No abstract

Motivated by the recent observation of double-charm quark pair production by the Belle Collaboration, we calculate the complete O(␣ s 2 ) inclusive production cross sections for c , J/, and cJ (Jϭ0,1,2) plus cc in e ϩ e Ϫ annihilation through a virtual photon. We consider both color-singlet and color-octet contributions, and give the analytical expressions for these cross sections. The complete color-singlet calculations are compared with the approximate fragmentation calculations as functions of the center-of-mass energy ͱ s. We find that most of the fragmentation results substantially overestimate the cross sections ͑e.g., by a factor of ϳ4 for c1 and c2 ) at the Belle and BaBar energy ͱ sϭ10.6 GeV. The fragmentation results become a good approximation only when ͱ s is higher than about 100 GeV. We further calculate the color-octet contributions to these cross sections with analytical expressions. We find that while the color-octet contribution to J/ inclusive production via double charm is negligible ͑only about 7%͒, the color-octet contributions to c1 and c2 can be very significant.

We suggest searching for excited charmonium states in e + e − annihilation via double charmonium production at √ 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 χ c0 (nP ) (n=2,3) and η c (mS) (m=3,4) may have appreciable potentials to be observed;while for the C=-states, the η c h c production and especially the χ 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.