  We update the theoretical predictions for direct Y(nS) hadroproduction in the
framework of NRQCD. We show that the next-to-leading order corrections in
alpha_s to the color-singlet transition significantly raise the differential
cross section at high pT and substantially affect the polarization of the
Upsilon. Motivated by the remaining gap between the NLO yield and the cross
section measurements at the Tevatron, we evaluate the leading part of the
alpha_s^5 contributions, namely those coming from Y(nS) associated with three
light partons. The differential color-singlet cross section at alpha_s^5 is in
substantial agreement with the data, so that there is no evidence for the need
of color-octet contributions. Furthermore, we find that the polarization of the
Y(nS) is longitudinal. We also present our predictions for Y(nS) production at
the LHC.
