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

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