A bstract We give predictions of J/ψ and ψ (2 S ) yields and polarizations in prompt production at hadron colliders based on non-relativistic QCD factorization formula. We calculate short-distance coefficients of all important color-octet intermediate channels as well as color-singlet channels up to O α S 4 $$ mathcal{O}left({lpha}_S^4ight) $$ , i.e. next-to-leading order in α ~( S ). For prompt J/ψ production, we also take into account feeddown contributions from χ ~( cJ )(J=0,1,2) and ψ (2 S ) decays. Color-singlet long-distance matrix elements (LDMEs) are estimated by using potential model, and color-octet LDMEs are extracted by fitting the Tevatron yield data only. The predictions are satisfactory for both yields and polarizations of prompt J/ψ and prompt ψ (2 S ) production at the Tevatron and the LHC. In particular, we find our predictions for polarizations of prompt J/ψ production have only a little difference from our previous predictions for polarizations of direct J/ψ production.
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