Direct [Formula presented] and [Formula presented] polarization and cross sections at the Fermilab Tevatron

Transverse polarization of [Formula presented] charmonium states, produced directly in [Formula presented] collisions at asymptotically large transverse momentum [Formula presented] 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 [Formula presented]–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 [Formula presented] GeV, but the angular distribution is predicted to change dramatically as [Formula presented] increases to [Formula presented] GeV.