Fragmentation production of triply heavy baryons at the CERN LHC

The triply heavy baryons in the standard model formed in direct c and b quark fragmentation are the {omega}{sub ccc}, {omega}{sub ccb}, {omega}{sub cbb} and {omega}{sub bbb} baryons. We calculate their fragmentation functions in leading order of perturbative QCD. The universal fragmentation probabilities fall within the range of 10{sup -5}-10{sup -7}.We also evaluate their cross section at the LHC ({radical}(s)=14 TeV) using next-to-leading order matrix elements for heavy quark-antiquark pair production. We present the differential cross sections as functions of the transverse momentum as well as the total cross sections. They range from a few nb to a few pb.