The next-to-leading-order QCD correction to inclusive J/ψ(Υ) production in Z^0 decay

Details The next-to-leading-order QCD correction to inclusive J/ψ(Υ) production in Z^0 decay The next-to-leading-order QCD correction to inclusive J/ψ(Υ) production in Z^0 decay

2010-07-14

arxiv.org/abs/1007.2368v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

8 pages, 8 figures

Scientific paper

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. The results are about half of the central value of the experimental measurement 2.1$\times10^{-4}$. Furthermore, the $J/\psi$ energy distribution in our calculation is not well consistent with the experimental data. Therefore, even at QCD NLO, the contribution to $Z \to J/\psi_{prompt}+X$ from the CSM can not fully account for the experimental measurement. And there should be contributions from other mechanisms, such as the color-octet(COM) contributions. We define $R_{c\bar{c}}=\frac{\Gamma(Z \to J/\psi c\bar{c}X)}{\Gamma(Z \to J/\psi X)}$ and obtain $R_{cc}=0.84$ for only CSM contribution and $R_{cc}=0.49$ for COM and CSM contributions together. Then $R_{cc}$ measurement could be used to clarify the COM contributions.

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