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 $\bar b$ antiquark to fragment into longitudinally and transversely polarized $B_c^*$ ($^3S_1$) 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 $c\to \psi$ and $b\to\Upsilon$. 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 $m_b \to \infty$ 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, $\alpha(z)$, is consistent with the existing CLEO data for $D^*$. The scaling behavior of $\langle z \rangle$ is studied in detail. We find excellent agreement between the predictions of $\langle z \rangle$ 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 $p_\perp$ of the vector mesons relative to the fragmentation axis.