On recent puzzles in the production of heavy quarkonia

Recently, several surprising experimental observations in the production of heavy quarkonium have been reported. In $e^+e^-$ annihilation at $\sqrt{s}=10.6$ GeV, Belle Collaboration finds that $J/\psi$ mesons are predominantly produced in association with an extra $\bar{c}c$ pair, with $\sigma(e^+e^- \to J/\psi \bar{c}c) / \sigma(e^+e^- \to J/\psi X) = 0.59^{+0.15}_{-0.13}\pm 0.12$, and the BaBar collaboration reports that the produced $J/\psi$'s have mostly longitudinal polarization. In $\bar{p}p$ collisions at the Tevatron, the CDF Collaboration reported an excess of $J/\psi$ and $\psi^{\prime}$ mesons at high $p_{\perp}$ over the perturbative QCD predictions; non--perturbative approach of NRQCD can accomodate the magnitude of the production cross section but not the observed experimentally polarization of quarkonia. In this note we propose possible solutions to these puzzles, and devise further experimental tests.