The next-to-leading-order QCD correction to inclusive J/\psi(\Upsilon) production in Z^0 decay

Understand

In this paper, we study the $J/\psi(\Upsilon)$ production in Z boson decay in color-singlet model(CSM).

• We calculate the next-to-leading-order (NLO) QCD correction to $Z \to Quarkonium+Q\bar{Q}$, the dominant contribution in the CSM, with the vector and axial-vector parts in $ZQ\bar{Q}$ vertex being treated separately.
• The results show that the vector and axial-vector parts have the same K factor (the ratio of NLO result to leading-order result) 1.13 with the renormalization scale $\mu$=2$m_c$ and $m_c=1.5GeV$, and the K factor falls to 0.918 when applying the Brodsky, Lepage, and Mackenzie(BLM) renormalization scale scheme with obtained $\mu_{BLM}=2.28GeV$ 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 $Z \to J/\psi_{prompt}+X$ is $(7.3 \sim 10.0)\times 10^{-5}$ with the uncertainty consideration for the renormalization scale and Charm quark mass.