We use current-current interaction to calculate the fragmentation functions to describe the production of spin-$1/2$, spin-$1/2^{\prime }$, and spin-$3/2$ baryons with massive constituents in a relativistic quark-diquark model. Our results are in their analytic forms and are applicable for singly, doubly, and triply heavy baryons. We discuss the production of ${\Omega }_{bbc}$, ${\Omega }_{bcc}$, and ${\Omega }_{ccc}$ baryons in some detail. The results are satisfactorily compared with those obtained for triply heavy baryons calculated in a perturbative regime within reasonable values of the parameters involved.

• Received 18 August 2007

DOI:https://doi.org/10.1103/PhysRevD.76.114006