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Sizable amount of heavy-quarkonium events can be produced through $W$-bosondecays at the LHC. Such channels will provide a suitable platform to study theheavy-quarkonium properties. The "improved trace technology", which disposesthe amplitude ${\cal M}$ at the amplitude-level, is helpful for derivingcompact analytical results for complex processes. As an important newapplication, in addition to the production of the lower-level Fock states$|(Q\bar{Q'})[1S]>$ and $|(Q\bar{Q'})[1P]>$, we make a further study on theproduction of higher-excited $|(Q\bar{Q'})>$-quarkonium Fock 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. We showthat sizable amount of events for those higher-excited states can also beproduced at the LHC. Therefore, we need to take them into consideration for asound estimation.

Excited Heavy Quarkonium Production at the LHC through $W$-Boson Decays