QCD fragmentation functions forBcandBc*production

The dominant production mechanism for $\overline{b}c$ bound states with a large transverse momentum in high energy processes is the production of a high energy $\overline{b}$ antiquark, followed by its fragmentation into the $\overline{b}c$ state. We calculate the fragmentation functions for the production of the $S$-wave states $B_c$ and $B_c^{*}$ to leading order in the QCD coupling constant. The fragmentation probabilities for $\overline{b}\to B_c$ and $\overline{b}\to B_c^{*}$ are approximately 3.8 × ${10}^{-4\mathrm{}}$ and 5.4 × ${10}^{-4\mathrm{}}$, while those for $c\to B_c$ and $c\to B_c^{*}$ are smaller by two orders of magnitude.