  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. A quantitative analysis
indicates that theoretical corrections to the short-distance coefficients
change only the values of the LDMEs but not the phenomenological results.
