psi' Polarization as a test of colour octet quarkonium production

We calculate the alpha(s) corrections to the transverse polarization fraction of Psi''s produced at the Tevatron. If the Psi'-anomaly' is explained by gluon fragmentation into a colour octet Fock component of the Psi', the Psi''s should be 100% transversely polarized at leading order in alpha(s) up to spin symmetry breaking long-distance corrections. We find that the short-distance correction (due to gluon fragmentation) to the transverse polarization fraction is a few percent. A polarization measurement would thus provide a reliable test of the colour octet mechanism, particularly at large p tau where a potential loss of polarization due to non-fragmentation processes is avoided.