Heavy Quarkonium Production through the Semi-Exclusive e+ e- Annihilation Channels around the Z⁰ Peak

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Within the framework of the non-relativistic QCD, we present a detailed discussion on the heavy quarkonium production at the leading order in αₛ at a e+ e- collider with the collision energy around the Z⁰ peak. Quarkonia are produced through the semi-exclusive channels e⁺e⁻ → |HQQ +X with X=QQ or gg, where Q indicates a heavy quark (respectively b or c). It is noted that in addition to the color-singlet 1S-level quarkonium states, the 2S and 1P color-singlet states and the color-octet |(QQ)[1³S₁(8)]g state also provide sizable contributions. The heavy quarkonium transverse momentum and rapidity distributions for the e+ e- collision energy Ecm=mZ are presented. For both charmonium and bottomonium production via the Z⁰ propagator, there is approximate "spin degeneracy" between the spin-triplet and spin-singlet quarkonium states. Uncertainties for the total cross sections are estimated by taking mc=1.50±0.15 GeV and mb=4.90±0.15 GeV. Around Ecm=mZ, due to the Z⁰-boson resonance effect, total cross sections for the channels via the Z⁰-propagator become much larger than the channels via the virtual photon propagator. We conclude that, in addition to the B factories as BaBar and Belle and the hadronic colliders as Tevatron and LHC, such a super Z-factory will present an excellent platform for studying the heavy quarkonium properties.