  The gluon collision process that creates a heavy-quark-antiquark pair with
small relative momentum and large transverse momentum predicts at leading-order
in the QCD coupling constant that the transverse polarization of the pair
should increase with its transverse momentum. Measurements at the Fermilab
Tevatron of the polarization of charmonium and bottomonium states with respect
to a particular spin-quantization axis are inconsistent with this prediction.
However the predicted rate of approach to complete transverse polarization
depends on the choice of spin-quantization axis. We introduce axes that
maximize and minimize the transverse polarization from the leading-order gluon
collision process. They are determined by the direction of the jet that
provides most of the balancing transverse momentum.
