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

We give predictions of $\jpsi$ and $\psits$ 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 $\mathcal{O}(\alpha_S^4)$, i.e. next-to-leading order in $\alpha_S$. For prompt $\jpsi$ production, we also take into account feeddown contributions from $\chi_{cJ}$(J=0,1,2) and $\psits$ 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 $\jpsi$ and prompt $\psits$ production at the Tevatron and the LHC. In particular, we find our predictions for polarizations of prompt $\jpsi$ production have only a little difference from our previous predictions for polarizations of direct $\jpsi$ production.