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Within the nonrelativistic QCD (NRQCD) factorization framework, we computethe long-awaited ${\mathcal O}(\alpha_s^2)$ correction for the exclusive doublecharmonium production process at $B$ factories, {\it i.e.}, $e^+e^-\toJ/\psi+\eta_c$ at $\sqrt{s}=10.58$ GeV. For the first time, we confirm thatNRQCD factorization does hold at next-to-next-to-leading-order (NNLO) forexclusive double charmonium production. It is found that including the NNLO QCDcorrection considerably reduces the renormalization scale dependence, and alsoimplies the reasonable perturbative convergence behavior for this process. Ourstate-of-the-art prediction is consistent with the BaBar measurement withinerrors.

Next-to-next-to-leading-order QCD corrections to $e^+e^-\to J/\psi+\eta_c$ at $B$ factories