arXiv 1709.093202017-09hep-ph

$Z$ -玻色子衰变为矢量夸克偶素加光子

$Z$-boson decays to a vector quarkonium plus a photon

Geoffrey T. Bodwin, Hee Sok Chung, June-Haak Ee, Jungil Lee

备注：: 26 pages, [v2] references added / [v3] Equation (27) modified, 3 sentences added after Eq. (27), Reference [17] added / [v4] PRD version
发表信息：: Phys. Rev. D 97, 016009 (2018)
DOI：: 10.1103/PhysRevD.97.016009

摘要：

我们计算了过程$Z\to V+γ$的衰变率，其中$Z$是$Z$玻色子，$γ$是光子，$V$是矢量夸克偶素$J/ψ$或$Υ(nS)$之一，具有$n=1$，$2$或$3$。我们的计算包括通过相对订单$α_s$和$v^2$和重新计算的$m_Z^2/m_Q^2$，在$α_s$中的所有订单，在NLL的精度。（$v$是重夸克$Q$或重反夸克$\bar{Q}$在夸克偶素静止坐标系中的速度，$m_Z$和$m_Q$分别是$Z$和$Q$的质量。）我们的计算是第一个包括顺序$α_s$光锥分布振幅的修正和重新计算的$m_Z^2/m_Q^2$和$Υ(3S)$的最终状态的$Υ(2S)$和$Υ(3S)$。用Abel-Padé方法计算了与$α_s$阶数和$v^2$阶数相关的$m_Z^2/m_Q^2$的谱线。我们证实了分析结果的顺序$v^2$校正，在以前的出版物中提出的，我们纠正的直接和间接的幅度和一些选择的尺度在该出版物中的相对符号。我们的$Z\to J/ψ+γ$和$Z\to Υ(1S)+γ$的分支分数分别与关于该主题的最新出版物中给出的分支分数相差$2.0\,σ$和$-4.0\,σ$（以该出版物中给出的不确定度为单位）。然而，我们认为该出版物低估了利率的不确定性。

英文摘要：

We compute the decay rates for the processes $Z\to V+γ$, where $Z$ is the $Z$ boson, $γ$ is the photon, and $V$ is one of the vector quarkonia $J/ψ$ or $Υ(nS)$, with $n=1$, $2$, or $3$. Our computations include corrections through relative orders $α_s$ and $v^2$ and resummations of logarithms of $m_Z^2/m_Q^2$, to all orders in $α_s$, at NLL accuracy. ($v$ is the velocity of the heavy quark $Q$ or the heavy antiquark $\bar{Q}$ in the quarkonium rest frame, and $m_Z$ and $m_Q$ are the masses of $Z$ and $Q$, respectively.) Our calculations are the first to include both the order-$α_s$ correction to the light-cone distributions amplitude and the resummation of logarithms of $m_Z^2/m_Q^2$ and are the first calculations for the $Υ(2S)$ and $Υ(3S)$ final states. The resummations of logarithms of $m_Z^2/m_Q^2$ that are associated with the order-$α_s$ and order-$v^2$ corrections are carried out by making use of the Abel-Padé method. We confirm the analytic result for the order-$v^2$ correction that was presented in a previous publication, and we correct the relative sign of the direct and indirect amplitudes and some choices of scales in that publication. Our branching fractions for $Z\to J/ψ+γ$ and $Z\to Υ(1S)+γ$ differ by $2.0\,σ$ and $-4.0\,σ$, respectively, from the branching fractions that are given in the most recent publication on this topic (in units of the uncertainties that are given in that publication). However, we argue that the uncertainties in the rates are underestimated in that publication.

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英文摘要：

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