The Paradox of Charmonium Production

The CDF preliminary analysis on polarized charmonium production at moderate transverse momentum, $p_T\sim 4-20$ GeV, severely challenges the color octet model (COM), which predicts quarkonium to be transversely polarized with increasing $p_T$. Based on this data, we analyze the compatibility of the Tevatron and the photoproduction at HERA in the context of the COM. Due to the uncertainty on the extraction of non-relativistic QCD (NRQCD) matrix elements and a lack of complete next-to-leading order calculations, one cannot completely rule out the COM. Nonetheless, both collider experiments seem to push the input matrix elements to opposite directions, and the puzzle of quarkonium polarization remains unsolved.