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

Abstract

We calculate the process-independent fragmentation functions for a $\bar{b}$ antiquark to fragment into longitudinally and transversely polarized $B_c^{\ast }$ (${}^3{S}_1$) 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 $b\to {\rm Y}$. 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 $D^{\ast }$ and $B^{\ast }$. The spin asymmetry parameter, $\alpha (z)$, is consistent with the existing CLEO data for $D^{\ast }$. 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 $D^{\ast }$ and $B^{\ast }$ 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.

Comments: 32 pages, 8 figures (not included but will send upon request), standard LaTeX file, Report # NUHEP-TH-94-7 and UCD-94-4