$J/\psi$ and $\Upsilon$ Polarization in Hadronic Production Processes

Both charm and bottom quarks form nonrelativistic bound states analogous to positronium. The J/psi and psi(2S) charmonium states and the first three Upsilon(nS) bottomonium states, all spin-triplet S-wave quarkonium states below open heavy-flavor thresholds, have relatively large branching ratios to e(-)e(+) or mu(-)mu(+) pairs. In hadron collisions, experiments measuring lepton pairs can determine polarization by using angular correlation techniques. The polarization, in turn, can be related theoretically to the production mechanism for the bound state. This review summarizes experimental studies with proton beams at fixed-target and colliding-beam accelerators, covering a center-of-mass energy range from 39 to 7,000 GeV for nucleon and antiproton targets. Analyses using various polarization frames and spin-quantization axes are described and results compared. A pattern emerges that connects experimental results over the whole energy span. The theoretical implications of the pattern are presented, and a set of new measurements is proposed.