Spin Alignment in the Production of Vector Mesons with Charm and/or Beauty via Heavy Quark Fragmentation

We calculate the process-independent fragmentation functions for a b̄ antiquark to fragment into longitudinally and transversely polarized B c ( S1) mesons to leading order in the QCD strong coupling constant. In the special case of equal quark mass we recover previous results for the fragmentation of c → ψ and b → Υ. Various spin asymmetry parameters are defined as measures of the relative population of the longitudinally and transversely polarized vector meson states. In the heavy quark mass limit mb → ∞ our polarized fragmentation functions obey heavy quark spin symmetry, we therefore apply them as a model to describe the fragmentation of charm and bottom into heavy-light mesons like D and B. The spin asymmetry parameter, α(z), is consistent with the existing CLEO data for D. The scaling behavior of 〈z〉 is studied in detail. We find excellent agreement between the predictions of 〈z〉 from our fragmentation functions and the experimental data for D and B from the LEP, CLEO, and ARGUS detectors. Finally, we also point out that the spin asymmetry depends significantly on the transverse momentum p⊥ of the vector mesons relative to the fragmentation axis.