QCD corrections to e^+ e^- to J/ψ(ψ(2S))+χ_{cJ} (J=0,1,2) at B Factories

We analytically calculate the cross sections of double charmonium production in $e^+ e^- \to J/ψ(ψ(2S))χ_{cJ}$ (J=0,1,2) at next-to-leading order (NLO) in $α_s$ in nonrelativistic QCD, and confirm factorization of these processes. In contrast to $χ_{c0}$ production, for which the NLO correction is large and positive, the NLO corrections for $χ_{c1,2}$ production can be negative, resulting in decreased $K$ factors of 0.91 and 0.78 for J=1 and 2 respectively when $μ= 2 m_{c}$. Consequently, the NLO QCD corrections markedly enlarge the difference between cross sections of $χ_{c0}$ and $χ_{c1,2}$. This may explain why $e^+ e^- \to J/ψ(ψ(2S))χ_{c0}$ but not $e^+ e^- \to J/ψ(ψ(2S))χ_{c1,2}$ is observed experimentally. Moreover, for $J/ψ(ψ(2S))χ_{c1,2}$, the NLO QCD corrections substantially reduce the $μ$ dependence and lead to predictions with small theoretical uncertainties.

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