Production of a Heavy Quarkonium with a Photon or via ISR at $Z$ Peak in $e^{+}{e}^{-}$ Collider

Abstract

Considering the possibility to build an $e^{+}{e}^{-}$ collider at the energies around $Z$-boson resonance with a luminosity so high as $\mathcal{L}\propto 10^{34}c{m}^{-2}{s}^{-1}$ (even higher) and the abilities of a modern synthesis detector, we systematically calculate the exclusive two body processes: $e^{+}{e}^{-}$ annihilates into a heavy quarkonium and a photon (initiate state radiation i.e. ISR is involved), at the energies around the $Z$-boson resonance. Since the couplings of $Z$-boson to quarks contain axial vector as well as vector, so here the produced heavy quarkonium may stand for a charmonium such as $J/\psi ,{\eta }_c,h_c,{\chi }_{cJ}\cdots$ and a bottomonium such as ${\rm Y},{\eta }_b,h_b,{\chi }_{bJ}\cdots$ respectively. If we call such a collider with so high luminosity and running around the $Z$-boson resonance as a $Z$-factory, then our results obtained here indicate that experimental studies at a $Z$-factory about the various heavy quarkona (their ground and excited states) via the two-body processes, especially, the production of the bound states with quantum number $J^{PC}=1^{--}$ via ISR, have outstanding advantages.

11 page, 3 figures

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