Reconciling charmonium production and polarization data within the nonrelativistic QCD framework
A thorough study reveals that the only key parameter for $ψ$ ($J/ψ$, $ψ'$) polarization is the ratio $\langle O^ψ(^3S_1^{[8]})\rangle/\langle O^ψ(^3P_0^{[8]})\rangle$, if the velocity scaling rule holds. The fit of the yield data is incapable of the determination of this parameter. We provide a universal approach to fixing the long-distance matrix elements (LDMEs) for the $J/ψ$ and $ψ'$ production. Further, with the existing data, we implement this approach, and obtain a favorable set of the LDMEs, and manage to reconcile the charmonia production and polarization experiment. A quantitative analysis indicates that theoretical corrections to the short-distance coefficients change only the values of the LDMEs but not the phenomenological results.