Prompt J/psi production at e^+e^- colliders

In this paper, we discuss the prompt j/psi production at e^+e^- colliders via color-singlet and color-octet production mechanisms. The color-singlet production processes include 1) e^+e^- to J/\psi gg; 2) e^+e^- to J/\psi c\bar{c}; 3) e^+e^- to q \bar q ggJ/\psi and e^+e^- to q \bar q g\chi_c followed by \chi_c to J/\psi \gamma. The color-octet production processes include 1) e^+e^- to J/\psi g; 2) e^+e^- to j/psi q\bar q. Of all these production channels, we find that the color-octet contributions dominate over the color-singlet contributions at any energy scales. At low energies (\sqrt{s}< 20 GeV), the dominant channel is e^+e^- to J/\psi g whereas at high energies e+e^- to j/psi q\bar q will take the leading part. We also find that the energy spectrum for the color-octet j/psi production in process e^+e^- to j/psi q\bar q is very soft, and the mean energy of the produced j/psi is only about 10 GeV~ 20 GeV even at very high energies (e.g. at 1000 GeV). The extraction of color-octet matrix elements from j/psi production in e^+e^- collisions is also discussed.