  Nonrelativistic QCD provides a systematic approach for inclusive decays and
productions of a quarkonium. By taking color-octet components into account, the
approach can explain the $\psi'$-anomaly at Tevatron, where the measured
production rate at large transverse momentum $p_\perp$ is in order of magnitude
larger than the predicted with color-singlet components only. With the approach
one can predict that the produced $J/\psi$ and $\psi'$ at large $p_\perp$ will
be transversely polarized. But the prediction fails in confronting with
experimental measurements and this generates a puzzle. We examine the role of
spin-flip interactions in the spin density matrix of the transition of a
color-octet charm quark pair into $J/\psi$ and $\psi'$. These interactions will
introduce new nonperturbative parameters in the spin density matrix. Our result
shows that the impact of the interactions is always to dilute the polarization
and can be very significant. Taking the impact into account, predictions for
the polarization are more close to the measured than the previous predicted.
The same can also be expected for the polarization of $J/\psi$.
