processes observed by Belle

We calculate the production cross sections for D∗+D∗−, D+D∗− and D+D− in e+e− annihilation through one virtual photon in the framework of perturbative QCD with constituent quarks. The calculated cross sections for D∗+D∗− and D+D∗− production are roughly in agreement with the recent Belle data. The helicity decomposition for D ∗ meson production is also calculated. The fraction of the D L D ∗∓ T final state in e + e − → D∗+D∗− process is found to be 65%. The fraction of DD T production is 100% and DD L is forbidden in e + e − annihilation through one virtual photon. We further consider e+e− annihilation through two virtual photons, and then find the fraction of DD T in e + e − → DD process to be about 91%. PACS number(s): 12.40.Nn, 13.85.Ni, 14.40.Gx Recently, heavy meson production in ee annihilation has become a very interesting subject both experimentally and theoretically. For instance, for charmonium production in ee annihilation at the B-factory energy √ s = 10.6GeV, there are large differences between the experimental data [1, 2, 3] and the calculated cross sections for both exclusive processes [4] and inclusive processes [5]. Even by including the effects of ee annihilation into two photons in the exclusive double-charmonium production [6] and inclusive charmonium production [7], the large discrepancies still exist [8]. Moreover, most recently the Belle Collaboration has measured [9] the charmed meson pair DD production in ee annihilation and also found a large differences between observed data and theoretical predictions[10]. The measured cross sections are σ(ee → DD) = 0.65±0.04±0.07 pb and σ(ee → DD) = 0.71 ± 0.05 ± 0.09 pb, which are, however, lower than those predicted in Ref.[10] by an order of magnitude (see [9] for the comparison). The Belle measurements of the exclusive D meson pair production in ee annihilation could be another challenge to the theoretical studies. In order to understand these production processes, in this letter we will present a calculation in the framework of perturbative QCD with constituent quarks. Namely, we will treat the charmed mesons D as bound states of a constituent charmed quark and a constituent light antiquark, and the virtual photon will couple to the charm quark, which will subsequently emit a light quark pair with constituent quark masses through a virtual gluon (see the upper diagram in Fig. 1). The virtuality of the virtual gluon could be large enough for the application of perturbative QCD. In addition, the case of the