Exclusive J/ψProductions at e^+ e^- Colliders

TL;DR

The paper examines exclusive heavy quarkonium pair production in $e^+e^-$ annihilation within NRQCD, focusing on $J/\psi+\eta_c$ at Belle energies and exploring $J/\psi+J/\psi$ and $\Upsilon+\Upsilon$ production at LEP. It derives NRQCD-based helicity amplitudes including $\gamma^*$ and $Z$ exchanges, and provides triple angular distributions of the $J/\psi$ decay to test the hadronic state's quantum numbers. A key finding is that the LO NRQCD prediction underestimates the Belle cross section by a large factor, requiring a renormalization $K$-factor of about $24 \pm 12$, with some relief from higher-order corrections but likely additional contributions needed (e.g., $\gamma^*\gamma^*$ or non-$\eta_c$ processes). The study also shows that exclusive $J/\psi+J/\psi$ or $\Upsilon+\Upsilon$ production via $Z$-exchange would be too rare to observe at LEP, highlighting limitations of LO NRQCD and motivating further theoretical and experimental scrutiny of exclusive heavy quarkonium production. Overall, it provides concrete angular-distribution tests and a framework for assessing discrepancies between theory and data in quarkonium formation.

Abstract

Exclusive quarkonium pair production in electron-positron collisions is studied in non-relativistic QCD. The obtained cross section for J/ψ+ η_c production in the leading order is confronted against the recent measurements by the Belle Collaboration at KEKB. It is shown that a large renormalization K-factor is necessary to explain the experimental data. We point out that the J^{PC}=0^{-+} nature of the hadronic systems that are assigned to be η_c should be tested by the triple angular distributions in terms of the scattering angle, and, polar and azimuthal angles of J/ψinto leptons. We further study J/ψ+ J/ψand Υ+ Υproductions at LEP energies. Although the axial-vector couplings of the Z-boson to charm and bottom quarks allow production of such pairs when one of them is polarised transversally and the other longitudinally, we find that the integrated luminosity at Z pole accumulated by LEP is not large enough to observe the exclusive pair production of quarkonium.

Figures (2)

• Figure 1: Feynman diagrams for the $J/\psi\ \eta_c$ production from $e^+ + e^-$ annihilation.
• Figure 2: The $\sqrt{s}$ dependence of the total cross section for the exclusive 1S double-quarkonium production (in Log-scale) integrated over $|\cos\theta|\leq 0.9$ is shown. The $K$-factor defined in Eq. (\ref{['eq:22']}) is multiplied for the $J/\psi\ \eta_c$ and $\Upsilon\ \eta_b$ production processes and the $J/\psi\ J/\psi$ and $\Upsilon\ \Upsilon$ processes from the intermediated $Z$ boson.