Inclusive Charmonium Production via Double $c\bar{c}$ in $e^{+}{e}^{-}$ Annihilation

Abstract

Motivated by the recent observation of double charm quark pair production by the Belle Collaboration, we calculate the complete $\mathcal{O}({\alpha }_s^2)$ inclusive production cross sections for ${\eta }_c$, $J/\psi$, and ${\chi }_{cJ}$(J=0, 1, 2) plus $c\bar{c}$ in $e^{+}{e}^{-}$ 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 $\sqrt{s}$. We find that most of the fragmentation results substantially overestimate the cross sections (e.g. by a factor of $\sim$4 for ${\chi }_{c1}$ and ${\chi }_{c2}$) at the Belle and BaBar energy $\sqrt{s}=10.6$GeV. The fragmentation results become a good approximation only when $\sqrt{s}$ is higher than about 100GeV. We further calculate the color-octet contributions to these cross sections with analytical expressions. We find that while the color-octet contribution to $J/\psi$ inclusive production via double charm is negligible (only about 3%), the color-octet contributions to ${\chi }_{c1}$ and ${\chi }_{c2}$ can be significant.

23 pages, 9 figures; color-octet contributions to the double charm inclusive production of J/psi and chi_{cJ} (J=0,1,2) are added; references are added; No change for the color-singlet part

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