Next-to-next-to-leading-order QCD corrections to double J/ψ production at the B factories

In this paper, we study the next-to-next-to-leading-order (NNLO) QCD corrections for the process e⁺e⁻ → J/ψ + J/ψ at the B factories. By including the NNLO corrections, the cross section turns negative due to the poor convergence of perturbative expansion. Consequently, to obtain a reasonable estimation for the cross section, the square of the amplitude up to NNLO is used. In addition, the contributions from the bottom quark and the light-by-light part, which are usually neglected, are also included. The final cross section is obtained as ${1.76}_{-1.66}^{+2.42}$ \( {1.76}_{-1.66}^{+2.42} \) fb at a center-of-mass energy of $\sqrt{s}$ \( \sqrt{s} \) = 10.58 GeV. Our result for total cross section and differential cross section could be compared with precise experimental measurement in future at the B factories.