Perturbative QCD fragmentation functions for production ofP-wave charm and bottom mesons

We calculate the leading order QCD fragmentation functions for the production of P-wave charmed b mesons. Long-distance effects are factored into two nonperturbative parameters: the derivative of the radial wave function at the origin and a second parameter related to the probability for a (b¯c) heavy quark pair that is produced in a color-octet S-wave state to form a color-singlet P-wave bound state. The four 2P states and those 3P states which lie below the BD flavor threshold eventually all decay into the 1S ground state ${\mathit{B}}_{\mathit{c}}$ through hadronic cascades or by emitting photons. The total fragmentation probabilities for production of the 1S ground state ${\mathit{B}}_{\mathit{c}}$ from the cascades of the 2P and 3P states are about 1.7×${10}^{\mathrm{-}4}$ and 2.3×${10}^{\mathrm{-}4}$, respectively. Thus the direct production of the P-wave states via fragmentation may account for a significant fraction of the inclusive production rate of the ${\mathit{B}}_{\mathit{c}}$ at large transverse momentum in high energy colliders. Our analytic results for the P-wave fragmentation functions disagree with those obtained earlier in the literature. Our results also cover the P-wave heavy quarkonium case in the equal mass limit.