Heavy Quark Fragmentation Functions for D-wave Quarkonium and Charmed Beauty Mesons

At the large transverse momentum region, the production of heavy-heavy bound-states such as charmonium, bottomonium, and $\bar bc$ mesons in high energy $e^+e^-$ and hadronic collisions is dominated by parton fragmentation. We calculate the heavy quark fragmentation functions into the D-wave quarkonium and $\bar bc$ mesons to leading order in the strong coupling constant and in the non-relativistic expansion. In the $\bar b c$ meson case, one set of its D-wave states is expected to lie below the open flavor threshold. The total fragmentation 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\% of the total pseudo-scalar ground state $B_c$ comes from the cascades of these orbitally excited states.