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A thorough study reveals that the only key parameter for $\psi$ ($J/\psi$,$\psi'$) polarization is the ratio $\langle O^\psi(^3S_1^{[8]})\rangle/\langleO^\psi(^3P_0^{[8]})\rangle$, if the velocity scaling rule holds. The fit of theyield data is incapable of the determination of this parameter. We provide auniversal approach to fixing the long-distance matrix elements (LDMEs) for the$J/\psi$ and $\psi'$ production. Further, with the existing data, we implementthis approach, and obtain a favorable set of the LDMEs, and manage to reconcilethe charmonia production and polarization experiment. A quantitative analysisindicates that theoretical corrections to the short-distance coefficientschange only the values of the LDMEs but not the phenomenological results.

Reconciling charmonium production and polarization data within the nonrelativistic QCD framework