Next-to-leading-order tests of nonrelativistic-QCD factorization with $J/ψ$ yield and polarization

We report on recent progress in testing the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD) at next-to-leading order (NLO) for $J/\psi$ yield and polarization. We demonstrate that it is possible to unambiguously determine the leading color-octet long-distance matrix elements (LDMEs) in compliance with the velocity scaling rules through a global fit to experimental data of unpolarized $J/\psi$ production in $pp$, $p\bar{p}$, $ep$, $\gamma\gamma$, and $e^+e^-$ collisions.Three data sets not included in the fit, from hadroproduction and from photoproduction in the fixed-target and colliding-beam modes, are nicely reproduced. The polarization observables measured in different frames at DESY HERA and CERN LHC reasonably agree with NLO NRQCD predictions obtained using the LDMEs extracted from the global fit, while measurements from the FNAL Tevatron exhibit severe disagreement. We demonstrate that alternative LDME sets recently obtained in two other NLO NRQCD analyses of $J/\psi$ yield and polarization, with different philosophies, also fail to reconcile the Tevatron polarization data with the other available world data.