Hadronic production of baryons, containing two heavy quarks

In the framework of QCD perturbation theory, total and differential cross sections of the $\Xi_{bc}'$, $\Xi_{bc}^{(*)}$ and $\Xi_{cc}^{(*)}$ baryons production in gluon collisions are calculated in the leading order over $\alpha_s$ for the doubly heavy ($b c$) and ($c c$) diquarks. At both small and large transverse momenta of the baryons, a use of the mechanism of the heavy quark fragmentation into the heavy diquark is shown to underestimate the cross section values in comparison with the exact numerical calculations of complete set of diagrams. The expected in Tevatron experiments yield of baryons with two heavy quarks is evaluated as $(1.3\pm 0.3) \cdot 10^5 \,\, bcq$-baryons and $(1.6\pm 0.3) \cdot 10^4 \,\, ccq$-baryons at $p_T>5$ GeV and $|y|<1$ of the baryon momentum and rapidity cuts, with account for the antiparticle yields.