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We calculate the production and polarization of direct $J/\psi$ in theimproved color evaporation model at $\mathcal{O}(\alpha_s^3)$ in the collinearfactorization approach. We present the first calculation of polarizationparameters $\lambda_\vartheta$, $\lambda_{\phi}$, and $\lambda_{\vartheta\phi}$ in the helicity and the Collins-Soper frames, as well as theframe-invariant polarization parameter $\tilde{\lambda}$ as a function oftransverse momentum. We find agreement with both $J/\psi$ cross sections andthe invariant polarization parameters at small and moderate $p_T$.

Production and polarization of direct $J/\psi$ to ${\mathcal O}(\alpha_s^3)$ in the improved color evaporation model in collinear factorization