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Polarization for Prompt J/psi, psi(2s) production at the Tevatron and LHC

Based on nonrelativistic QCD, we present the first complete next-to-leading order study on the polarization of prompt J/psi hadroproduction by including feeddown from chi_c(^3P_J^1,^3S_1^8) and psi(2s) which turn out to be a very important part. By using the color-octet long-distance matrix elements obtained from a combined fit of the differential cross section measurements at the Tevatron and LHC for J/psi, psi(2s) and chi_c with p_t>7GeV, the prompt J/psi polarization predictions are presented, and the results are in agree with the CDF Run-I data (except two points), but in conflict with the CDF Run-II data, while are close to the ALICE data (inclusive J/psi) at LHC. The experimental measurements at the LHC are strongly expected to clarify the situation.