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

TL;DR

This study calculates the NLO QCD corrections to J/ψ and Υ production in Z boson decay within the color-singlet model, revealing limitations of the model and suggesting additional mechanisms like color-octet contributions are needed to match experimental data.

Contribution

It provides the first NLO QCD correction calculations for Z decay into quarkonium in the color-singlet model, including vector and axial-vector parts separately, and compares results with experimental data.

Findings

NLO K factor is approximately 1.13 with standard scale and 0.918 with BLM scale.

Predicted branching ratio is about half of the experimental value.

Color-singlet model alone cannot fully explain the observed J/ψ production in Z decay.

Abstract

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.