  We calculate the production and polarization of direct $J/\psi$ in the
improved color evaporation model at $\mathcal{O}(\alpha_s^3)$ in the collinear
factorization approach. We present the first calculation of polarization
parameters $\lambda_\vartheta$, $\lambda_{\phi}$, $\lambda_{\vartheta \phi}$ in
the helicity and the Collins-Soper frames, as well as the frame-invariant
polarization parameter $\tilde{\lambda}$ as a function of transverse momentum.
We find agreement with both $J/\psi$ cross sections and polarization
measurements.
