Search for excited charmonium states in e^+e^- Annihilation at sqrt{s}=10.6 GeV

We suggest searching for excited charmonium states in $e^+e^-$ annihilation via double charmonium production at $\sqrt{s}=10.6$ GeV with $B$ factories, based on a more complete leading order calculation including both QCD and QED contributions for various processes. In particular, for the C=+ states, the $\chi_{c0}(nP)$ (n=2,3) and $\eta_c(mS)$ (m=3,4) may have appreciable potentials to be observed; while for the C=- states, the $\eta_ch_c$ production and especially the $\chi_{c1}h_c$ production might provide opportunities for observing the $h_c$ with higher statistics in the future. A brief discussion for the X(3940) observed in the double charmonium production is included.