We propose the measurement of chi (cJ) polarizations at high energy hadron
colliders to study heavy quarkonium production mechanism. We find that the
color-singlet model in the k(t) factorization approach predicts very differ
ent behavior for chi (cJ) polarizations at the Fermilab Tevatron compared w
ith the NRQCD predictions in the collinear parton model. In the color-singl
et k(t) factorization approach, for both chi (c1) and chi (c2) productions,
the helicity h = 0 states dominate over other helicity states at large p(T
). These properties are very useful in distinguishing between the two produ
ction mechanisms which are related to the interesting issue of J psi and ps
i' polarizations, and may provide a crucial test for the k(t) factorization
approach. (C) 2001 Elsevier Science B.V. All rights reserved.