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$O(α_s)$ corrections to $J/ψ+χ_{cJ}$ production at $B$ factories

We investigate the ${\cal O}(α_s)$ corrections to $e^+e^-\to J/ψ(ψ')+χ_{cJ}$ ($J=0,1,2$) in the NRQCD factorization approach. These next-to-leading order (NLO) corrections are calculated at the level of helicity amplitude. We have made a detailed analysis for both polarized and unpolarized cross sections, and compared our predictions with the measurements at the $B$ factories. We also derive the asymptotic expressions for each of the NLO helicity amplitudes, and confirm the earlier speculation that at NLO in $α_s$, the double logarithm of type $\ln^2 (s/m_c^2)$ appearing in the NRQCD short-distance coefficient is always associated with the helicity-suppressed channels.