Perturbative QCD for J/ψ inclusive production via initial state radiation in e~+e~- collisions

The process e+e-→J/ψ+X with the center-of-mass(CM)energy in the range from 3.7 to 10.6 GeV is calculated up to the next-to-leading order(NLO)in quantum chromodynamics(QCD).At 10.6 GeV,the result is consistent with the experimental result from Belle.However,the predictions are much smaller than the background in the measurements at BESIII in the low CM energy range from 3.7 to 4.6 GeV.This indicates that the convergence of the QCD perturbative expansion becomes worse as the CM energy is closer to the inclusive J/ψ production threshold.For a further study of the QCD mechanism of J/ψ production in e~+e~-collisions with different CM energies,the initial state radiation effect of e~+e~-→J/ψ +gg and e~+e~-→J/ψ+cc are calculated in QCD NLO.The results are plotted and the number of events for different CM energy bins are provided for SuperKEKB.This provides a method to precisely test the validity of perturbative predictions for J/ψ production in future measurements.