Polarization of Y(nS) at the Fermilab Tevatron

The polarization of inclusive Y(n5) at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework. We use a recent determination of the NRQCD matrix elements from fitting the CDF data on bottomonium production from run IB of the Tevatron. The result for the polarization of Y(1S) integrated over the transverse momentum bin 8<p_T<20 GeV is consistent with a recent measurement by the CDF Collaboration. The transverse polarization of Y(15) is predicted to increase steadily, for p_T greater than about 10 GeV. The Y(2S) and Y(3S) are predicted to have significantly larger transverse polarizations than Y(15).