We study inclusive heavy quarkonium production with definite polarizations in polarized proton-proton collisions using the non-relativistic QCD color-octet mechanism. We present results for rapidity distributions of cross sections and spin asymmetries for the production of J/psi and psi with specific polarizations in polarized p-p collisions at sqrt s = 200 GeV and 500 GeV at the RHIC within the PHENIX detector acceptance range.
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