Gluon fragmentation to ${}^3{D}_J$ quarkonium and test of color-octet production mechanism

We report the recent progress in the studies of D-wave heavy quarkonia production from gluon fragmentation at the Tevatron and in Z^0 decays, and the D-wave charmonia production in B decays. We show that the color-octet contributions are of crucial importance to the production of D-wave quarkonia. Signals, as strong as that for J/\psi and \psi^\prime, should be seen for the D-wave charmonium in the processes. These will provide a test of the color-octet production mechanism.