including the terms connected with the transformation law of the bound-state wave function to the reference frame of the moving bound state.
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