We present a calculation of the leading order QCD fragmentation functions for gluons to split into spin-triplet $D$-wave quarkonia. We apply them to evaluate the gluon fragmentation contributions to inclusive ${}^3{D}_J$ quarkonium production at large transverse momentum processes such as the Fermilab Tevatron and find that the $D$-wave quarkonia, especially the charmonium $2^{--}$ state, could be observed through the color-octet mechanism with present luminosity. Since there are distinctively large gaps between the contributions of two different (i.e., color-singlet and color-octet) quarkonium production mechanisms, our results may stand as a unique test of the NRQCD color-octet quarkonium production mechanism.

• Received 30 December 1996

DOI:https://doi.org/10.1103/PhysRevD.55.5437