论文标题
生产双重Quarkonium通过$ e^ +e^ - \至γ^*/z^0 \ to |（q \ bar {q'}）[n] \ rangle +|（q'\ bar {q}）
Production double heavy quarkonium via $e^+e^-\to γ^*/Z^0 \to|(Q\bar{Q'})[n]\rangle +|(Q'\bar{Q})[n']\rangle$ at Z mass pole
论文作者
论文摘要
全面研究了双重兴奋的Quarkonium的独家生产，即通过$ E^ +e^ +e^ - \toγ^*/z^0 \ to |（q \ bar {q'}）[q'} [n] \ rangle +| （$ q/q'= c $ - 或$ b $ - quarks）在未来的$ z $工厂下，在非依赖性量子性铬动力学框架下，其中$ [n] $〜/$ [n''$代表着色quarkonium theelelet heavy quarkonium state $ [^1s_0] \ rangle，〜rangle， $ [^3p_j] \ rangle $（$ j = 0,1,2 $）。采用“改进的痕量技术”来计算复杂的$ p $波频道，以在振幅级别得出分析表达式。根据我们的研究，在未来的$ z $工厂中，双重重夸金的生产率相当大。我们以$σ{（|（c \ bar {c}）[n] \ rangle+|（c \ bar {c}）[n''] \ rangle} _ {total}} = 1.167^= 1.167^{+0.113} _ $ 0.164} { - 0.164}^fber $σ{（|（b \ bar {b}）[n] \ rangle+|（b \ bar {b}）[n'] \ rangle）_ {total}} = 0.1132^{+0.1132^{+0.0139} _ { - 0.0139} _ { - 0.0139} $ bc $ bc $ $σ{（|（c \ bar {b}）[n] \ rangle+|（b \ bar {c}）[n'] \ rangle）_ {total}} = 3.692^{+0.124} _ { - 0.124} _ { - 0.097} 〜fb $。主要的不确定性来自重量夸克的质量，在不同潜在模型下，原点及其衍生物的径向波函数。数值结果表明，这样的超级$ z $工厂应该是研究双兴奋charmon的属性的好平台，即双兴奋的底池，尤其是双重兴奋的$ bc $ -mesons。
The exclusive production of double excited quarkonium is comprehensive studied, i.e., the production of double excitedcharmonium, double excited bottomonium, and double excited $Bc$-mesons via $e^+e^-\to γ^*/Z^0 \to|(Q\bar{Q'})[n]\rangle +|(Q'\bar{Q})[n']\rangle$ ($Q/Q'=c$- or $b$-quarks) at a future $Z$ factory under the nonrelativistic quantum chromodynamics framework, where the $[n]$~/$[n']$ represents the color-singlet heavy quarkonium states $[^1S_0]\rangle, ~[^3S_1]\rangle, ~[^1P_1]\rangle$, and $[^3P_J]\rangle$ ($J=0,1,2$). The "improved trace technology" is adopted for calculating the complicated $P$-wave channels for derive the analytic expressions at the amplitude level. According to our study, the production rates of double heavy quarkonium are considerable at the future $Z$ factory. We obtain the cross sections for the production of double excited charmonium for $σ{(|(c\bar{c})[n]\rangle+|(c\bar{c})[n']\rangle)_{total}}=1.167^{+0.113}_{-0.164}\times 10^{-2}~fb$, the cross sections of double excited bottomonium for $σ{(|(b\bar{b})[n]\rangle+|(b\bar{b})[n']\rangle)_{total}}=0.1132^{+0.0139}_{-0.0130}~fb$, and the cross sections of double excited $Bc$-mesons for $σ{(|(c\bar{b})[n]\rangle+|(b\bar{c})[n']\rangle)_{total}}=3.692^{+0.124}_{-0.097}~fb$. The main uncertainties come from the mass of the heavy quarkonium and the radial wave functions at the origin and their derivatives at the origin under different potential models. The numerical results show that such the super $Z$ factory should be a good platform to study the properties of the double excited charmonium, the double excited bottomonium , especially the double excited $Bc$-mesons.
