Complete next-to-leading order calculation of the J/ψ and ψ′ production at hadron colliders

A complete next-to-leading-order calculation in alpha(s) for the J/psi and psi ' prompt production at the Tevatron, LHC, and RHIC in nonrelativistic QCD is presented. We argue that the next-to-next-to-leading-order color-singlet contribution may not be so important as to resolve the large discrepancy between theory and experiment in J/psi large p(T) production cross sections. Therefore, a complete next-to-leading-order calculation, including both color-singlet and color-octet contribution, is necessary and essential to give a good description for J/psi and psi ' 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/psi and psi ' production, our predictions are found to agree with all data. In particular, the recently released large p(T) data (up to 60-70 GeV) at the LHC are in good agreement with our predictions. Our results imply that the universality of color-octet matrix elements holds approximately in charmonium hadroproduction, when one uses fixed-order perturbative calculation to describe data (the data in small p(T) 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.