Direct J/psi and psi' polarization and cross sections at the Fermilab Tevatron

Transverse polarization of S-3(1) charmonium states, produced directly in <p(p)over bar> collisions at asymptotically large transverse momentum p(t), has emerged as the most prominent test of color octet contributions and spin symmetry in quarkonium production. We present predictions for the polar angle distribution at moderate values of p(t) similar to 4-20 GeV, covered by the Fermilab Tevatron run I data. We update the fits of NRQCD matrix elements and discuss their theoretical uncertainties. With our best fit values, no transverse polarization is expected at p(t) similar to 5 GeV, but the angular distribution is predicted to change dramatically as p(t) increases to 20 GeV.