Next-to-Leading Order QCD Correction to ${\mathbf{e}}^{+}{\mathbf{e}}^{-}\to \mathbf{J}/\mathbf{\psi }+{\mathbf{\eta }}_{\mathbf{c}}$ at $\sqrt{s}=10.6$GeV}

Abstract

One of the most challenging open problems in heavy quarkonium physics is the double charm production in $e^{+}{e}^{-}$ annihilation at B factories. The measured cross section of $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ is much larger than leading order (LO) theoretical predictions. With the nonrelativistic QCD factorization formalism, we calculate the next-to-leading order (NLO) QCD correction to this process. Taking all one-loop self-energy, triangle, box, and pentagon diagrams into account, and factoring the Coulomb-singular term into the $c\bar{c}$ bound state wave function, we get an ultraviolet and infrared finite correction to the cross section of $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ at $\sqrt{s}=10.6$ GeV. We find that the NLO QCD correction can substantially enhance the cross section with a K factor (the ratio of NLO to LO) of about 1.8-2.1; hence it greatly reduces the large discrepancy between theory and experiment. With $m_c=1.4\mathrm{GeV}$ and $\mu =2m_c$, the NLO cross section is estimated to be 18.9 fb, which reaches to the lower bound of experiment.

Version appeared in PRL, Figure 3 added showing the renormalization scale dependence of the cross section, new BaBar data added

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