Color-Singlet $\psi_Q$ Production at $e^+e^-$ Colliders

We calculate in closed form the complete ${\mathcal O}(\alpha_s^2)$ color-singlet differential cross section for $e^+e^- \to \gamma^* \to \psi_Q+X$ scattering. The cross section reduces at high energies to a heavy quark fragmentation form. We find that the energy scale at which the approximate fragmentation result becomes reliable exceeds the $\psi_Q$ mass by more than an order of magnitude. We also discuss the color-singlet model's predictions for direct $J/\psi$ angular and energy distributions at CLEO.