Understanding the $e^{+}{e}^{-}\to D^{(\ast )+}{D}^{(\ast )-}$ processes observed by Belle

Abstract

We calculate the production cross sections for $D^{\ast +}{D}^{\ast -}$, $D^{+}{D}^{\ast -}$ 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 $D^{\ast +}{D}^{\ast -}$ and $D^{+}{D}^{\ast -}$ production are roughly in agreement with the recent Belle data. The helicity decomposition for $D^{\ast }$ meson production is also calculated. The fraction of the $D_L^{\ast \pm }{D}_T^{\ast \mp }$ final state in $e^{+}{e}^{-}\to D^{\ast +}{D}^{\ast -}$ process is found to be 65%. The fraction of $D{D}_T^{\ast }$ production is 100% and $D{D}_L^{\ast }$ 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 $D{D}_T^{\ast }$ in $e^{+}{e}^{-}\to D{D}^{\ast }$ process to be about 91%.

8 pages, 2 figures

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• Bridging light-cone and NRQCD approaches: asymptotic behavior of $B_c$ electromagnetic form factor
• Exclusive double $B_c$ meson production from $e^{+}{e}^{-}$ annihilation into two virtual photons