Qi-Li Liao, Xing-Gang Wu, Jun Jiang, Zhi Yang, Zhen-Yun Fang, Jia-Wei Zhang
Sizable heavy-quarkonium events can be produced through $W$-boson decays at the LHC. Such channels will provide a suitable platform to study the heavy quarkonium properties. As a sequential work of Ref.[1], in addition to the production of the $(Q\bar{Q'})|1S>$ and $(Q\bar{Q'})|1P>$ states, we make a further study on the production of higher-excited $(Q\bar{Q'})$-quarkonium states $(Q\bar{Q'})|2S>$, $(Q\bar{Q'})|3S>$ and $(Q\bar{Q'})|2P>$. Here $(Q\bar{Q'})$ stands for the $(c\bar{c})$-charmonium, $(c\bar{b})$-quarkonium and $(b\bar{b})$-bottomonium respectively. The "improved trace technology", which deals the hard-scattering amplitude at the amplitude level, is helpful for deriving compact analytical results. As an application, we adopt it for the present purpose. We show that sizable events for those higher Fock-states can also be produced at the LHC. Therefore, we need to take them into consideration for a sound estimation on the heavy quarkonium production. If assuming all excited heavy-quarkonium states decay to the ground spin-singlet $[1{^1S_0}]$-wave state with 100% efficiency via electromagnetic or hadronic interactions, we obtain the total decay width by adding all the mentioned Fock states together; i.e. by taking the bound-state parameters under the Buchm\"{u}ller-Tye potential model, we obtain $\Gamma_{W^+\to (c\bar{c})+c\bar{s}} =591.3$ KeV, $\Gamma_{W^+\to (c\bar{b})+b\bar{s}} =27.0$ KeV and $\Gamma_{W^+\to (c\bar{b})+c\bar{c}}= 2.01$ KeV. At the LHC with the luminosity ${\cal L}\propto 10^{34}cm^{-2}s^{-1}$ and the center-of-mass energy $\sqrt{S}=14$ TeV, this shows that $8.7\times10^6$ $\eta_c$ and $J/\Psi$, $4.3\times10^5$ $B_c$ and $B^*_c$, $1.4\times10^3$ $\eta_b$ and $\Upsilon$ events per year can be obtained through $W^+$ decays.
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http://arxiv.org/abs/1204.2594
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