ar X iv : h ep - p h / 03 05 07 9 v 2 2 6 M ay 2 00 3

We study inclusive production of doubly heavy baryon at a e + e − collider and at hadron colliders through fragmentation. We study the production by factorizing nonpertubative-and perturbative effects. In our approach the production can be thought as a two-step process: A pair of heavy quarks can be produced perturbatively and then the pair is transformed into the baryon. The transformation is nonperturbative. Since a heavy quark moves with a small velocity in the baryon in its rest frame, we can use NRQCD to describe the transformation and perform a systematic expansion in the small velocity. At the leading order we find that the baryon can be formed from two states of the heavy-quark pair, one state is with the pair in 3 S 1 state and in color ¯ 3, another is with the pair in 1 S 0 state and in color 6. Two matrix elements are defined for the transformation from the two states, their perturbative coefficients in the contribution to the cross-section at a e + e − collider and to the function of heavy quark fragmentation are calculated. Our approach is different than previous approaches where only the pair in 3 S 1 state and in color ¯ 3 is taken into account. Numerical results for e + e − colliders at the two B-factories and for hadronic colliders LHC and Tevatron are given.