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We calculate the next-to-leading order QCD corrections to the excitedcharmonium $\chi_{cJ}$ associated with $ W^+ b $ production from top-quarkdecay. Our results show that detecting the $\chi_{c0}$ production fromtop-quark decay is very difficult, but the $\chi_{c1}$ and $\chi_{c2}$productions have the potential to be detected at the LHC. If the prompt$\chi_{cJ}$ production from top-quark decay is really detected at the LHC, itwill be useful not only for investigating $J/\psi$ production from top-quarkdecay but also for understanding the heavy quarkonium production mechanism.

Next-to-leading order QCD corrections to $\chi_{cJ} W^+ b$ associated production from top-quark decay