The polarization of inclusive ${\rm Y}\mathrm{}\left(\mathrm{nS}\right)\mathrm{}$ 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 ${\rm Y}\mathrm{}\left(1S\right)\mathrm{}$ integrated over the transverse momentum bin $8<\mathrm{}{p}_T<20\mathrm{}$ GeV is consistent with a recent measurement by the CDF Collaboration. The transverse polarization of ${\rm Y}\mathrm{}\left(1S\right)\mathrm{}$ is predicted to increase steadily for $p_T$ greater than about 10 GeV. The ${\rm Y}\mathrm{}\left(2S\right)\mathrm{}$ and ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}$ are predicted to have significantly larger transverse polarizations than ${\rm Y}\mathrm{}\left(1S\right).$

• Received 18 December 2000

DOI:https://doi.org/10.1103/PhysRevD.63.071501