Next-to-leading-order QCD correction to inclusive J/ψ(Y) production in Z0 decay

In this paper, we study the J/psi(Y) production in Z boson decay in a color-singlet model (CSM). We calculate the next-to-leading-order (NLO) QCD correction to Z -> quarkonium + Q (Q) over bar, the dominant contribution in the CSM, with the vector and axial-vector parts in the ZQ (Q) over bar vertex being treated separately. The results show that the vector and axial-vector parts have the same K factor (the ratio of the NLO result to the leading-order result) 1.13 with the renormalization scale mu = 2m(c) and m(c) 1.5 GeV, and the K factor falls to 0.918 when applying the Brodsky, Lepage, and Mackenzie (BLM) renormalization scale scheme with obtained mu(BLM) 2.28 GeV and m(c) = 1.5 GeV. By including the contributions from the next-dominant ones, the photon and gluon fragmentation processes, the branching ratio for Z -> J/psi prompt + X is (7.3-10.0) x 10(-5) with the uncertainty consideration for the renormalization scale and charm quark mass. The results are about one-half of the central value of the experimental measurement 2.1 x 10(-4). Furthermore, the J/psi energy distribution in our calculation cannot describe the experimental data. Therefore, even at QCD NLO, the contribution to Z -> J/psi(prompt) + X from the CSM cannot fully account for the experimental measurement. And there should be contributions from other mechanisms, such as the color-octet (COM) contributions. We define Rc (c) over bar = Gamma(Z-J/psi c (c) over barX)/Gamma(Z -> J/psi X) and obtain R-cc = 0.84 for only the CSM contribution and R-cc = 0.49 for COM and CSM contributions together. Then the Rcc measurement could be used to clarify the COM contributions.