Complete next-to-leading order calculation of theJ/ψandψ′production at hadron colliders

A complete next-to-leading order (NLO) calculation in αs for the J/ψ and ψ ′ prompt production at the Tevatron, LHC, and RHIC in nonrelativistic QCD is presented. We argue that the nextto-next-to-leading order (NNLO) color-singlet contribution may not be so important as to resolve the large discrepancy between theory and experiment in J/ψ large pT production cross sections. Therefore, a complete NLO calculation, including both color-singlet and color-octet contribution, is necessary and essential to give a good description for J/ψ and ψ′ production. We also study the methods to fit the long-distance matrix elements using either two linear combined matrix elements or three matrix elements, and find these two methods can give consistent results. Compared with the measurements at the LHC and RHIC for prompt J/ψ and ψ′ production, our predictions are found to agree with all data. In particular, the recently released large pT data (up to 60-70 GeV) at the LHC are in good agreement with our predictions. Our results imply that the universality of coloroctet matrix elements holds approximately in charmonium hadroproduction, when one uses fixed order perturbative calculation to describe data (the data in small pT region are not included). Our work may provide a new test for the universality of color-octet matrix elements, and the color-octet mechanism in general.