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

TL;DR

This paper calculates the production rates of heavy quarkonium states in high-luminosity $e^+e^-$ colliders operating at the $Z$-boson resonance, highlighting the potential for detailed experimental studies of these states via two-body processes involving ISR.

Contribution

It provides systematic calculations of heavy quarkonium production in $e^+e^-$ collisions at the $Z$-peak, emphasizing the advantages of a high-luminosity $Z$-factory for studying various quarkonium states.

Findings

High production rates of heavy quarkonia at $Z$-factories.

Enhanced study potential for $J^{PC}=1^{--}$ states via ISR.

Feasibility of detailed spectroscopy of charmonium and bottomonium.

Abstract

Considering the possibility to build an $e^+e^-$ collider at the energies around $Z$-boson resonance with a luminosity so high as ${\cal L} \propto 10^{34}cm^{-2}s^{-1}$ (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 ${\Upsilon,\eta_b,h_b,\chi_{bJ}}\cdots$ 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.