Color-Singlet $ψ_Q$ Production at $e^+e^-$ Colliders

TL;DR

The paper addresses heavy quarkonium production in e+e- annihilation within the NRQCD color-singlet framework, computing the complete O(α_s^2) cross section for e^+e^- → ψ_Q + X via two color-singlet channels. It shows that at high energies the cross section matches the heavy-quark fragmentation result, but fragmentation is reliable only when the center-of-mass energy is substantially larger than the quark mass. The work applies these results to direct J/ψ production at CLEO, predicting angular and energy distributions and highlighting how color-octet effects could modify endpoint behavior. Overall, it provides closed-form analytic cross sections, clarifies the energy scales at which fragmentation approximations are valid, and informs tests of NRQCD via e^+e^- collider data.

Abstract

We calculate in closed form the complete ${\mathcal O}(α_s^2)$ color-singlet differential cross section for $e^+e^- \to γ^* \to ψ_Q+X$ scattering. The cross section reduces at high energies to a heavy quark fragmentation form. We find that the energy scale at which the approximate fragmentation result becomes reliable exceeds the $ψ_Q$ mass by more than an order of magnitude. We also discuss the color-singlet model's predictions for direct $J/ψ$ angular and energy distributions at CLEO.

Figures (5)

• Figure 1: Leading order Feynman graphs which mediate $e^+e^- \to \gamma^* \to Q\bar{Q}[{}^3S_1^{(1)}] + g + g$$\to \psi_Q + X$ scattering.
• Figure 2: Leading order Feynman graphs which mediate $e^+e^- \to \gamma^* \to Q\bar{Q}[{}^3S_1^{(1)}]+Q+\bar{Q}$$\to \psi_Q + X$ scattering.
• Figure 3: Angular coefficient functions $\alpha_{\mathrm gluon}$ (dashed line), $\alpha_{\mathrm quark}$ (dotted line) and $\alpha_{\mathrm total}$ (solid line) plotted against dimensionless energy variable $z_3$.
• Figure 4: Contributions to $d\sigma/dz_3$ from the gluon (dashed line) and quark (dotted line) modes plotted against $z_3$. The CSM prediction for the total direct $J/\psi$ energy distribution is represented by the solid curve.
• Figure 5: Integrated cross sections for the gluon (dashed line) and charm quark (dotted line) modes plotted as a function of $\sqrt{S}$. The sum of the two is shown by the solid curve. The approximate charm quark fragmentation cross section is depicted by the dot-dashed curve.