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At the large transverse momentum region, the production of heavy-heavybound-states such as charmonium, bottomonium, and $\bar bc$ mesons in highenergy $e^+e^-$ and hadronic collisions is dominated by parton fragmentation.We calculate the heavy quark fragmentation functions into the D-wave quarkoniumand $\bar bc$ mesons to leading order in the strong coupling constant and inthe non-relativistic expansion. In the $\bar b c$ meson case, one set of itsD-wave states is expected to lie below the open flavor threshold. The totalfragmentation probability for a $\bar b$ antiquark to split into the D-wave$\bar b c$ mesons is about $2 \times 10^{-5}$, which implies that only 2\% ofthe total pseudo-scalar ground state $B_c$ comes from the cascades of theseorbitally excited states.

Heavy quark fragmentation functions forD-wave quarkonium and charmedb-flavored mesons