Polarized J/psi production at CLEO

Polarizations of the prompt $J/\psi$'s produced in the $e^+e^-$ annihilation at CLEO energy ($\sqrt{s} = 10.58$ GeV) are considered in the framework of NRQCD factorization formalism. We find that the $J/\psi$ polarization has strong dependence on the production mechanism. At CLEO energy, the most dominant $J/\psi$ production mechanism in the most phase space is the color-singlet mechanism, $e^+e^- \to J/\psi+gg$, for which $J/\psi$'s are highly longitudinally polarized. On the other hand, the dominant $J/\psi$ production mechanism at the upper end point of $J/\psi$ energy distribution is the color-octet process, $e^+e^- \to (c\bar{c})^{(8)} +g$, for which $J/\psi$'s are almost unpolarized. Thus, the measurement of the polarization of the end point $J/\psi$'s can give another test of color-octet mechanism, and constraint on the NRQCD matrix elements.