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NLO QCD Corrections to $η_c+h_c(1P)/ψ_{1,2}(1D)$ Production at B-factories

We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to double charmonium production processes $e^+e^-\toγ^*\toη_c+h_c(1P)/ψ_{1,2}(1D)$ within the non-relativistic QCD (NRQCD) factorization framework. We find that the corrections to $η_c+h_c(1P)$ production are positive, while those to $η_c+ψ_{1,2}(1D)$ are negative. Unlike the $J/ψ+ η_c$ case, all the corrections here are not large. Uncertainties in the renormalization scale, quark mass and running energy of center-of-mass are discussed, and the scale dependence of these processes is found to be greatly reduced with the NLO QCD corrections.