Reconciling charmonium production and polarization data within the nonrelativistic QCD framework

Understand

A thorough study reveals that the only key parameter for $\psi$ ($J/\psi$, $\psi'$) polarization is the ratio $\langle O^\psi(^3S_1^{[8]})\rangle/\langle O^\psi(^3P_0^{[8]})\rangle$, 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 $J/\psi$ and $\psi'$ 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.