arXiv 1007.23682010-07-14hep-ph

Z^0衰变中包含J/ψ（ψ）产生的次首阶QCD修正

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

Rong Li, Jian-Xiong Wang

备注：: 8 pages, 8 figures
发表信息：: Phys.Rev.D82:054006,2010
DOI：: 10.1103/PhysRevD.82.054006

摘要：

本文在色单重态模型（CSM）下研究了Z玻色子衰变过程中$J/ψ(Υ)$的产生。我们计算了对CSM中主要贡献的$Z \to Quarkonium+Q\bar{Q}$的次首阶（NLO）QCD修正，其中$ZQ\bar{Q}$顶点的矢量和轴矢量部分被分开处理。结果表明，当重整化标度$μ$ =2 $μ_{BLM}=2.28GeV$和$m_c=1.5GeV$时，矢量和轴向矢量部分的K因子（NLO结果与首阶结果的比值）均为1.13，当采用Brodsky，Lepage，and Mackenzie（BLM）重整化标度方案时，K因子降为0.918.考虑到重整化标度和Charm夸克质量的不确定性，考虑次主导过程、光子和胶子碎裂过程的贡献，得到了$Z \to J/ψ_{prompt}+X$的分支比为$(7.3 \sim 10.0)\times 10^{-5}$.结果约为实验测量值2.1 $\times10^{-4}$的中心值的一半。此外，在我们的计算$J/ψ$的能量分布是不符合实验数据。因此，即使在QCD非线性光学下，CSM对$Z \to J/ψ_{prompt}+X$的贡献也不能完全解释实验测量。应该有来自其他机制的贡献，例如颜色八位组（COM）的贡献。我们定义了$R_{c\bar{c}}=\frac{Γ(Z \to J/ψc\bar{c}X)}{Γ(Z \to J/ψX)}$，并获得了$R_{cc}=0.84$的CSM贡献和$R_{cc}=0.49$ COM和CSM的贡献。然后，$R_{cc}$测量可以用来澄清COM的贡献。

英文摘要：

In this paper, we study the $J/ψ(Υ)$ 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 $μ$=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 $μ_{BLM}=2.28GeV$ 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 $Z \to J/ψ_{prompt}+X$ 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 $J/ψ$ energy distribution in our calculation is not well consistent with the experimental data. Therefore, even at QCD NLO, the contribution to $Z \to J/ψ_{prompt}+X$ 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 $R_{c\bar{c}}=\frac{Γ(Z \to J/ψc\bar{c}X)}{Γ(Z \to J/ψX)}$ 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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