Triply Heavy Baryons

The triply heavy baryons are very different in their mass. They are essentially $\Omega_{ccc}$, $\Omega_{ccb}$, $\Omega_{cbb}$ and $\Omega_{bbb}$ baryons which may be produced in a $c$ or a $b$ quark fragmentation. Here we briefly review the direct fragmentation production of these states and choose $\Omega_{ccc}$ and $\Omega_{bbb}$ baryons as prototype of them to consider their production at the hadron colliders with different $\sqrt{s}$. It becomes clear that their production cross sections fall within a rather diverse range according to $\sqrt{s}$, minimum transverse momentum and rapidity. We present and compare transverse momentum distributions of the differential cross sections, $p_T^{\rm min}$ distributions of total cross sections and the integrated total cross sections for all triply heavy baryons at CERN LHC and simlar quantities for $\Omega_{ccc}$ and $\Omega_{bbb}$ at RHIC, Tevatron Run II and the CERN LHC. While some of them possess considerable event rates even at RHIC proton-proton collider, others need much more energetic hadron collider with appropriate kinematical cuts to be produced