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We give predictions of $\jpsi$ and $\psits$ yields and polarizations inprompt production at hadron colliders based on non-relativistic QCDfactorization formula. We calculate short-distance coefficients of allimportant color-octet intermediate channels as well as color-singlet channelsup to $\mathcal{O}(\alpha_S^4)$, i.e. next-to-leading order in $\alpha_S$. Forprompt $\jpsi$ production, we also take into account feeddown contributionsfrom $\chi_{cJ}$(J=0,1,2) and $\psits$ decays. Color-singlet long-distancematrix elements (LDMEs) are estimated by using potential model, and color-octetLDMEs are extracted by fitting the Tevatron yield data only. The predictionsare satisfactory for both yields and polarizations of prompt $\jpsi$ and prompt$\psits$ production at the Tevatron and the LHC. In particular, we find ourpredictions for polarizations of prompt $\jpsi$ production have only a littledifference from our previous predictions for polarizations of direct $\jpsi$production.

Yields and polarizations of prompt $\jpsi$ and $\psits$ production in hadronic collisions