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 ψ ′ -anomaly at Tevatron, where the measured production rate at large transverse momentum p ⊥ is in order of magnitude larger than the predicted with color-singlet components only. With the approach one can predict that the produced J/ψ and ψ ′ at large p ⊥ 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/ψ and ψ ′ . 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/ψ. Quarkonia with their rich dynamics at different energy scales provide a special place to understand QCD. With its heavy mass m a heavy quark Q will move with a small velocity v inside a quarkonium. This results in a hierarchy of energy scales m >> mv >> mv 2 and the dynamics at different energy scales is different. A systematical separation of effects from the dynamics at different energy scales will provide a systematic understanding of quarkonium physics. Indeed, nonrelativistic QCD (NRQCD) provides such a systematic approach for inclusive decay and production [1]. In this approach a factorization can be made by expanding the small v to do the separation, a power counting in v based on the hierarchy is obtained to determine which nonperturbative effects, represented by NRQCD matrix elements, are relevant [1,2]. A comprehensive review of quarkonium physics can be found in [3]. In this approach, effects of higher-Fock components of a quarkonium state can be taken into account systematically. Although the probability to find such higher-Fock components is suppressed, but the effects of these higher-Fock states can be very significant. This has been shown in the explanation of the ψ ′ -anomaly at Tevatron, where the inclusive ψ ′production rates with large transverse momentum p ⊥ are in order of magnitude larger than the predicted if one only takes the main Fock state into account. By taking color-octet QQ components into account, the Tevatron data[4] can be explained [5]. This is regarded as a great triumph of the NRQCD approach.Despite many successes of the approach, some problems still remain unsolved. Among them a crucial one is that the approach fails to predict the polarization of J/ψ and ψ ′ at large p ⊥ measured at Tevatron. At large p ⊥ , the production of J/ψ and ψ ′ is dominant by the gluon fragmentation in which a gluon fragments into a color-octet cc pair in 3 S 1 state, the color-octet cc pair is then transmitte...