Excited Heavy Quarkonium Production via Z^0 Decays at a High Luminosity Collider

Abstract

We present a systematic study of the production of the heavy quarkonium, i.e., $|(c\bar{c})[n]⟩$ , $|(b\bar{c})[n]⟩$ (or $|(c\bar{b})[n]⟩$), and $|(b\bar{b})[n]⟩$ quarkonium [$|(Q\overline{Q^{\prime }})[n]⟩$ quarkonium for short], through $Z^0$ boson semi-exclusive decays with new parameters \cite{lx} for the heavy quarkonium under the framework of the NRQCD, where $[n]$ stands for $n^1{S}_0$, $n^3{S}_1$, $n^1{P}_0$, $n^3{P}_J$ ($n=1,\cdots ,6$; $J=(0,1,2)$). "Improved trace technology" is adopted to derive the simplified analytic expressions at the amplitude level, which shall be useful for dealing with these decay channels. If all higher $|(Q\overline{Q^{\prime }})[n]⟩$ quarkonium states decay to the ground state $|(Q\overline{Q^{\prime }})[1^1{S}_0]⟩$ with $100\%$ efficiency via electromagnetic or hadronic interactions, we obtain $\hat{I}“(Z^0\to |(c\bar{c})[1^1{S}_0]⟩)=1476$ KeV, $\hat{I}“(Z^0\to |(b\bar{c})[1^1{S}_0]⟩)=1485$ KeV, $\hat{I}“(Z^0\to |(b\bar{b})[1^1{S}_0]⟩)=127.5$ KeV. At the LHC and ILC with the luminosity $\mathcal{L}\propto 10^{34}c{m}^{-2}{s}^{-1}$, sizable heavy quarkonium events can be produced through $Z^0$ boson decays, i.e., about $5.9\times 10^5$ $(c\bar{c})$, $6.0\times 10^5$ $(b\bar{c})$ (or $(c\bar{b})$), $5.1\times 10^4$ $(b\bar{b})$ events per year can be obtained.

10 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:1408.5563