Crucial test for the color-octet production mechanism inZ0decays

The direct production rates of $D$-wave charmonia in the decays of $Z^0$ are evaluated. The color-octet production processes $Z^0{\to }^3{D}_J\left(c\overline{c}\right)q\mathrm{q¯}$ are shown to have distinctively large branching ratios as compared with other $D$-wave charmonium production mechanisms under a proper assumption. This may suggest a crucial channel to test the color-octet mechanism as well as to observe the $D$-wave charmonium states in $Z^0$ decays. In addition, a signal for the ${}^3{D}_J$ charmonium states with a large transverse momentum at the Fermilab Tevatron should be observed.