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Exclusive Double-Charmonium Production from e^+ e^- Annihilation into a Virtual Photon

We calculate the exclusive cross sections for e^+ e^- annihilation into two charmonium states through a virtual photon. Purely electromagnetic contributions are surprisingly large, changing the cross sections by as much as 21%. The predicted cross section for J/psi + eta_c is about an order of magnitude smaller than a recent measurement by the BELLE Collaboration, although part of the discrepancy can be attributed to large relativistic corrections. The cross sections for S-wave + P-wave, P-wave + P-wave, and S-wave + D-wave charmonium states are also calculated. It may be possible to discover the D-wave state eta_{c2}(1D) at the B factories through the mode J/psi+η_{c2}, whose cross section is predicted to be about a factor of 10 smaller than J/psi + eta_c.