Polarization for prompt J/ψ and ψ(2s) production at the Tevatron and LHC.

With nonrelativistic QCD factorization, we present the first complete next-to-leading order study on the polarization of prompt J/ψ hadroproduction by including feeddown from χ(c)((3)P(J)(1),(3)S(1)(8)) and ψ(2s) which turn out to be very important parts. By using the color-octet long-distance matrix elements obtained from a combined fit of the measurements at the Tevatron and LHC for J/ψ, ψ(2s) and χ(c), the prompt J/ψ polarization predictions are presented, and the results are in agreement with the CDF run I data (except two points), but in conflict with the CDF run II data, while they are close to the ALICE data (inclusive J/ψ). The measurements at the LHC are expected to clarify the situation.