Heavy Quarkonium Production through the Semi-Exclusive $e^{+}{e}^{-}$ Annihilation Channels around the $Z^0$ Peak

Abstract

Within the framework of the non-relativistic QCD, we present a detailed discussion on the heavy quarkonium production at the leading order in ${\alpha }_s$ at a $e^{+}{e}^{-}$ collider with the collision energy around the $Z^0$ peak. Quarkonia are produced through the semi-exclusive channels $e^{+}{e}^{-}\to |H_{Q\bar{Q}}⟩+X$ with $X=Q\bar{Q}$ 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 $|(Q\bar{Q})[1^3{S}_1^{(8)}]g⟩$ state also provide sizable contributions. The heavy quarkonium transverse momentum and rapidity distributions for the $e^{+}{e}^{-}$ collision energy $E_{cm}=m_Z$ are presented. For both charmonium and bottomonium production via the $Z^0$ 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 $m_c=1.50\pm 0.15$ GeV and $m_b=4.90\pm 0.15$ GeV. Around $E_{cm}=m_Z$, due to the $Z^0$-boson resonance effect, total cross sections for the channels via the $Z^0$-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.

28 pages, 20 figures, 15 tables. to be published in Phys.Rev.D. We are grateful for the anonymous referee's comments and suggestions that substantially improve the manuscript

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