Production of a heavy quarkonium with a photon or via ISR at Z peak in e+e− collider

Considering the possibility to build an e + e − collider at the energies around Z -boson resonance with a luminosity so high as L ∝ 10 34 cm −2 s −1 (even higher) and the abilities of a modern synthesis detector, we systematically calculate the exclusive two body processes of the heavy quarkonium production: e + e − annihilates into a heavy quarkonium and a photon, involving the initial state radiation (i.e. ISR) cases, at the energies around the Z -boson resonance. Since the couplings of Z -boson to quarks contain an axial vector term as well as a vector one, a charmonium such as J /ψ or η c or h c or χ cJ …, or a bottomonium such as ϒ or η b or h b or χ bJ …, associating with a photon, may be produced respectively via Z -boson annihilation. 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 of the various heavy quarkona (their ground and excited states) via the two-body processes at a Z -factory have outstanding advantages, especially, the production of the possible states with quantum numbers J PC = 1 −− via ISR.