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

TL;DR

This paper analyzes heavy quarkonium production at electron-positron colliders near the Z boson peak using non-relativistic QCD, highlighting significant contributions from various states and the potential of a super Z-factory for quarkonium studies.

Contribution

It provides a detailed leading-order calculation of heavy quarkonium production at the Z peak, including multiple states and color configurations, emphasizing the importance of Z-resonance effects.

Findings

Total cross sections are significantly enhanced at the Z peak due to resonance.

Multiple quarkonium states, including excited and color-octet states, contribute sizably.

Approximate spin degeneracy observed between spin-triplet and spin-singlet states.

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 $e^{+}e^{-} \rightarrow |H_{Q\bar{Q}}\rangle +X$ 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 $|(Q\bar{Q})[1^3S_1^{({\bf 8})}]g\rangle$ 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 $m_c=1.50\pm0.15$ GeV and $m_b=4.90\pm0.15$ 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.