ψ′ polarization as a test of colour octet quarkonium production

We calculate the α_s corrections to the transverse polarization fraction of ψ′'s produced at the Tevatron. If the 'ψ′-anomaly' is explained by gluon fragmentation into a colour octet Fock component of the ψ′, the ψ′'s should be 100% transversely polarized at leading order in α_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_T, where a potential loss of polarization due to non-fragmentation processes is avoided.