Optimal spin-quantization axes for quarkonium with large transverse momentum

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.