  In heavy quarkonium production, the measured ratio $R_{c \bar
c}=\sigma[J/\psi+ c\bar c + X]/\sigma[J/\psi +X]$ at B factories is much larger
than existing theoretical predictions. To clarify this discrepancy, in
nonrelativistic QCD (NRQCD) we find the next-to-leading-order (NLO) QCD
correction to $e^+ e^- \to J/\psi +gg$ can enhance the cross section by about
20%. Together with the calculated NLO result for $e^+ e^- \to J/\psi +c\bar c$,
we show that the NLO corrections can significantly improve the fit to the ratio
$R_{c \bar c}$. The effects of leading logarithm resummation near the end point
on the $J/\psi$ momentum distribution and total cross section are also
considered. Comparison of the calculated cross section for $e^+ e^- \to J/\psi
+gg$ with observed cross section for $e^+ e^- \to J/\psi +non(c\bar c)$ is
expected to provide unique information on the issue of color-octet
contributions.
